@yuichirominato 2019.02.16更新 87views

[quantum annealing]Graph coloring application with javascript


Introduction

I made this application 3years before and it is useful to see how the annealing process is done. This is written in simulated annealing but of course it is possible to replace the algorithm on quantum annealing.

The structure is very simple, let’s see it.

On the left there is a console. There used to be possible to command directly for the operation but now it is not work from the console.

The upper area there are 4 boxes, cost function, temperature, bit flip probability, and time to calculate.

The biggest area shows the chimera graph of the ising model. The map on the right show the color to paint. The simple table just show the relation between neighbor in other state of Canada.

Code

The code is very simple using bootstrap3 and jquery. Now cdn is used, if you download the jquery and bootstrap3 you can use it on your local machine without connecting to the cdn network.

This is the demo site.

http://blueqat.com/edu2/

Code is very simple working on js/html.

<!doctype html>
<html>
<head>
<!-- Latest compiled and minified CSS -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" integrity="sha384-BVYiiSIFeK1dGmJRAkycuHAHRg32OmUcww7on3RYdg4Va+PmSTsz/K68vbdEjh4u" crossorigin="anonymous">

<script
  src="https://code.jquery.com/jquery-2.2.4.min.js"
  integrity="sha256-BbhdlvQf/xTY9gja0Dq3HiwQF8LaCRTXxZKRutelT44="
  crossorigin="anonymous"></script>
  
<script>

window.onload = function(){

var N = 512;
var rptN = N;
var kTinit =3;
var kT;
var clinit = 0.99;
var cl;
var kTF = 0.02;
var q = new Array(N);
var a = new Array(N);
var b = new Array(N*2);
var c = new Array(N/2);
var d = new Array(N/2);
var Einit=0;
var E;
var inter =0;
var start = $.now();
var timeinit = 0;
var time;
var sq = Math.floor(Math.sqrt(N/8));
var run = 0;
var rpt = 2000;

function initparam(){
kT = kTinit;
E = Einit;
cl = clinit;
time = timeinit;
};

function initarray(){

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};

 function inittable(){
  $('#mx').empty();
  for(var i=0;i<sq;i++){
   for(var j=0;j<sq;j++){
    $('#mx').append('<div class="unit" id="unit'+(j+i*sq)+'"><div class="ver on" id="'+(j*sq+i*sq*sq)+'" style="left:10px;"></div><div class="ver on" id="'+(1+j*8+i*64)+'" style="left:25px;"></div><div class="ver on" id="'+(2+j*8+i*64)+'" style="left:40px;"></div><div class="ver on" id="'+(3+j*8+i*64)+'" style="left:55px;"></div><div class="hor on" id="'+(4+j*8+i*64)+'" style="top:10px;"></div><div class="hor on" id="'+(5+j*8+i*64)+'" style="top:25px;"></div><div class="hor on" id="'+(6+j*8+i*64)+'" style="top:40px;"></div><div class="hor on" id="'+(7+j*8+i*64)+'" style="top:55px;"></div></div>')
   };
   $('#mx').append('<br style="clear:both;">');
  };

  for(var i=0;i<sq;i++){
   for(var j=0;j<sq;j++){

    for(var k=0;k<4;k++){
     $('#unit'+(i*8+j)).append('<div class="lognum lognum-purple" style="top:-14px;left:'+(8+k*15)+'px;">'+a[k+j*8+i*64]+'</div>');
    };

    for(var k=4;k<8;k++){
     $('#unit'+(i*8+j)).append('<div class="lognum lognum-purple" style="left:-10px;top:'+(3+(k-4)*15)+'px;">'+a[k+j*8+i*64]+'</div>');
    };

    for(var k=0;k<16;k++){
     $('#unit'+(i*sq+j)).append('<div class="lognum lognum-blue" style="top:'+(5+15*(k%4))+'px;left:'+(8+15*(Math.floor(k/4)))+'px;">'+b[k+j*16+i*128]+'</div>');
    };

