<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@Deutsch-Josza_algorithm__1_of_2_" data-request-token="5efd5e471eda11f097b012192c274abf" 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">Deutsch-Josza algorithm (1 of 2)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_I"> <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@Deutsch-Josza_algorithm_I" data-request-token="5efd5e471eda11f097b012192c274abf" 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_Deutsch-Josza_algorithm_I" class="problems-wrapper" role="group" aria-labelledby="Deutsch-Josza_algorithm_I-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_I" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_I/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;Deutsch-Josza_algorithm_I-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_I-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Deutsch-Josza algorithm I &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_I-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;div id=&#34;fig1&#34; class=&#34;figure&#34;&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/c6adf0427cde25ac7af2cfb663713ed7/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_ps3a_DJ.png&#34; width=&#34;400&#34; style=&#34;scale:0.5&#34;/&gt; &lt;/center&gt; &lt;div class=&#34;caption&#34;&gt;&lt;b&gt;Figure 1&lt;/b&gt;: &lt;span&gt;Deutsch-Josza algorithm&lt;/span&gt;&lt;/div&gt; &lt;/div&gt; &lt;p&gt; The Deutsch-Josza algorithm allows one to determine whether a function over [mathjaxinline]n[/mathjaxinline] bit string [mathjaxinline]f: \{ 0,1\} ^ n \rightarrow \{ 0,1\}[/mathjaxinline] is constant or balanced by only one application of unitary. [mathjaxinline]f[/mathjaxinline] is constant if [mathjaxinline]f(x) = c[/mathjaxinline] for all [mathjaxinline]x\in \{ 0,1\} ^ n[/mathjaxinline] for some constant [mathjaxinline]c\in \{ 0,1\}[/mathjaxinline]. [mathjaxinline]f[/mathjaxinline] is balanced if [mathjaxinline]f(x)=0[/mathjaxinline] for [mathjaxinline]2^{n-1}[/mathjaxinline] [mathjaxinline]x[/mathjaxinline]&#39;s and [mathjaxinline]f(x)=1[/mathjaxinline] for the other [mathjaxinline]2^{n-1}[/mathjaxinline] [mathjaxinline]x[/mathjaxinline]&#39;s. &lt;/p&gt; &lt;p&gt; Let [mathjaxinline]U[/mathjaxinline] be a unitary such that [mathjaxinline]U|{x}\rangle |{y}\rangle =|{x}\rangle |{y\oplus f(x)}\rangle[/mathjaxinline]. The circuit for the Deutsch-Josza algorithm is depicted in the figure above. The top wire refers to the [mathjaxinline]n[/mathjaxinline]-qubit wires and the Hadamard gate is applied to each qubit. The measurement at the end is done for each qubit with [mathjaxinline]\{ |{0}\rangle , |{1}\rangle \}[/mathjaxinline] basis. We call the first [mathjaxinline]n[/mathjaxinline] qubits &#34;data qubits&#34; and the last one qubit &#34;work qubit&#34;. &lt;/p&gt; &lt;p&gt; In this problem, we consider specific examples for [mathjaxinline]n=2[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Let [mathjaxinline]f(x)=x\cdot j[/mathjaxinline] where [mathjaxinline]j=00[/mathjaxinline]. We define inner product between [mathjaxinline]n[/mathjaxinline] digit numbers [mathjaxinline]a=a_1a_2\dots a_ n[/mathjaxinline] and [mathjaxinline]b=b_1b_2\dots b_ n[/mathjaxinline] as [mathjaxinline]a\cdot b=\sum _{i=1}^ n a_ i b_ i[/mathjaxinline]. &lt;/p&gt; &lt;ul class=&#34;itemize&#34;&gt; &lt;li&gt; &lt;p&gt; Is this [mathjaxinline]f[/mathjaxinline] constant or balanced? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;inputtype option-input inline&#34;&gt; &lt;select name=&#34;input_Deutsch-Josza_algorithm_I_2_1&#34; id=&#34;input_Deutsch-Josza_algorithm_I_2_1&#34; aria-describedby=&#34;status_Deutsch-Josza_algorithm_I_2_1&#34;&gt; &lt;option value=&#34;option_Deutsch-Josza_algorithm_I_2_1_dummy_default&#34;&gt;Select an option&lt;/option&gt; &lt;option value=&#34;constant&#34;&gt; constant&lt;/option&gt; &lt;option value=&#34;balanced&#34;&gt; balanced&lt;/option&gt; &lt;/select&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Deutsch-Josza_algorithm_I_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;/div&gt; &lt;p class=&#34;answer&#34; id=&#34;answer_Deutsch-Josza_algorithm_I_2_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/li&gt; &lt;li&gt; &lt;p&gt; Write the state of data qubits right after the application of [mathjaxinline]U[/mathjaxinline] with [mathjaxinline]\{ |{00}\rangle ,|{01}\rangle ,|{10}\rangle ,|{11}\rangle \}[/mathjaxinline] basis. 