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Dihedral HSP problem
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<p>
This is a concept question, provided to check your understanding of the previous lecture video clips. </p>
<p>
Which of the following are true? </p>
<p>
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<text>The dihedral group is abelian.</text>
</label>
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<text>The dihedral group [mathjaxinline]D_ N[/mathjaxinline] has [mathjaxinline]2N[/mathjaxinline] elements.</text>
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<text>In the algorithm we described for dihedral HSP we first create a superposition over group elements and then discard the second register. After this step we get a superposition over 2 group elements.</text>
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<text>The algorithm we described for dihedral HSP on [mathjaxinline]D_ N[/mathjaxinline] runs in polynomial in [mathjaxinline]N[/mathjaxinline].</text>
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Dihedral HSP algorithm
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Which of the following are true? </p>
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<text>In the algorithm we described for dihedral HSP when we measure [mathjaxinline]k[/mathjaxinline] the probability is concentrated around few values of [mathjaxinline]k[/mathjaxinline].</text>
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<text>The main strategy in the algorithm for dihedral HSP is to obtain certain values of [mathjaxinline]k[/mathjaxinline] using many copies of [mathjaxinline]|{\psi _ k}\rangle[/mathjaxinline].</text>
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<text>[mathjaxinline]\{ (2 x,0),(2 x + 1 ,1) : x \in \mathbb {Z}_{N/2}\}[/mathjaxinline] is a subgroup of [mathjaxinline]D_ N[/mathjaxinline].</text>
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<text>If we obtain [mathjaxinline]k = 2^{n-1}[/mathjaxinline] then we can immediately find [mathjaxinline]y[/mathjaxinline] by doing a Hadamard.</text>
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<h2 class="hd hd-2 unit-title">CQ: Shortest vector problem (SVP)</h2>
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Shortest vector problem (SVP)
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This is a concept question, provided to check your understanding of the previous lecture video clips. </p>
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Which of the following are true? </p>
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<text>A lattice consists of infinite number of points.</text>
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<text>Regev's result shows that Dihderal HSP in polynomial time implies P = NP.</text>
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<text>Kuperberg's algorithm gives [mathjaxinline]2^{O(\sqrt n)}[/mathjaxinline] time algorithm to SVP.</text>
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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;
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}
$("#site-search-box").keypress(function(event) {
if (event.which == 13) {
event.preventDefault();
go_to_search();
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// $('#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,
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vid = vuid[5];
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var rb = String.fromCharCode(62);
var mke = function(x){ return lb + x + rb; }
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html += "contribute transcript fix" + mke("/a") + mke("/span");
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vblock.after(html)
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console.log("going to ", gurl);
window.open(gurl, "MITx 8.370x subtitle source");
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<div class="video-player">
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<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
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<div class="closed-captions"></div>
<div class="video-controls is-hidden">
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return this.indexOf(str) === 0;
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{
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{
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var amp = String.fromCharCode(38);
var rlb = rb + lb;
var mke = function(x){ return lb + x + rb; }
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var cid = $('div.xblock').data('course-id');
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var course_root_link = $('span.nav-item-course').find('a').attr('href');
if (course_root_link){
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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
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}
$("#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,
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return;
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var vblock = $(vblock_e);
var vuid = vblock.data('usage-id').split('@');
var vid;
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vuid = vblock.data('usage-id').split(';_')
vid = vuid[5];
}else{
vid = vuid[2];
}
var mfnpre = vid.split("_video",1)[0];
var mfnid = mfnpre; // no periods
mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename
var lb = String.fromCharCode(60);
var rb = String.fromCharCode(62);
var mke = function(x){ return lb + x + rb; }
var ftid = "fix_transcript_" + mfnid;
if (!$('#' + 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();
}
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<h2 class="hd hd-2 unit-title">The nonabelian quantum Fourier transform - application to HSP</h2>
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<h2 class="hd hd-2 unit-title">CQ: Nonabelian QFT</h2>
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Nonabelian QFT
</h3>
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<p>
This is a concept question, provided to check your understanding of the previous lecture video clips. </p>
<p>
Which of the following are true? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_cq_M2L18_LB_Nonabelian_QFT_RB_2_1">
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<input type="checkbox" name="input_cq_M2L18_LB_Nonabelian_QFT_RB_2_1[]" id="input_cq_M2L18_LB_Nonabelian_QFT_RB_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="cq_M2L18_LB_Nonabelian_QFT_RB_2_1-choice_0-label" for="input_cq_M2L18_LB_Nonabelian_QFT_RB_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_cq_M2L18_LB_Nonabelian_QFT_RB_2_1">
<text>Every representation of a finite group is equivalent to some unitary representation.</text>
</label>
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<text>A regular representation is always irreducible.</text>
</label>
</div>
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<text>Any matrix that commutes with all group elements of an irreducible representation is proportional to identity.</text>
</label>
</div>
<div class="field">
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<text>Kuperberg's algorithm is equivalent to weak Fourier sampling in the nonabelian QFT picture.</text>
</label>
</div>
<span id="answer_cq_M2L18_LB_Nonabelian_QFT_RB_2_1"/>
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String.prototype.startsWith = function (str){
return this.indexOf(str) === 0;
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{
String.prototype.trim = function()
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get_search_module();
var sterm = $('#site-search-box').val();
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new_url = search_module_url + "?q=" + sterm;
console.log("sterm = ", sterm, " ; going to ", new_url);
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}
if (!$('#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) {
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event.preventDefault();
go_to_search();
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});
// $('#site-search-box').bind("enterKey", go_to_search);
var get = function(x){
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}
return {'course_static_url': course_static_url,
'jump_to_url': jump_to_url,
'go_to_search': go_to_search,
'get_search_module': get_search_module,
'get_search_module_ficus': get_search_module_ficus,
'get': get,
}
}
var the_site_search = add_site_search();
var add_fix_transcript = function(){
if ($('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>
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