    if((i*sq+j)%8<7){
     for(var k=0;k<4;k++){
      $('#unit'+(i*sq+j)).append('<div class="lognum lognum-green" style="right:15px;top:'+(3+k*15)+'px;">'+c[k+j*4+i*4*sq]+'</div>');
     };
    };

    if((i*sq+j)<56){
     for(var k=0;k<4;k++){
      $('#unit'+(i*8+j)).append('<div class="lognum lognum-green" style="bottom:-9px;left:'+(8+k*15)+'px;">'+d[k+j*4+i*32]+'</div>');
     };
    };

   };
  };

 };

function qinit(){
for(var i=0;i<N;i++){
q[i] = 1;
};

for(var i=0;i<N;i++){
if((i<256 && i%64>39) || i>=256 || Math.floor(i/8)==16 || Math.floor(i/8) == 24 || Math.floor(i/8) == 25 || Math.floor(i/8) == 26){
q[i] = 0;
$('#'+i).toggleClass('on');
};
};

};

function loadtxt(txt){
$('#cd').append('<span style="color:#348fe2">#</span> <span style="color:#00acac;">'+txt+' loaded</span><br>');
};

function loadcanada(){
loadtxt('canada');
initarray();
inittable();
qinit();
};

function stcanada(){
$('#plot').empty();
initarray();
rptN=232;
if(run == 0){
initparam();
inittable();
qinit();
start = $.now();
startAnnealing();
var date = new Date($.now());
$('#cd').append('start at '+date+"<br>");
run = 1;
}else{
run = 1;
$('#cd').append('now running<br>');
} 
};

initarray();
qinit();
inittable();
loadcanada();

 function startAnnealing(){
  annealing=setInterval(function(){
   var stop = 0;

   for(var i=0;i<rpt;i++){
    var s = Math.floor(Math.random()*rptN);
    var r = Math.floor(s/8);
    if((s%64)>39 || r==16 || r==24 || r==25 || r==26){
    }else{

    if(s%8<4){
     var dE = (a[s]+b[s*4-r*16]*q[r*8+4]+b[s*4-r*16+1]*q[r*8+5]+b[s*4-r*16+2]*q[r*8+6]+b[s*4-r*16+3]*q[r*8+7])*(q[s]-0.5)*(-2);
     if(s<448){
      dE += (d[s%4+r*4]*q[s+64])*(q[s]-0.5)*(-2);
     };
     if(s>63){
      dE += (d[s%4+r*4-32]*q[s-64])*(q[s]-0.5)*(-2);
     };
    }else{
     var dE = (a[s]+b[s-4+r*8]*q[r*8]+b[s+r*8]*q[r*8+1]+b[s+4+r*8]*q[r*8+2]+b[s+8+r*8]*q[r*8+3])*(q[s]-0.5)*(-2);
     if(s%64<59){
      dE += (c[s%4+r*4]*q[s+8])*(q[s]-0.5)*(-2);
     };
     if(s%64>8){
      dE += (c[s%4+r*4-4]*q[s-8])*(q[s]-0.5)*(-2);
     };
    };

    var p =Math.exp(-dE/kT);
    if(p>1){p=1};
    if(dE < 0 || p > Math.random()){
     q[s] = -q[s]+1;
     $('#'+s).toggleClass('on');
     E=E+dE;
     stop = 0;
    };
   };
   stop++;
   };

clring(0,"NL","CA-NL");
clring(8,"ON","CA-ON");
clring(16,"MB","CA-MB");
clring(24,"SK","CA-SK");
clring(32,"AB","CA-AB");
clring(64,"PE","CA-PE");
clring(72,"QC","CA-QC path");
clring(80,"NU","CA-NU path");
clring(88,"NT","CA-NT path");
clring(136,"NB","CA-NB");
clring(144,"NS","CA-NS path");
clring(160,"BC","CA-BC path");
clring(216,"YT","CA-YT");

kT=kT*cl;

if(kT<kTF){
var date = new Date($.now());
$('#cd').append("finish at "+date+" , E = "+E+"<br>");    
stopAnnealing();
run = 0;
return false;
};

time = ($.now() - start)/1000;