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 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_Deutsch-Josza_algorithm_I_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_Deutsch-Josza_algorithm_I_3_1&#34; id=&#34;input_Deutsch-Josza_algorithm_I_3_1&#34; aria-describedby=&#34;status_Deutsch-Josza_algorithm_I_3_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Deutsch-Josza_algorithm_I_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Deutsch-Josza_algorithm_I_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_Deutsch-Josza_algorithm_I_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Deutsch-Josza_algorithm_I_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Deutsch-Josza_algorithm_I_3_1_dynamath&#34; name=&#34;input_Deutsch-Josza_algorithm_I_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; What is the probability of getting measurement result 00? &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_Deutsch-Josza_algorithm_I_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_Deutsch-Josza_algorithm_I_4_1&#34; id=&#34;input_Deutsch-Josza_algorithm_I_4_1&#34; aria-describedby=&#34;status_Deutsch-Josza_algorithm_I_4_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Deutsch-Josza_algorithm_I_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Deutsch-Josza_algorithm_I_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_Deutsch-Josza_algorithm_I_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Deutsch-Josza_algorithm_I_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Deutsch-Josza_algorithm_I_4_1_dynamath&#34; name=&#34;input_Deutsch-Josza_algorithm_I_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_Deutsch-Josza_algorithm_I_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;Deutsch-Josza algorithm I&#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_Deutsch-Josza_algorithm_I&#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_Deutsch-Josza_algorithm_I&#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@Deutsch-Josza_algorithm__2_of_2_" data-request-token="5efd5e471eda11f097b012192c274abf" 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">Deutsch-Josza algorithm (2 of 2)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_II"> <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@Deutsch-Josza_algorithm_II" data-request-token="5efd5e471eda11f097b012192c274abf" 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_Deutsch-Josza_algorithm_II" class="problems-wrapper" role="group" aria-labelledby="Deutsch-Josza_algorithm_II-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_II" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_II/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;Deutsch-Josza_algorithm_II-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_II-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Deutsch-Josza algorithm II &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Deutsch-Josza_algorithm_II-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Continuing in the scenario of the Deutsch-Jozsa algorithm problem part I: &lt;/p&gt; &lt;div id=&#34;fig2&#34; class=&#34;figure&#34;&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/c6adf0427cde25ac7af2cfb663713ed7/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_ps3a_DJ.png&#34; width=&#34;400&#34; style=&#34;scale:0.5&#34;/&gt; &lt;/center&gt; &lt;div class=&#34;caption&#34;&gt;&lt;b&gt;Figure 2&lt;/b&gt;: &lt;span&gt;Deutsch-Josza algorithm&lt;/span&gt;&lt;/div&gt; &lt;/div&gt; &lt;ul class=&#34;itemize&#34;&gt; &lt;li&gt; &lt;p&gt; Let [mathjaxinline]f(x)=x\cdot j[/mathjaxinline] where [mathjaxinline]j=01[/mathjaxinline]. We define inner product between [mathjaxinline]n[/mathjaxinline] digit numbers [mathjaxinline]a=a_1a_2\dots a_ n[/mathjaxinline] and [mathjaxinline]b=b_1b_2\dots b_ n[/mathjaxinline] as [mathjaxinline]a\cdot b=\sum _{i=1}^ n a_ i b_ i[/mathjaxinline]. &lt;/p&gt; &lt;ul class=&#34;itemize&#34;&gt; &lt;li&gt; &lt;p&gt; Is this [mathjaxinline]f[/mathjaxinline] constant or balanced? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;inputtype option-input inline&#34;&gt; &lt;select name=&#34;input_Deutsch-Josza_algorithm_II_2_1&#34; id=&#34;input_Deutsch-Josza_algorithm_II_2_1&#34; aria-describedby=&#34;status_Deutsch-Josza_algorithm_II_2_1&#34;&gt; &lt;option value=&#34;option_Deutsch-Josza_algorithm_II_2_1_dummy_default&#34;&gt;Select an option&lt;/option&gt; &lt;option value=&#34;constant&#34;&gt; constant&lt;/option&gt; &lt;option value=&#34;balanced&#34;&gt; balanced&lt;/option&gt; &lt;/select&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Deutsch-Josza_algorithm_II_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;/div&gt; &lt;p class=&#34;answer&#34; id=&#34;answer_Deutsch-Josza_algorithm_II_2_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/li&gt; &lt;li&gt; &lt;p&gt; Write the state of data qubits right after the application of [mathjaxinline]U[/mathjaxinline] with [mathjaxinline]\{ |{00}\rangle ,|{01}\rangle ,|{10}\rangle ,|{11}\rangle \}[/mathjaxinline] basis. 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 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_Deutsch-Josza_algorithm_II_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_Deutsch-Josza_algorithm_II_3_1&#34; id=&#34;input_Deutsch-Josza_algorithm_II_3_1&#34; aria-describedby=&#34;status_Deutsch-Josza_algorithm_II_3_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Deutsch-Josza_algorithm_II_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Deutsch-Josza_algorithm_II_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_Deutsch-Josza_algorithm_II_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Deutsch-Josza_algorithm_II_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Deutsch-Josza_algorithm_II_3_1_dynamath&#34; name=&#34;input_Deutsch-Josza_algorithm_II_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; What is the probability of getting measurement result 00? &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_Deutsch-Josza_algorithm_II_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_Deutsch-Josza_algorithm_II_4_1&#34; id=&#34;input_Deutsch-Josza_algorithm_II_4_1&#34; aria-describedby=&#34;status_Deutsch-Josza_algorithm_II_4_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Deutsch-Josza_algorithm_II_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Deutsch-Josza_algorithm_II_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_Deutsch-Josza_algorithm_II_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Deutsch-Josza_algorithm_II_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Deutsch-Josza_algorithm_II_4_1_dynamath&#34; name=&#34;input_Deutsch-Josza_algorithm_II_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/li&gt; &lt;/ul&gt; &lt;/li&gt; &lt;/ul&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_Deutsch-Josza_algorithm_II_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;Deutsch-Josza algorithm 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_Deutsch-Josza_algorithm_II&#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_Deutsch-Josza_algorithm_II&#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;Deutsch-Josza_algorithm_II-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;Deutsch-Josza_algorithm_II-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;Deutsch-Josza_algorithm_II-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> </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@Simons_algorithm__1_of_2_" data-request-token="5efd5e471eda11f097b012192c274abf" 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">Simon&#39;s algorithm (1 of 2)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_I"> <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@Simons_algorithm_I" data-request-token="5efd5e471eda11f097b012192c274abf" 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_Simons_algorithm_I" class="problems-wrapper" role="group" aria-labelledby="Simons_algorithm_I-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_I" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_I/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;Simons_algorithm_I-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_I-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Simon&amp;#39;s algorithm I &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_I-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Let [mathjaxinline]f:\{ 0,1\} ^ n \rightarrow \{ 0,1\} ^ n[/mathjaxinline] be a function over [mathjaxinline]n[/mathjaxinline] bits whose output is also [mathjaxinline]n[/mathjaxinline] bit. Suppose that [mathjaxinline]f[/mathjaxinline] is a function such that [mathjaxinline]f(x)=f(y)[/mathjaxinline] if and only if [mathjaxinline]x \oplus s = y[/mathjaxinline] for fixed [mathjaxinline]n[/mathjaxinline] bit string [mathjaxinline]s[/mathjaxinline]. Note that [mathjaxinline]\oplus[/mathjaxinline] is the bitwise addition modulo 2. Classically, finding such [mathjaxinline]s[/mathjaxinline] takes