<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@vertical+block@Grover_for_two_qubits" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Grover for two qubits</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Grover_for_two_qubtis"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Grover_for_two_qubtis" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_Grover_for_two_qubtis" class="problems-wrapper" role="group" aria-labelledby="Grover_for_two_qubtis-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Grover_for_two_qubtis" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@Grover_for_two_qubtis/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="3" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;Grover_for_two_qubtis-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Grover_for_two_qubtis-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Grover for two qubtis &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Grover_for_two_qubtis-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Let us consider the task where we are supposed to find [mathjaxinline]M[/mathjaxinline] marked bit strings out of [mathjaxinline]N=2^ n[/mathjaxinline] possible strings in [mathjaxinline]\{ 0,1\} ^ n[/mathjaxinline]. We suppose [mathjaxinline]M[/mathjaxinline] is constant. Classically, it takes [mathjaxinline]\mathcal{O}(N/M)[/mathjaxinline] queries to find a marked string. Grover&#39;s algorithm allows one to accomplish this task with [mathjaxinline]\mathcal{O}(\sqrt{N/M})[/mathjaxinline], which is a quadratic speedup. In this problem, we set [mathjaxinline]M=1[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; The following figures show the circuit for the Grover&#39;s algorithm. [mathjaxinline]f[/mathjaxinline] for the oracle outputs [mathjaxinline]f(x) = 1[/mathjaxinline] if [mathjaxinline]x[/mathjaxinline] is a marked state and [mathjaxinline]f(x) = 0[/mathjaxinline] if it is not. Piecewise measurements over the [mathjaxinline]n[/mathjaxinline] qubits are made after some number of applications of [mathjaxinline]G[/mathjaxinline] and we declare that the measurement result is a marked state. The contents in [mathjaxinline]G[/mathjaxinline] is shown in the second figure. &lt;/p&gt; &lt;div class=&#34;figure&#34;&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/2fa11bc79336dbe5c15259e658a7b97c/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_ps3b_grover_circuit1.png&#34; width=&#34;400&#34; style=&#34;scale:0.6&#34;/&gt; &lt;/center&gt; &lt;/div&gt; &lt;div class=&#34;figure&#34;&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/c84f4352e2e5fa020fa8b9181113d8fc/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_ps3b_grover_circuit2.png&#34; width=&#34;400&#34; style=&#34;scale:0.4&#34;/&gt; &lt;/center&gt; &lt;/div&gt; &lt;p&gt; In this problem, we consider [mathjaxinline]n=2[/mathjaxinline], [mathjaxinline]M=1[/mathjaxinline] case to follow what is going on. Let us suppose that 01 is a marked string out of four possible strings 00,01,10,11. The following figure shows the circuit for [mathjaxinline]G[/mathjaxinline] for [mathjaxinline]n=2[/mathjaxinline]. [mathjaxinline]|{-}\rangle[/mathjaxinline] is injected to the third input for the oracle. &lt;/p&gt; &lt;div class=&#34;figure&#34;&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/fd283876d31a1090885c7cf49c0a87f2/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_ps3b_grover_2bits.png&#34; width=&#34;400&#34; style=&#34;scale:0.4&#34;/&gt; &lt;/center&gt; &lt;/div&gt; &lt;ul class=&#34;itemize&#34;&gt; &lt;li&gt; &lt;p&gt; What is the state of two qubits after the first application of oracle? Answer using the ket notation. Choose the global phase so that the coefficients are real. &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_Grover_for_two_qubtis_2_1&#34; class=&#34;text-input-dynamath capa_inputtype textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data &#34; data-preprocessor=&#34;MathjaxPreprocessorForQM&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/95fe583d41f010195cf50c9f61992d94/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/mathjax_preprocessor_for_QM_H.js&#34;/&gt; &lt;div class=&#34;unanswered &#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_Grover_for_two_qubtis_2_1&#34; id=&#34;input_Grover_for_two_qubtis_2_1&#34; aria-describedby=&#34;status_Grover_for_two_qubtis_2_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Grover_for_two_qubtis_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Grover_for_two_qubtis_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_Grover_for_two_qubtis_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Grover_for_two_qubtis_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Grover_for_two_qubtis_2_1_dynamath&#34; name=&#34;input_Grover_for_two_qubtis_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/li&gt; &lt;li&gt; &lt;p&gt; Find the probability of finding the marked string if we finish the algorithm by making the measurement after the first application of [mathjaxinline]G[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_Grover_for_two_qubtis_3_1&#34; class=&#34;text-input-dynamath capa_inputtype textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data &#34; data-preprocessor=&#34;MathjaxPreprocessorForQM&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/95fe583d41f010195cf50c9f61992d94/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/mathjax_preprocessor_for_QM_H.js&#34;/&gt; &lt;div class=&#34;unanswered &#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_Grover_for_two_qubtis_3_1&#34; id=&#34;input_Grover_for_two_qubtis_3_1&#34; aria-describedby=&#34;status_Grover_for_two_qubtis_3_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Grover_for_two_qubtis_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Grover_for_two_qubtis_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_Grover_for_two_qubtis_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Grover_for_two_qubtis_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Grover_for_two_qubtis_3_1_dynamath&#34; name=&#34;input_Grover_for_two_qubtis_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/li&gt; &lt;li&gt; &lt;p&gt; Find the probability of finding the marked string if we finish the algorithm by making the measurement after the second application of [mathjaxinline]G[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_Grover_for_two_qubtis_4_1&#34; class=&#34;text-input-dynamath capa_inputtype textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data &#34; data-preprocessor=&#34;MathjaxPreprocessorForQM&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/95fe583d41f010195cf50c9f61992d94/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/mathjax_preprocessor_for_QM_H.js&#34;/&gt; &lt;div class=&#34;unanswered &#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_Grover_for_two_qubtis_4_1&#34; id=&#34;input_Grover_for_two_qubtis_4_1&#34; aria-describedby=&#34;status_Grover_for_two_qubtis_4_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Grover_for_two_qubtis_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Grover_for_two_qubtis_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_Grover_for_two_qubtis_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Grover_for_two_qubtis_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Grover_for_two_qubtis_4_1_dynamath&#34; name=&#34;input_Grover_for_two_qubtis_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/li&gt; &lt;/ul&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_Grover_for_two_qubtis_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Grover for two qubtis&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_Grover_for_two_qubtis&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_Grover_for_two_qubtis&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. 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String.prototype.startsWith = function (str){ return this.indexOf(str) === 0; }; } if(typeof(String.prototype.trim) === "undefined") { String.prototype.trim = function() { return String(this).replace(/^\s+|\s+$/g, ''); }; } var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var amp = String.fromCharCode(38); var rlb = rb + lb; var mke = function(x){ return lb + x + rb; } var search_module_url = ""; var get_search_module_ficus = function(){ var cid = $('div.xblock').data('course-id'); if (cid){ console.log("cid = ", cid); // search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/" + cid + "/courseware/welcome/Search_this_course/"; search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/courseware/welcome/Search_this_course/"; // automatically rewritten console.log("3. search_module_url = ", search_module_url); return; } var course_root_link = $('span.nav-item-course').find('a').attr('href'); if (course_root_link){ console.log("course_root_link = ", course_root_link); search_module_url = course_root_link.replace("course/", "courseware/welcome/Search_this_course/"); console.log("2. search_module_url = ", search_module_url); return } console.log("cannot determine search module url"); } var get_search_module = function(){ // find search this module link if (!($('div.course-index').length)){ return get_search_module_ficus(); } $('div.course-index').find('nav').find('a').each(function(){ if ($(this).text().trim().startsWith("Search this course")){ search_module_url = $(this).attr('href'); console.log("search_module_url = ", search_module_url); } }); } var go_to_search = function(){ get_search_module(); var sterm = $('#site-search-box').val(); // new_url = jump_to_url + "/Search_this_module/?q=" + sterm; new_url = search_module_url + "?q=" + sterm; console.log("sterm = ", sterm, " ; going to ", new_url); window.location.href = new_url; } if (!$('#site-search-box').length){ $("nav.courseware").find("ol").append(lb + "section style='float:right'" + rlb + "input size='20'" + " id='site-search-box'" + rlb + "img src='" + course_static_url + "/images_search_glass.png'/" + rlb + "/input" + rlb + "/section" + rb); } $("#site-search-box").keypress(function(event) { if (event.which == 13) { event.preventDefault(); go_to_search(); } }); // $('#site-search-box').bind("enterKey", go_to_search); var get = function(x){ return eval(x); } return {'course_static_url': course_static_url, 'jump_to_url': jump_to_url, 'go_to_search': go_to_search, 'get_search_module': get_search_module, 'get_search_module_ficus': get_search_module_ficus, 'get': get, } } var the_site_search = add_site_search(); var add_fix_transcript = function(){ if ($('div.wrap-instructor-info').length==0){ return; } $('div.xblock-student_view-video').each(function(key, vblock_e){ var vblock = $(vblock_e); var vuid = vblock.data('usage-id').split('@'); var vid; if (vuid.length==1){ vuid = vblock.data('usage-id').split(';_') vid = vuid[5]; }else{ vid = vuid[2]; } var mfnpre = vid.split("_video",1)[0]; var mfnid = mfnpre; // no periods mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var mke = function(x){ return lb + x + rb; } var ftid = "fix_transcript_" + mfnid; if (!$('#' + ftid).length){ var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb; html += "contribute transcript fix" + mke("/a") + mke("/span"); console.log("html = ", html); vblock.after(html) } $('#' + ftid).click(function(){ var cst = $('ol.subtitles').find('li.current'); var cindex = Number(cst.data('index')); var gurl; if (mfnpre.endsWith('_cq_sol')){ gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/"; }else{ gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/"; } gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1); console.log("going to ", gurl); window.open(gurl, "MITx 8.370x subtitle source"); }); }); } try{ add_fix_transcript(); } catch(err){ console.log(err); } try{ var rb = String.fromCharCode(62); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 3000); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000); } catch(err){ console.log(err); } </script></span> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@vertical+block@Quantum_search_by_continuous-time_simulation__1_of_4_" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Quantum search by continuous-time simulation (1 of 4)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_s14-wk4-gsearch" class="problems-wrapper" role="group" aria-labelledby="s14-wk4-gsearch-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="1" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;s14-wk4-gsearch-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Quantum search by continuous-time simulation &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Grover&#39;s quantum search algorithm can also be constructed as a continuous time quantum algorithm involving the simulation of a particular Hamiltonian. Consider the Hamiltonian &lt;/p&gt; &lt;table id=&#34;a0000000005&#34; class=&#34;equation&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; cellpadding=&#34;7&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr&gt; &lt;td class=&#34;equation&#34; style=&#34;width:80%; border:none&#34;&gt;[mathjax]H = |x\rangle \langle x|+|\psi \rangle \langle \psi | \, ,[/mathjax]&lt;/td&gt; &lt;td class=&#34;eqnnum&#34; style=&#34;width:20%; border:none;text-align:right&#34;&gt;(1.3)&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; where [mathjaxinline]|\psi \rangle[/mathjaxinline] is the initial state of the system, and [mathjaxinline]|x\rangle[/mathjaxinline] is the solution state (with an unknown [mathjaxinline]x[/mathjaxinline]). Suppose you are given an oracle which you can call, which implements [mathjaxinline]U_ x(\Delta