$('#plot').append('<div class="dot bg-green" style="top:'+(-E/3-40)+'px;left:'+(time*10)+'px;"></div>');

$('#tstats').html(kT.toFixed(3));
$('#pstats').html(p.toFixed(6));
$('#cstats').html(E.toFixed(0));
$('#ttstats').html(time.toFixed(3)+"s");

if(inter%10 ==0){
$('#tprogress').css('width',kT*35+'%');
$('#pprogress').css('width',p*100+'%');
$('#cprogress').css('width',((E+1500)/15) +'%');
$('#ttprogress').css('width',time*4 +'%');
};

inter++;
if(stop >1000){
stopAnnealing();
run = 0;
}
},10);
};

function stopAnnealing(){
clearInterval(annealing);
};

$("#canadastart").click(function(){
stcanada();
});

function clring(a,tb,map){
var col = "#d3d3d3";
if((q[a]+q[a+1]+q[a+2]+q[a+3]+q[a+4]+q[a+5]+q[a+6]+q[a+7]) == 2){
if(q[a+0]+q[a+4]==2){
col = "red";
}else if(q[a+1]+q[a+5]==2){
col = "green";
}else if(q[a+2]+q[a+6]==2){
col = "blue";
}else if(q[a+3]+q[a+7]==2){
col = "yellow";
};
};
$('#'+tb).css('background',col);
$('#'+map).attr("fill",col);
};
};
</script>

<style>
body{
 font-size:10px;
 background:#efefef;
 font-family:sans-serif;
 margin-top:52px;
}

.on{
 background:red!important;
}

.unit{
 float:left;
 width:12%;
 height:70px;
 position:relative;
 margin:0 0 20px 0.4%;
}

.ver{
 position:absolute;
 height:68px;
 width:4px;
 background:#1a2229;
 opacity:0.5;
}

.hor{
 position:absolute;
 height:4px;
 width:68px;
 background:#1a2229;
 opacity:0.5;
}

#sidebar{
 padding:10px;
 padding-top:62px;
 width:220px;
 position:fixed;
 height:100%;
 background:#2d353c;
 top:0;
 left:0;
 color:white;
 overflow:auto;
}

#sidebar input:focus{
 outline:none;
}

.panel{
 border:0;
}

.panel-inverse>.panel-heading {
 background: #242a30;
 color:white;
}

.info{
 height:100px;
 overflow:hidden;
 font-size:10px;
 background:#2d353c;
 color:white;
}

#pinfo,#tinfo{
 position:absolute;
 top:5px;
 right:5px;
 z-index:2;
 opacity:0.3;
}

#plot,#plot2{
 height:100px;
 position:absolute;
 left:50px;
 top:0;
}

.widget{
  border-radius:3px;
  margin-bottom:10px;
  color:#fff;
  padding:15px;
  overflow:hidden;
  position:relative;
}

.stats-title{
  color: #fff;
  color: rgba(255,255,255,.6);
  position: relative;
  font-size: 12px;
  line-height:24px;
  float:left;
}

.stats-number{
  font-size:24px;
  font-weight:300;
  float:right;
  z-index:3
}

.stats-progress{
  background:rgba(0,0,0,.2);
  height:2px;
  margin:0 -15px 2px;
  z-index:4
}

.stats-progress .progress-bar{
  background: #fff;
}

.bg-green{
 background:#00acac!important;
}

.bg-blue{
 background:#348fe2!important;
}

.bg-purple{
 background:#727cb6!important;
}

.bg-black{
 background:#2d353c!important;
}

#content{
 margin-left:220px;
 padding:10px;
}

#plot2{
 opacity:0.4;
}

.lognum{
 position:absolute;
 color:white;
 z-index:1000;
 font-size:8px;
}

.lognum-green{
 color:#00acac!important;
}

.lognum-blue{
 color:#348fe2!important;
}

.lognum-purple{
 color:#727cb6!important;
}

.dot{
 height:2px;
 width:2px;
 border-radius:1px;
 position:absolute;
 z-index:200;
}