exponentially many queries to a classical oracle which outputs [mathjaxinline]f(x)[/mathjaxinline] for input [mathjaxinline]x[/mathjaxinline]. Simon&#39;s algorithm is a quantum algorithm that allows one to reduce the number of queries to polynomially many times. The circuit for the Simon&#39;s algorithm is shown below. &lt;/p&gt; &lt;div class=&#34;figure&#34; id=&#34;fig2&#34;&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/fbf484cab02a02017edae9ba8d55ea53/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_ps3b_simon.png&#34; width=&#34;400&#34; style=&#34;scale:0.7&#34;/&gt; &lt;/center&gt; &lt;/div&gt; &lt;p&gt; The quantum oracle we consider is the unitary [mathjaxinline]U[/mathjaxinline] such that [mathjaxinline]U|{x}\rangle |{y}\rangle = |{x}\rangle |{y\oplus f(x)}\rangle[/mathjaxinline]. The circuit for the Simon&#39;s algorithm is described above. Let us call the upper [mathjaxinline]n[/mathjaxinline] qubits [mathjaxinline]A[/mathjaxinline] and lower [mathjaxinline]n[/mathjaxinline] qubits [mathjaxinline]B[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; The procedure of the Simon&#39;s algorithm is the following. &lt;/p&gt; &lt;ol class=&#34;enumerate&#34;&gt; &lt;li value=&#34;1&#34;&gt; &lt;p&gt; Get the measurement result in [mathjaxinline]A[/mathjaxinline]. Store the result as [mathjaxinline]z_1[/mathjaxinline]. &lt;/p&gt; &lt;/li&gt; &lt;li value=&#34;2&#34;&gt; &lt;p&gt; Repeat the above step [mathjaxinline]n-1[/mathjaxinline] times and store those results as [mathjaxinline]z_2,z_3,\dots z_{n-1}[/mathjaxinline]. &lt;/p&gt; &lt;/li&gt; &lt;li value=&#34;3&#34;&gt; &lt;p&gt; Solve [mathjaxinline]z_ i \cdot s =0, \ i=1,2,\dots , n-1[/mathjaxinline] for [mathjaxinline]s[/mathjaxinline] where [mathjaxinline]\cdot[/mathjaxinline] is an inner product modulo 2, i.e. [mathjaxinline]x \cdot y = x_1 y_1 \oplus \dots x_ n y_ n[/mathjaxinline]. &lt;/p&gt; &lt;/li&gt; &lt;li value=&#34;4&#34;&gt; &lt;p&gt; If there exists unique solution for [mathjaxinline]s\neq 0^ n[/mathjaxinline], check if [mathjaxinline]f(s) = f(0^ n)[/mathjaxinline]. If it is satisfied, we conclude it is the [mathjaxinline]s[/mathjaxinline] we are looking for. If it is not satisfied, we conclude [mathjaxinline]s = 0^ n[/mathjaxinline]. If there is no unique solution ([mathjaxinline]n-1[/mathjaxinline] equations are not independent), the algorithm is abolished and start from the beginning. &lt;/p&gt; &lt;/li&gt; &lt;/ol&gt; &lt;p&gt; In this problem, we are going to get our hands on to work out specific examples with [mathjaxinline]n=2[/mathjaxinline] so that one can get an idea what is going on. &lt;/p&gt; &lt;p&gt; Suppose [mathjaxinline]f(x)=\sigma (x)[/mathjaxinline] where [mathjaxinline]\sigma[/mathjaxinline] is the permutation such that &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]\pi = \begin{pmatrix} 00 &amp;amp; 01 &amp;amp; 10 &amp;amp; 11 \\ 01 &amp;amp; 10 &amp;amp; 11 &amp;amp; 00 \end{pmatrix}[/mathjax]&lt;/td&gt; &lt;td class=&#34;eqnnum&#34; style=&#34;width:20%; border:none;text-align:right&#34;&gt;(1.2)&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; which maps [mathjaxinline]00\rightarrow 01[/mathjaxinline], [mathjaxinline]01\rightarrow 10[/mathjaxinline] etc. &lt;/p&gt; &lt;ul class=&#34;itemize&#34;&gt; &lt;li&gt; &lt;p&gt; Suppose we get the result 00 for the measurement in [mathjaxinline]B[/mathjaxinline]. What is the 2-qubit state [mathjaxinline]A[/mathjaxinline] right before the measurement in [mathjaxinline]A[/mathjaxinline]? Answer with the ket notation taking 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_Simons_algorithm_I_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_Simons_algorithm_I_2_1&#34; id=&#34;input_Simons_algorithm_I_2_1&#34; aria-describedby=&#34;status_Simons_algorithm_I_2_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_I_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_I_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_Simons_algorithm_I_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_I_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_I_2_1_dynamath&#34; name=&#34;input_Simons_algorithm_I_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; Suppose we ran this algorithm and obtained [mathjaxinline]z_1=01[/mathjaxinline] for the measurement in [mathjaxinline]A[/mathjaxinline]. What [mathjaxinline]s[/mathjaxinline] is obtained by solving [mathjaxinline]z_1 \cdot s =0[/mathjaxinline] other than the