t) = \exp (-i |x\rangle \langle x| \Delta t)[/mathjaxinline] for a specified value of [mathjaxinline]\Delta t[/mathjaxinline] (your choice). Moreover, you also have available [mathjaxinline]U_{\psi }(\Delta t) = \exp (-i |\psi \rangle \langle \psi | \Delta t)[/mathjaxinline] (you can perform this yourself, since [mathjaxinline]|\psi \rangle[/mathjaxinline] is known). &lt;/p&gt; &lt;p&gt; It is convenient in analyzing this problem to use the &lt;a href=&#34;https://en.wikipedia.org/wiki/Bloch_sphere&#34; target=&#34;_blank&#34;&gt;Bloch vector representation&lt;/a&gt;, [mathjaxinline]|x\rangle \langle x| = (I+Z)/2 =(I+\hat z \cdot \vec\sigma )/2[/mathjaxinline], with [mathjaxinline]\hat z \equiv (0,0,1)[/mathjaxinline] being the unit vector in the [mathjaxinline]z[/mathjaxinline] direction, and [mathjaxinline]|\psi \rangle \langle \psi | = (I+\vec\psi \cdot \vec\sigma )/2[/mathjaxinline]. Here, [mathjaxinline]\vec\sigma[/mathjaxinline] denotes a vector of Pauli matrices. &lt;/p&gt; &lt;p&gt; Note that we may choose [mathjaxinline]\vec\psi = (\sin \phi , 0,\cos \phi )[/mathjaxinline], where [mathjaxinline]\sin \phi = 2\alpha \beta[/mathjaxinline], and [mathjaxinline]\cos \phi = (\alpha ^2-\beta ^2)[/mathjaxinline], by recognizing that [mathjaxinline]H[/mathjaxinline] acts only in a two-dimensional space spanned by [mathjaxinline]|x\rangle[/mathjaxinline] and [mathjaxinline]|y\rangle = |\psi \rangle - \langle x|\psi \rangle |x\rangle[/mathjaxinline] (un-normalized). &lt;/p&gt; &lt;p&gt; This is illustrated in this figure: &lt;/p&gt; &lt;p&gt; &lt;img src=&#34;/assets/courseware/v1/e3274dd9d6ddff5ac91de58fec5c295f/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-cont-time-search.png&#34; width=&#34;600&#34;/&gt; &lt;/p&gt; &lt;p&gt; Use this Bloch vector representation to fill in the following formula for [mathjaxinline]U(\Delta t) = U_{\psi }(\Delta t)U_{x}(\Delta t)[/mathjaxinline], up to an irrelevant global phase: &lt;/p&gt; 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&lt;/div&gt;&lt;/span&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_s14-wk4-gsearch_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Quantum search by continuous-time simulation&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_s14-wk4-gsearch&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_s14-wk4-gsearch&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@html_site_search_box1xxxx"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-has-score="False" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@html_site_search_box1xxxx" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="html"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <span><a href="/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/NONE" id="dummy_course_static_link" style="display:none"/><a href="/courses/course-v1:MITx+8.370.2x+1T2018/jump_to_id/NONE" id="dummy_jump_link" style="display:none"/><script type="text/javascript"> var add_site_search = function(){ course_static_url = $('#dummy_course_static_link').attr('href').replace('/NONE', ''); jump_to_url = $('#dummy_jump_link').attr('href').replace('/NONE', ''); if (typeof String.prototype.startsWith != 'function') { // see below for better implementation! String.prototype.startsWith = function (str){ return this.indexOf(str) === 0; }; } if(typeof(String.prototype.trim) === "undefined") { String.prototype.trim = function() { return String(this).replace(/^\s+|\s+$/g, ''); }; } var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var amp = String.fromCharCode(38); var rlb = rb + lb; var mke = function(x){ return lb + x + rb; } var search_module_url = ""; var get_search_module_ficus = function(){ var cid = $('div.xblock').data('course-id'); if (cid){ console.log("cid = ", cid); // search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/" + cid + "/courseware/welcome/Search_this_course/"; search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/courseware/welcome/Search_this_course/"; // automatically rewritten console.log("3. search_module_url = ", search_module_url); return; } var course_root_link = $('span.nav-item-course').find('a').attr('href'); if (course_root_link){ console.log("course_root_link = ", course_root_link); search_module_url = course_root_link.replace("course/", "courseware/welcome/Search_this_course/"); console.log("2. search_module_url = ", search_module_url); return } console.log("cannot determine search module url"); } var get_search_module = function(){ // find search this module link if (!($('div.course-index').length)){ return get_search_module_ficus(); } $('div.course-index').find('nav').find('a').each(function(){ if ($(this).text().trim().startsWith("Search this course")){ search_module_url = $(this).attr('href'); console.log("search_module_url = ", search_module_url); } }); } var go_to_search = function(){ get_search_module(); var sterm = $('#site-search-box').val(); // new_url = jump_to_url + "/Search_this_module/?q=" + sterm; new_url = search_module_url + "?q=" + sterm; console.log("sterm = ", sterm, " ; going to ", new_url); window.location.href = new_url; } if (!$('#site-search-box').length){ $("nav.courseware").find("ol").append(lb + "section style='float:right'" + rlb + "input size='20'" + " id='site-search-box'" + rlb + "img src='" + course_static_url + "/images_search_glass.png'/" + rlb + "/input" + rlb + "/section" + rb); } $("#site-search-box").keypress(function(event) { if (event.which == 13) { event.preventDefault(); go_to_search(); } }); // $('#site-search-box').bind("enterKey", go_to_search); var get = function(x){ return eval(x); } return {'course_static_url': course_static_url, 'jump_to_url': jump_to_url, 'go_to_search': go_to_search, 'get_search_module': get_search_module, 'get_search_module_ficus': get_search_module_ficus, 'get': get, } } var the_site_search = add_site_search(); var add_fix_transcript = function(){ if ($('div.wrap-instructor-info').length==0){ return; } $('div.xblock-student_view-video').each(function(key, vblock_e){ var vblock = $(vblock_e); var vuid = vblock.data('usage-id').split('@'); var vid; if (vuid.length==1){ vuid = vblock.data('usage-id').split(';_') vid = vuid[5]; }else{ vid = vuid[2]; } var mfnpre = vid.split("_video",1)[0]; var mfnid = mfnpre; // no periods mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var mke = function(x){ return lb + x + rb; } var ftid = "fix_transcript_" + mfnid; if (!