.navbar-header{
 width:100%;
 padding-right:15px;
}

.panel{
 margin-bottom:10px;
}

#cd{
 word-wrap:break-word;
}
</style>

</head>
<body>
<nav class="navbar navbar-inverse navbar-fixed-top">
 <div class="container-fluid">
  <div class="navbar-header">
   <a class="navbar-brand" href="./qmpg.html">MDR-playground-beta</a>
  </div>
 </div>
</nav>

<div id="sidebar">
 <div id="cd">
 </div>
</div>

<div id="content">
<div class="container-fluid common-main" id="dashboard">
 <div class="row" id="statsrow">

  <div class="col-xs-3">
   <div class="widget bg-black" id="plotfunc" style="position:relative">
    <div class="stats-title">COST</div>
    <div class="stats-number" id="cstats">0</div><br style="clear:both;">
    <div id="plot"></div>
    <div class="stats-progress progress">
     <div class="progress-bar" style="width:100%;" id="cprogress"></div>
    </div>
   </div>
  </div>

  <div class="col-xs-3">
   <div class="widget bg-blue">
    <div class="stats-title">T</div>
    <div class="stats-number" id="tstats">0</div><br style="clear:both;">
    <div id="tinfo"></div>
    <div class="stats-progress progress">
     <div class="progress-bar" style="width:100%;" id="tprogress"></div>
    </div>
   </div>
  </div>

  <div class="col-xs-3">
   <div class="widget bg-purple">
    <div class="stats-title">FLIP</div>
    <div class="stats-number" id="pstats">0</div><br style="clear:both;">
    <div id="pinfo"></div>
    <div class="stats-progress progress">
     <div class="progress-bar" style="width:100%;" id="pprogress"></div>
    </div>
   </div>
  </div>

  <div class="col-xs-3">
   <div class="widget bg-green" style="position:relative">
    <div class="stats-title">TIME</div>
    <div class="stats-number" id="ttstats">0</div><br style="clear:both;">
    <div class="stats-progress progress">
     <div class="progress-bar" style="width:0%;" id="ttprogress"></div>
    </div>
   </div>
  </div>

 </div>

<div class="row">
<div class="col-xs-9">
<div class="panel panel-inverse">
<div class="panel-heading">Ising Model</div>
<div class="panel-body main bg-black" id="mx"></div>
</div>
</div>

<div class="col-xs-3">

<div class="panel panel-inverse">
<div class="panel-heading">Control Panel</div>
<div class="panel-body">
<div style="height:220px;">