trivial solution [mathjaxinline]s = 00[/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_Simons_algorithm_I_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_Simons_algorithm_I_3_1&#34; id=&#34;input_Simons_algorithm_I_3_1&#34; aria-describedby=&#34;status_Simons_algorithm_I_3_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_I_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_I_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_Simons_algorithm_I_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_I_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_I_3_1_dynamath&#34; name=&#34;input_Simons_algorithm_I_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; Check whether this [mathjaxinline]s[/mathjaxinline] gives [mathjaxinline]f(s) = f(00)[/mathjaxinline] and conclude the true value [mathjaxinline]s[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]s=[/mathjaxinline]&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_Simons_algorithm_I_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_Simons_algorithm_I_4_1&#34; id=&#34;input_Simons_algorithm_I_4_1&#34; aria-describedby=&#34;status_Simons_algorithm_I_4_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_I_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_I_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_Simons_algorithm_I_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_I_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_I_4_1_dynamath&#34; name=&#34;input_Simons_algorithm_I_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_Simons_algorithm_I_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;Simon&amp;#39;s algorithm I&#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_Simons_algorithm_I&#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_Simons_algorithm_I&#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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<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@Simons_algorithm__2_of_2_" data-request-token="5efd5e471eda11f097b012192c274abf" 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">Simon&#39;s algorithm (2 of 2)</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_II"> <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@Simons_algorithm_II" data-request-token="5efd5e471eda11f097b012192c274abf" 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_Simons_algorithm_II" class="problems-wrapper" role="group" aria-labelledby="Simons_algorithm_II-problem-title" data-problem-id="block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_II" data-url="/courses/course-v1:MITx+8.370.2x+1T2018/xblock/block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_II/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="5" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;Simons_algorithm_II-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_II-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Simon&amp;#39;s algorithm II &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.370.2x+1T2018+type@problem+block@Simons_algorithm_II-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Continuing in the scenario of Simon&#39;s algorithm problem part I: &lt;/p&gt; &lt;div class=&#34;figure&#34; id=&#34;fig2&#34;&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/fbf484cab02a02017edae9ba8d55ea53/asset-v1:MITx+8.370.2x+1T2018+type@asset+block/images_ps3b_simon.png&#34; width=&#34;400&#34; style=&#34;scale:0.7&#34;/&gt; &lt;/center&gt; &lt;/div&gt; &lt;p&gt; Suppose [mathjaxinline]f(x)=x&#39;[/mathjaxinline] where [mathjaxinline]x&#39;[/mathjaxinline] is the string with 0 for the first bit and having the same bits for the rest. For instance, [mathjaxinline]f(11)=01[/mathjaxinline] and [mathjaxinline]f(00)=00[/mathjaxinline]. &lt;/p&gt; &lt;ul class=&#34;itemize&#34;&gt; &lt;li&gt; &lt;p&gt; Suppose we get the result 00 for the measurement in [mathjaxinline]B[/mathjaxinline]. What is the 2-qubit state [mathjaxinline]A[/mathjaxinline] right before the measurement in [mathjaxinline]A[/mathjaxinline]? Answer with the ket notation taking 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_Simons_algorithm_II_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_Simons_algorithm_II_2_1&#34; id=&#34;input_Simons_algorithm_II_2_1&#34; aria-describedby=&#34;status_Simons_algorithm_II_2_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_II_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_II_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_Simons_algorithm_II_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_II_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_II_2_1_dynamath&#34; name=&#34;input_Simons_algorithm_II_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; In