$('#' + ftid).length){ var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb; html += "contribute transcript fix" + mke("/a") + mke("/span"); console.log("html = ", html); vblock.after(html) } $('#' + ftid).click(function(){ var cst = $('ol.subtitles').find('li.current'); var cindex = Number(cst.data('index')); var gurl; if (mfnpre.endsWith('_cq_sol')){ gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/"; }else{ gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/"; } gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1); console.log("going to ", gurl); window.open(gurl, "MITx 8.370x subtitle source"); }); }); } try{ add_fix_transcript(); } catch(err){ console.log(err); } try{ var rb = String.fromCharCode(62); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 3000); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000); } catch(err){ console.log(err); } </script></span> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@vertical+block@Quantum_search_by_continuous-time_simulation__2_of_4_" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Quantum search by continuous-time simulation (2 of 4)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch2"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch2" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_s14-wk4-gsearch2" class="problems-wrapper" role="group" aria-labelledby="s14-wk4-gsearch2-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch2" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch2/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="1" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;s14-wk4-gsearch2-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch2-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Quantum search by continuous-time simulation II &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch2-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; The operation [mathjaxinline]U(\Delta t)[/mathjaxinline] can be interpreted as a rotation about an axis of rotation [mathjaxinline]\vec{r}[/mathjaxinline], through an angle [mathjaxinline]\theta[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Let [mathjaxinline]N[/mathjaxinline] be the size of the problem (the number of possible solutions marked by the Grover oracle). &lt;/p&gt; &lt;p&gt; Complete the following expressions for [mathjaxinline]\vec{r}[/mathjaxinline] and angle [mathjaxinline]\theta[/mathjaxinline]: &lt;/p&gt; &lt;span&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_s14-wk4-gsearch2_2_1&#34; class=&#34;capa_inputtype&#34;&gt; &lt;div class=&#34;drag_and_drop_problem_div&#34; id=&#34;drag_and_drop_div_s14-wk4-gsearch2_2_1&#34; data-plain-id=&#34;s14-wk4-gsearch2_2_1&#34;&gt; &lt;/div&gt; &lt;div class=&#34;drag_and_drop_problem_json&#34; id=&#34;drag_and_drop_json_s14-wk4-gsearch2_2_1&#34; style=&#34;display:none;&#34;&gt;{&#34;targets&#34;: [{&#34;w&#34;: &#34;171&#34;, &#34;id&#34;: &#34;1&#34;, &#34;y&#34;: &#34;1&#34;, &#34;h&#34;: &#34;88&#34;, &#34;x&#34;: &#34;129&#34;}, {&#34;w&#34;: &#34;171&#34;, &#34;id&#34;: &#34;2&#34;, &#34;y&#34;: &#34;1&#34;, &#34;h&#34;: &#34;88&#34;, &#34;x&#34;: &#34;465&#34;}, {&#34;w&#34;: &#34;172&#34;, &#34;id&#34;: &#34;3&#34;, &#34;y&#34;: &#34;128&#34;, &#34;h&#34;: &#34;88&#34;, &#34;x&#34;: &#34;337&#34;}, {&#34;w&#34;: &#34;172&#34;, &#34;id&#34;: &#34;4&#34;, &#34;y&#34;: &#34;250&#34;, &#34;h&#34;: &#34;88&#34;, &#34;x&#34;: &#34;337&#34;}], &#34;draggables&#34;: [{&#34;id&#34;: &#34;one&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/5be0d89d46ef512b7f7c8d34cf5694e2/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label1.png&#34;}, {&#34;id&#34;: &#34;two&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/3f3a789cecaaf57bc0ffc18972a4c2d7/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label2.png&#34;}, {&#34;id&#34;: &#34;sN&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/3f589288bcb31d18cbc380716bb60615/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label3.png&#34;}, {&#34;id&#34;: &#34;N&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/ceb1b1a6454526597057226cb3b49032/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label4.png&#34;}, {&#34;id&#34;: &#34;N2&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/d379b4864f84b1faa4d88ae4c6573155/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label5.png&#34;}, {&#34;id&#34;: &#34;cdt&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/9ba57da6300cecc6a222fea75b63e35e/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label6.png&#34;}, {&#34;id&#34;: &#34;sdt&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/68d009f964fbec21b71852a8925ab990/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label7.png&#34;}, {&#34;id&#34;: &#34;c2dt&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/93a08f43ff31c86aba38d6d579313087/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label8.png&#34;}, {&#34;id&#34;: &#34;tc2dt&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/275928b2b96f3718ae9b90060f39724d/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label9.png&#34;}, {&#34;id&#34;: &#34;s2dt&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/329ec8152dc3e3ca9c2d06a81c5b7972/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label10.png&#34;}, {&#34;id&#34;: &#34;ts2dt&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/e4b1ac4fc7f4c5c8c53cb4a4e323977f/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd_label11.png&#34;}], &#34;one_per_target&#34;: &#34;true&#34;, &#34;label_bg_color&#34;: &#34;rgb(222, 139, 238)&#34;, &#34;base_image&#34;: &#34;/assets/courseware/v1/afd1aeff897fe15e8c317218ff35841a/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-rth_wk4-grover-rth_dnd.png&#34;, &#34;target_outline&#34;: &#34;false&#34;}&lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/drag_and_drop.a31124208b9b.js&#34;/&gt; &lt;div class=&#34;unanswered&#34; id=&#34;status_s14-wk4-gsearch2_2_1&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_s14-wk4-gsearch2_2_1&#34; id=&#34;input_s14-wk4-gsearch2_2_1&#34; aria-describedby=&#34;answer_s14-wk4-gsearch2_2_1&#34; value=&#34;&#34; style=&#34;display:none;&#34;/&gt; &lt;p class=&#34;indicator-container drag-and-drop--status&#34; aria-describedby=&#34;input_s14-wk4-gsearch2_2_1&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_s14-wk4-gsearch2_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/p&gt; &lt;p id=&#34;answer_s14-wk4-gsearch2_2_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_s14-wk4-gsearch2_solution_1&#34;/&gt; &lt;/div&gt;&lt;/span&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Quantum search by continuous-time simulation II&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_s14-wk4-gsearch2&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_s14-wk4-gsearch2&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch2-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch2-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch2-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@html_site_search_box2xx"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-has-score="False" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@html_site_search_box2xx" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="html"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <span><a