the above case, what are the two possible measurement results for the measurement in [mathjaxinline]A[/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_Simons_algorithm_II_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_Simons_algorithm_II_3_1&#34; id=&#34;input_Simons_algorithm_II_3_1&#34; aria-describedby=&#34;status_Simons_algorithm_II_3_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_II_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_II_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_Simons_algorithm_II_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_II_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_II_3_1_dynamath&#34; name=&#34;input_Simons_algorithm_II_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&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_Simons_algorithm_II_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_Simons_algorithm_II_4_1&#34; id=&#34;input_Simons_algorithm_II_4_1&#34; aria-describedby=&#34;status_Simons_algorithm_II_4_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_II_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_II_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_Simons_algorithm_II_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_II_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_II_4_1_dynamath&#34; name=&#34;input_Simons_algorithm_II_4_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; Suppose we ran this algorithm and obtained [mathjaxinline]z_1[/mathjaxinline] such that [mathjaxinline]z \neq 00[/mathjaxinline] for the measurement in [mathjaxinline]A[/mathjaxinline]. What [mathjaxinline]s[/mathjaxinline] is obtained by solving [mathjaxinline]z_1 \cdot s =0[/mathjaxinline] other than the trivial solution [mathjaxinline]s = 00[/mathjaxinline]? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 4&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_Simons_algorithm_II_5_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_Simons_algorithm_II_5_1&#34; id=&#34;input_Simons_algorithm_II_5_1&#34; aria-describedby=&#34;status_Simons_algorithm_II_5_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_II_5_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_II_5_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_Simons_algorithm_II_5_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_II_5_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_II_5_1_dynamath&#34; name=&#34;input_Simons_algorithm_II_5_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; Check whether this [mathjaxinline]s[/mathjaxinline] gives [mathjaxinline]f(s) = f(00)[/mathjaxinline] and conclude the true value [mathjaxinline]s[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 5&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_Simons_algorithm_II_6_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_Simons_algorithm_II_6_1&#34; id=&#34;input_Simons_algorithm_II_6_1&#34; aria-describedby=&#34;status_Simons_algorithm_II_6_1&#34; value=&#34;&#34; class=&#34;math&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_Simons_algorithm_II_6_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_Simons_algorithm_II_6_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_Simons_algorithm_II_6_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_Simons_algorithm_II_6_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_Simons_algorithm_II_6_1_dynamath&#34; name=&#34;input_Simons_algorithm_II_6_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_Simons_algorithm_II_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;Simon&amp;#39;s algorithm 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_Simons_algorithm_II&#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_Simons_algorithm_II&#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;Simons_algorithm_II-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;Simons_algorithm_II-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;Simons_algorithm_II-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_box1xxx"> <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_box1xxx" data-request-token="5efd5e471eda11f097b012192c274abf" 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>