href="/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/NONE" id="dummy_course_static_link" style="display:none"/><a href="/courses/course-v1:MITx+8.370.2x+1T2018/jump_to_id/NONE" id="dummy_jump_link" style="display:none"/><script type="text/javascript"> var add_site_search = function(){ course_static_url = $('#dummy_course_static_link').attr('href').replace('/NONE', ''); jump_to_url = $('#dummy_jump_link').attr('href').replace('/NONE', ''); if (typeof String.prototype.startsWith != 'function') { // see below for better implementation! String.prototype.startsWith = function (str){ return this.indexOf(str) === 0; }; } if(typeof(String.prototype.trim) === "undefined") { String.prototype.trim = function() { return String(this).replace(/^\s+|\s+$/g, ''); }; } var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var amp = String.fromCharCode(38); var rlb = rb + lb; var mke = function(x){ return lb + x + rb; } var search_module_url = ""; var get_search_module_ficus = function(){ var cid = $('div.xblock').data('course-id'); if (cid){ console.log("cid = ", cid); // search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/" + cid + "/courseware/welcome/Search_this_course/"; search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/courseware/welcome/Search_this_course/"; // automatically rewritten console.log("3. search_module_url = ", search_module_url); return; } var course_root_link = $('span.nav-item-course').find('a').attr('href'); if (course_root_link){ console.log("course_root_link = ", course_root_link); search_module_url = course_root_link.replace("course/", "courseware/welcome/Search_this_course/"); console.log("2. search_module_url = ", search_module_url); return } console.log("cannot determine search module url"); } var get_search_module = function(){ // find search this module link if (!($('div.course-index').length)){ return get_search_module_ficus(); } $('div.course-index').find('nav').find('a').each(function(){ if ($(this).text().trim().startsWith("Search this course")){ search_module_url = $(this).attr('href'); console.log("search_module_url = ", search_module_url); } }); } var go_to_search = function(){ get_search_module(); var sterm = $('#site-search-box').val(); // new_url = jump_to_url + "/Search_this_module/?q=" + sterm; new_url = search_module_url + "?q=" + sterm; console.log("sterm = ", sterm, " ; going to ", new_url); window.location.href = new_url; } if (!$('#site-search-box').length){ $("nav.courseware").find("ol").append(lb + "section style='float:right'" + rlb + "input size='20'" + " id='site-search-box'" + rlb + "img src='" + course_static_url + "/images_search_glass.png'/" + rlb + "/input" + rlb + "/section" + rb); } $("#site-search-box").keypress(function(event) { if (event.which == 13) { event.preventDefault(); go_to_search(); } }); // $('#site-search-box').bind("enterKey", go_to_search); var get = function(x){ return eval(x); } return {'course_static_url': course_static_url, 'jump_to_url': jump_to_url, 'go_to_search': go_to_search, 'get_search_module': get_search_module, 'get_search_module_ficus': get_search_module_ficus, 'get': get, } } var the_site_search = add_site_search(); var add_fix_transcript = function(){ if ($('div.wrap-instructor-info').length==0){ return; } $('div.xblock-student_view-video').each(function(key, vblock_e){ var vblock = $(vblock_e); var vuid = vblock.data('usage-id').split('@'); var vid; if (vuid.length==1){ vuid = vblock.data('usage-id').split(';_') vid = vuid[5]; }else{ vid = vuid[2]; } var mfnpre = vid.split("_video",1)[0]; var mfnid = mfnpre; // no periods mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var mke = function(x){ return lb + x + rb; } var ftid = "fix_transcript_" + mfnid; if (!$('#' + ftid).length){ var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb; html += "contribute transcript fix" + mke("/a") + mke("/span"); console.log("html = ", html); vblock.after(html) } $('#' + ftid).click(function(){ var cst = $('ol.subtitles').find('li.current'); var cindex = Number(cst.data('index')); var gurl; if (mfnpre.endsWith('_cq_sol')){ gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/"; }else{ gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/"; } gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1); console.log("going to ", gurl); window.open(gurl, "MITx 8.370x subtitle source"); }); }); } try{ add_fix_transcript(); } catch(err){ console.log(err); } try{ var rb = String.fromCharCode(62); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 3000); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000); } catch(err){ console.log(err); } </script></span> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@vertical+block@Quantum_search_by_continuous-time_simulation__3_of_4_" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Quantum search by continuous-time simulation (3 of 4)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch3"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch3" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_s14-wk4-gsearch3" class="problems-wrapper" role="group" aria-labelledby="s14-wk4-gsearch3-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch3" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch3/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="2" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;s14-wk4-gsearch3-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch3-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Quantum search by continuous-time simulation III &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch3-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Give the smallest value for the time interval [mathjaxinline]\Delta t[/mathjaxinline] such that the operations [mathjaxinline]U_{\psi }[/mathjaxinline] and [mathjaxinline]U_ x[/mathjaxinline] are identical to the operations used in the quantum circuit model realization of the quantum simulation algorithm. &lt;/p&gt; &lt;p&gt; Also fill in the correct expressions for the two operations; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\Delta t =[/mathjaxinline]&lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; 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class=&#34;capa_inputtype&#34;&gt; &lt;div class=&#34;drag_and_drop_problem_div&#34; id=&#34;drag_and_drop_div_s14-wk4-gsearch3_3_1&#34; data-plain-id=&#34;s14-wk4-gsearch3_3_1&#34;&gt; &lt;/div&gt; &lt;div class=&#34;drag_and_drop_problem_json&#34; id=&#34;drag_and_drop_json_s14-wk4-gsearch3_3_1&#34; style=&#34;display:none;&#34;&gt;{&#34;targets&#34;: [{&#34;w&#34;: &#34;108&#34;, &#34;id&#34;: &#34;1&#34;, &#34;y&#34;: &#34;1&#34;, &#34;h&#34;: &#34;101&#34;, &#34;x&#34;: &#34;262&#34;}, {&#34;w&#34;: &#34;107&#34;, &#34;id&#34;: &#34;3&#34;, &#34;y&#34;: &#34;1&#34;, &#34;h&#34;: &#34;101&#34;, &#34;x&#34;: &#34;398&#34;}, {&#34;w&#34;: &#34;108&#34;, &#34;id&#34;: &#34;2&#34;, &#34;y&#34;: &#34;1&#34;, &#34;h&#34;: &#34;101&#34;, &#34;x&#34;: &#34;533&#34;}, {&#34;w&#34;: &#34;108&#34;, &#34;id&#34;: &#34;4&#34;, &#34;y&#34;: &#34;147&#34;, &#34;h&#34;: &#34;101&#34;, &#34;x&#34;: &#34;262&#34;}, {&#34;w&#34;: &#34;107&#34;, &#34;id&#34;: &#34;5&#34;, &#34;y&#34;: &#34;147&#34;, &#34;h&#34;: &#34;101&#34;, &#34;x&#34;: &#34;398&#34;}, {&#34;w&#34;: &#34;108&#34;, &#34;id&#34;: &#34;6&#34;, &#34;y&#34;: &#34;147&#34;, &#34;h&#34;: &#34;101&#34;, &#34;x&#34;: &#34;533&#34;}], &#34;draggables&#34;: [{&#34;id&#34;: &#34;I&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/fc742ec934b252faf01f7c558ac24444/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover2_wk4-grover2_dnd_label1.png&#34;}, {&#34;id&#34;: &#34;one&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/efd552cb7059079f0b257b6abe61feac/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover2_wk4-grover2_dnd_label2.png&#34;}, {&#34;id&#34;: &#34;eye&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/b722d35403ea7a359e94b0abd0342200/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover2_wk4-grover2_dnd_label3.png&#34;}, {&#34;id&#34;: &#34;two&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/efff55319c766670d10d0863e3e69158/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover2_wk4-grover2_dnd_label4.png&#34;}, {&#34;id&#34;: &#34;plus&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/65e25ba701d57871be2d3270d2019da7/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover2_wk4-grover2_dnd_label5.png&#34;}, {&#34;id&#34;: &#34;minus&#34;, &#34;can_reuse&#34;: &#34;true&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/4895ba2f572eab63c1728b2b273d21d6/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover2_wk4-grover2_dnd_label6.png&#34;}], &#34;one_per_target&#34;: &#34;true&#34;, &#34;label_bg_color&#34;: &#34;rgb(222, 139, 238)&#34;, &#34;base_image&#34;: &#34;/assets/courseware/v1/f3be23cbbac7dbd414f62690986bb74e/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover2_wk4-grover2_dnd.png&#34;, &#34;target_outline&#34;: &#34;false&#34;}&lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/drag_and_drop.a31124208b9b.js&#34;/&gt; &lt;div class=&#34;unanswered&#34; id=&#34;status_s14-wk4-gsearch3_3_1&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_s14-wk4-gsearch3_3_1&#34; id=&#34;input_s14-wk4-gsearch3_3_1&#34; aria-describedby=&#34;answer_s14-wk4-gsearch3_3_1&#34; value=&#34;&#34; style=&#34;display:none;&#34;/&gt; &lt;p class=&#34;indicator-container drag-and-drop--status&#34; aria-describedby=&#34;input_s14-wk4-gsearch3_3_1&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_s14-wk4-gsearch3_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/p&gt; &lt;p id=&#34;answer_s14-wk4-gsearch3_3_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_s14-wk4-gsearch3_solution_1&#34;/&gt; &lt;/div&gt;&lt;/span&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_s14-wk4-gsearch3_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Quantum search by continuous-time simulation III&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_s14-wk4-gsearch3&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_s14-wk4-gsearch3&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch3-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch3-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch3-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@html_site_search_box3xx"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-has-score="False" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@html_site_search_box3xx" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="html"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <span><a href="/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/NONE" id="dummy_course_static_link" style="display:none"/><a href="/courses/course-v1:MITx+8.370.2x+1T2018/jump_to_id/NONE" id="dummy_jump_link" style="display:none"/><script type="text/javascript"> var add_site_search = function(){ course_static_url = $('#dummy_course_static_link').attr('href').replace('/NONE', ''); jump_to_url = $('#dummy_jump_link').attr('href').replace('/NONE', ''); if (typeof String.prototype.startsWith != 'function') { // see below for better implementation! String.prototype.startsWith = function (str){ return this.indexOf(str) === 0; }; } if(typeof(String.prototype.trim) === "undefined") { String.prototype.trim = function() { return String(this).replace(/^\s+|\s+$/g, ''); }; } var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var amp = String.fromCharCode(38); var rlb = rb + lb; var mke = function(x){ return lb + x + rb; } var search_module_url = ""; var get_search_module_ficus = function(){ var cid = $('div.xblock').data('course-id'); if (cid){ console.log("cid = ", cid); // search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/" + cid + "/courseware/welcome/Search_this_course/"; search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/courseware/welcome/Search_this_course/"; // automatically rewritten console.log("3. search_module_url = ", search_module_url); return; } var course_root_link = $('span.nav-item-course').find('a').attr('href'); if (course_root_link){ console.log("course_root_link = ", course_root_link); search_module_url = course_root_link.replace("course/", "courseware/welcome/Search_this_course/"); console.log("2. search_module_url = ", search_module_url); return } console.log("cannot determine search module url"); } var get_search_module = function(){ // find search this module link if (!($('div.course-index').length)){ return get_search_module_ficus(); } $('div.course-index').find('nav').find('a').each(function(){ if ($(this).text().trim().startsWith("Search this course")){ search_module_url = $(this).attr('href'); console.log("search_module_url = ", search_module_url); } }); } var go_to_search = function(){ get_search_module(); var sterm = $('#site-search-box').val(); // new_url = jump_to_url + "/Search_this_module/?q=" + sterm; new_url = search_module_url + "?q=" + sterm; console.log("sterm = ", sterm, " ; going to ", new_url); window.location.href = new_url; } if (!$('#site-search-box').length){ $("nav.courseware").find("ol").append(lb + "section style='float:right'" + rlb + "input size='20'" + " id='site-search-box'" + rlb + "img src='" + course_static_url + "/images_search_glass.png'/" + rlb + "/input" + rlb + "/section" + rb); } $("#site-search-box").keypress(function(event) { if (event.which == 13) { event.preventDefault(); go_to_search(); } }); // $('#site-search-box').bind("enterKey", go_to_search); var get = function(x){ return eval(x); } return {'course_static_url': course_static_url, 'jump_to_url': jump_to_url, 'go_to_search': go_to_search, 'get_search_module': get_search_module, 'get_search_module_ficus': get_search_module_ficus, 'get': get, } } var the_site_search = add_site_search(); var add_fix_transcript = function(){ if ($('div.wrap-instructor-info').length==0){ return; } $('div.xblock-student_view-video').each(function(key, vblock_e){ var vblock = $(vblock_e); var vuid = vblock.data('usage-id').split('@'); var vid; if (vuid.length==1){ vuid = vblock.data('usage-id').split(';_') vid = vuid[5]; }else{ vid = vuid[2]; } var mfnpre = vid.split("_video",1)[0]; var mfnid = mfnpre; // no periods mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var mke = function(x){ return lb + x + rb; } var ftid = "fix_transcript_" + mfnid; if (!$('#' + ftid).length){ var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb; html += "contribute transcript fix" + mke("/a") + mke("/span"); console.log("html = ", html); vblock.after(html) } $('#' + ftid).click(function(){ var cst = $('ol.subtitles').find('li.current'); var cindex = Number(cst.data('index')); var gurl; if (mfnpre.endsWith('_cq_sol')){ gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/"; }else{ gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/"; } gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1); console.log("going to ", gurl); window.open(gurl, "MITx 8.370x subtitle source"); }); }); } try{ add_fix_transcript(); } catch(err){ console.log(err); } try{ var rb = String.fromCharCode(62); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 3000); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000); } catch(err){ console.log(err); } </script></span> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@vertical+block@Quantum_search_by_continuous-time_simulation__4_of_4_" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Quantum search by continuous-time simulation (4 of 4)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch4"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-has-score="True" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch4" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_s14-wk4-gsearch4" class="problems-wrapper" role="group" aria-labelledby="s14-wk4-gsearch4-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch4" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch4/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="1" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;s14-wk4-gsearch4-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch4-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Quantum search by continuous-time simulation IV &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@s14-wk4-gsearch4-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Unlike the usual quantum circuit version of Grover&#39;s algorithm, quantum search by continuous-time simulation can obtain the final state [mathjaxinline]|x\rangle[/mathjaxinline] &lt;em&gt;exactly&lt;/em&gt;, meaning that the algorithm works with probability [mathjaxinline]1[/mathjaxinline], rather than with some smaller probability. &lt;/p&gt; &lt;p&gt; This is done by choosing [mathjaxinline]\Delta t[/mathjaxinline] carefully. Let [mathjaxinline]K[/mathjaxinline] be the number of rotations made about the axis [mathjaxinline]\vec{r}[/mathjaxinline], each time by angle [mathjaxinline]\theta[/mathjaxinline]. [mathjaxinline]K[/mathjaxinline] is required to be of the order [mathjaxinline]\mathcal{O}(\sqrt{N})[/mathjaxinline]. Approximate the total rotation angle needed by the angle between [mathjaxinline]\hat{z}[/mathjaxinline] and [mathjaxinline]\vec{\psi }[/mathjaxinline], that is, [mathjaxinline]\cos ^{-1}( \hat{z}\cdot \vec{\psi })[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Using [mathjaxinline]K[/mathjaxinline] and that approximation, complete this expression for the time step size [mathjaxinline]\Delta t[/mathjaxinline] to obtain the final state exactly: &lt;/p&gt; &lt;span&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_s14-wk4-gsearch4_2_1&#34; class=&#34;capa_inputtype&#34;&gt; &lt;div class=&#34;drag_and_drop_problem_div&#34; id=&#34;drag_and_drop_div_s14-wk4-gsearch4_2_1&#34; data-plain-id=&#34;s14-wk4-gsearch4_2_1&#34;&gt; &lt;/div&gt; &lt;div class=&#34;drag_and_drop_problem_json&#34; id=&#34;drag_and_drop_json_s14-wk4-gsearch4_2_1&#34; style=&#34;display:none;&#34;&gt;{&#34;targets&#34;: [{&#34;w&#34;: &#34;102&#34;, &#34;id&#34;: &#34;2&#34;, &#34;y&#34;: &#34;19&#34;, &#34;h&#34;: &#34;72&#34;, &#34;x&#34;: &#34;549&#34;}, {&#34;w&#34;: &#34;102&#34;, &#34;id&#34;: &#34;3&#34;, &#34;y&#34;: &#34;114&#34;, &#34;h&#34;: &#34;72&#34;, &#34;x&#34;: &#34;549&#34;}, {&#34;w&#34;: &#34;102&#34;, &#34;id&#34;: &#34;4&#34;, &#34;y&#34;: &#34;215&#34;, &#34;h&#34;: &#34;72&#34;, &#34;x&#34;: &#34;463&#34;}], &#34;draggables&#34;: [{&#34;id&#34;: &#34;one&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/cb51e77dcfa7d57c24a909f33d057b55/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label1.png&#34;}, {&#34;id&#34;: &#34;two&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/7c213870995d4b82f5e189cca4d278bb/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label2.png&#34;}, {&#34;id&#34;: &#34;SN&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/f0751c73d82fca958b19a28b4c6dee5e/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label3.png&#34;}, {&#34;id&#34;: &#34;N&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/59284a34a8b0b0138391af28a28e8f72/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label4.png&#34;}, {&#34;id&#34;: &#34;N2&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/4214140bf7eaf727d551f3823a350f33/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label5.png&#34;}, {&#34;id&#34;: &#34;KN&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/65057113a2887ef59a63dc0f1acb9108/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label6.png&#34;}, {&#34;id&#34;: &#34;K&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/373687501af7575d8cb1ccea9c6c07da/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label7.png&#34;}, {&#34;id&#34;: &#34;TK&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/44bb3091e838066a61d59f48b7954a6e/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label8.png&#34;}, {&#34;id&#34;: &#34;KsN&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/fdb9682c040521cd9042d20455dd848d/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label9.png&#34;}, {&#34;id&#34;: &#34;NsK&#34;, &#34;can_reuse&#34;: &#34;&#34;, &#34;label&#34;: &#34;&#34;, &#34;target_fields&#34;: [], &#34;icon&#34;: &#34;/assets/courseware/v1/a6ed793661abbe9e5645ca79c7763658/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd_label10.png&#34;}], &#34;one_per_target&#34;: &#34;true&#34;, &#34;label_bg_color&#34;: &#34;rgb(222, 139, 238)&#34;, &#34;base_image&#34;: &#34;/assets/courseware/v1/7c4aed36839a18c8c76b8305713dfbda/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_wk4-grover-exact2b_wk4-grover-exact2b_dnd.png&#34;, &#34;target_outline&#34;: &#34;false&#34;}&lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/drag_and_drop.a31124208b9b.js&#34;/&gt; &lt;div class=&#34;unanswered&#34; id=&#34;status_s14-wk4-gsearch4_2_1&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_s14-wk4-gsearch4_2_1&#34; id=&#34;input_s14-wk4-gsearch4_2_1&#34; aria-describedby=&#34;answer_s14-wk4-gsearch4_2_1&#34; value=&#34;&#34; style=&#34;display:none;&#34;/&gt; &lt;p class=&#34;indicator-container drag-and-drop--status&#34; aria-describedby=&#34;input_s14-wk4-gsearch4_2_1&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_s14-wk4-gsearch4_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/p&gt; &lt;p id=&#34;answer_s14-wk4-gsearch4_2_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_s14-wk4-gsearch4_solution_1&#34;/&gt; &lt;/div&gt;&lt;/span&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_s14-wk4-gsearch4_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Quantum search by continuous-time simulation IV&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_s14-wk4-gsearch4&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_s14-wk4-gsearch4&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch4-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch4-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;s14-wk4-gsearch4-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@site_search_box030197"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-has-score="False" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.370.2x+1T2018+type@html+block@site_search_box030197" data-request-token="e2c78d361edb11f097b212192c274abf" data-runtime-version="1" data-graded="True" data-course-id="course-v1:MITx+8.370.2x+1T2018" data-runtime-class="LmsRuntime" data-block-type="html"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <span><a href="/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/NONE" id="dummy_course_static_link" style="display:none"/><a href="/courses/course-v1:MITx+8.370.2x+1T2018/jump_to_id/NONE" id="dummy_jump_link" style="display:none"/><script type="text/javascript"> var add_site_search = function(){ course_static_url = $('#dummy_course_static_link').attr('href').replace('/NONE', ''); jump_to_url = $('#dummy_jump_link').attr('href').replace('/NONE', ''); if (typeof String.prototype.startsWith != 'function') { // see below for better implementation! String.prototype.startsWith = function (str){ return this.indexOf(str) === 0; }; } if(typeof(String.prototype.trim) === "undefined") { String.prototype.trim = function() { return String(this).replace(/^\s+|\s+$/g, ''); }; } var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var amp = String.fromCharCode(38); var rlb = rb + lb; var mke = function(x){ return lb + x + rb; } var search_module_url = ""; var get_search_module_ficus = function(){ var cid = $('div.xblock').data('course-id'); if (cid){ console.log("cid = ", cid); // search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/" + cid + "/courseware/welcome/Search_this_course/"; search_module_url = "/courses/course-v1:MITx+8.370.2x+1T2018/courseware/welcome/Search_this_course/"; // automatically rewritten console.log("3. search_module_url = ", search_module_url); return; } var course_root_link = $('span.nav-item-course').find('a').attr('href'); if (course_root_link){ console.log("course_root_link = ", course_root_link); search_module_url = course_root_link.replace("course/", "courseware/welcome/Search_this_course/"); console.log("2. search_module_url = ", search_module_url); return } console.log("cannot determine search module url"); } var get_search_module = function(){ // find search this module link if (!($('div.course-index').length)){ return get_search_module_ficus(); } $('div.course-index').find('nav').find('a').each(function(){ if ($(this).text().trim().startsWith("Search this course")){ search_module_url = $(this).attr('href'); console.log("search_module_url = ", search_module_url); } }); } var go_to_search = function(){ get_search_module(); var sterm = $('#site-search-box').val(); // new_url = jump_to_url + "/Search_this_module/?q=" + sterm; new_url = search_module_url + "?q=" + sterm; console.log("sterm = ", sterm, " ; going to ", new_url); window.location.href = new_url; } if (!$('#site-search-box').length){ $("nav.courseware").find("ol").append(lb + "section style='float:right'" + rlb + "input size='20'" + " id='site-search-box'" + rlb + "img src='" + course_static_url + "/images_search_glass.png'/" + rlb + "/input" + rlb + "/section" + rb); } $("#site-search-box").keypress(function(event) { if (event.which == 13) { event.preventDefault(); go_to_search(); } }); // $('#site-search-box').bind("enterKey", go_to_search); var get = function(x){ return eval(x); } return {'course_static_url': course_static_url, 'jump_to_url': jump_to_url, 'go_to_search': go_to_search, 'get_search_module': get_search_module, 'get_search_module_ficus': get_search_module_ficus, 'get': get, } } var the_site_search = add_site_search(); var add_fix_transcript = function(){ if ($('div.wrap-instructor-info').length==0){ return; } $('div.xblock-student_view-video').each(function(key, vblock_e){ var vblock = $(vblock_e); var vuid = vblock.data('usage-id').split('@'); var vid; if (vuid.length==1){ vuid = vblock.data('usage-id').split(';_') vid = vuid[5]; }else{ vid = vuid[2]; } var mfnpre = vid.split("_video",1)[0]; var mfnid = mfnpre; // no periods mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename var lb = String.fromCharCode(60); var rb = String.fromCharCode(62); var mke = function(x){ return lb + x + rb; } var ftid = "fix_transcript_" + mfnid; if (!$('#' + ftid).length){ var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb; html += "contribute transcript fix" + mke("/a") + mke("/span"); console.log("html = ", html); vblock.after(html) } $('#' + ftid).click(function(){ var cst = $('ol.subtitles').find('li.current'); var cindex = Number(cst.data('index')); var gurl; if (mfnpre.endsWith('_cq_sol')){ gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/"; }else{ gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/"; } gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1); console.log("going to ", gurl); window.open(gurl, "MITx 8.370x subtitle source"); }); }); } try{ add_fix_transcript(); } catch(err){ console.log(err); } try{ var rb = String.fromCharCode(62); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 3000); setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000); } catch(err){ console.log(err); } </script></span> </div> </div> </div> </div>