<svg
   width="400pt"
   height="500pt"
   id="svg4468">
  <g id="Canada" style="fill:#d3d3d3" transform="translate(-150,0)scale(0.17)">
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1920.152,772.80985 1923.764,775.15364 1925.2671,775.5309 C 1926.7702,775.90815 1928,776.61803 1928,777.10841 C 1928,778.97028 1930.1155,777.85462 1934.3682,773.75 C 1937.6495,770.58296 1938.9448,768.45029 1939.4516,765.38051 C 1939.9305,762.47952 1940.7953,760.95868 1942.3751,760.23886 C 1943.76,759.60788 1945.1434,757.54878 1945.9902,754.85835 C 1947.5441,749.92097 1947.3769,739.53196 1945.6949,736.51115 C 1945.079,735.40502 1944.705,734.0596 1944.8638,733.52133 C 1945.0225,732.98306 1945.608,730.07856 1946.1647,727.06688 C 1947.0804,722.11324 1949.4472,718.54029 1951.1256,719.57763 C 1951.4818,719.79778 1952.0828,721.67038 1952.4611,723.73895 C 1953.3119,728.39068 1957.6216,736 1959.4055,736 C 1960.6224,736 1963.4699,745.99949 1962.965,748.5 C 1962.4144,751.22741 1963.2324,751.61081 1968.75,751.21156 L 1974.5,750.7955 L 1974.3475,757.14775 C 1974.2636,760.64149 1973.716,765.01998 1973.1306,766.87773 C 1972.4419,769.06346 1972.4031,770.88464 1973.0205,772.03835 C 1974.1809,774.20645 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<tr><td id="NL">NL</td><td id="ON">ON</td><td id="MB">MB</td><td id="SK">SK</td><td id="AB" rowspan="2">AB</td></tr>
<tr><td id="PE">PE</td><td id="QC">QC</td><td id="NU">NU</td><td id="NT" rowspan="2">NT</td></tr>
<tr><td></td><td id="NB">NB</td><td id="NS">NS</td><td id="BC" rowspan="2">BC</td></tr>
<tr><td></td><td></td><td></td><td id="YT">YT</td></tr>
</table>
<button class="btn btn-primary btn-block" id="canadastart">start</button>

</div>
</div>
</div>

<div class="col-xs-12">
tes
</div>


</div>
</div>
</div>

</body>
</html>

Initial params

Initial parameters are N=512, initial Temperature is T=3, decay multiply 0.99, final temperature is T=0.02.

var N = 512;
var rptN = N;
var kTinit =3;
var kT;
var clinit = 0.99;
var cl;
var kTF = 0.02;
var q = new Array(N);
var a = new Array(N);
var b = new Array(N*2);
var c = new Array(N/2);
var d = new Array(N/2);
var Einit=0;
var E;
var inter =0;
var start = $.now();
var timeinit = 0;
var time;
var sq = Math.floor(Math.sqrt(N/8));
var run = 0;
var rpt = 2000;

The main loop of algorithm

The algorithm is sa with metropolis. It is using css for the GUI, if you use canvas/html it will be faster than now.

 function startAnnealing(){
  annealing=setInterval(function(){
   var stop = 0;

   for(var i=0;i<rpt;i++){
    var s = Math.floor(Math.random()*rptN);
    var r = Math.floor(s/8);
    if((s%64)>39 || r==16 || r==24 || r==25 || r==26){
    }else{

    if(s%8<4){
     var dE = (a[s]+b[s*4-r*16]*q[r*8+4]+b[s*4-r*16+1]*q[r*8+5]+b[s*4-r*16+2]*q[r*8+6]+b[s*4-r*16+3]*q[r*8+7])*(q[s]-0.5)*(-2);
     if(s<448){
      dE += (d[s%4+r*4]*q[s+64])*(q[s]-0.5)*(-2);
     };
     if(s>63){
      dE += (d[s%4+r*4-32]*q[s-64])*(q[s]-0.5)*(-2);
     };
    }else{
     var dE = (a[s]+b[s-4+r*8]*q[r*8]+b[s+r*8]*q[r*8+1]+b[s+4+r*8]*q[r*8+2]+b[s+8+r*8]*q[r*8+3])*(q[s]-0.5)*(-2);
     if(s%64<59){
      dE += (c[s%4+r*4]*q[s+8])*(q[s]-0.5)*(-2);
     };
     if(s%64>8){
      dE += (c[s%4+r*4-4]*q[s-8])*(q[s]-0.5)*(-2);
     };
    };

    var p =Math.exp(-dE/kT);
    if(p>1){p=1};
    if(dE < 0 || p > Math.random()){
     q[s] = -q[s]+1;
     $('#'+s).toggleClass('on');
     E=E+dE;
     stop = 0;
    };
   };
   stop++;
   };

clring(0,"NL","CA-NL");
clring(8,"ON","CA-ON");
clring(16,"MB","CA-MB");
clring(24,"SK","CA-SK");
clring(32,"AB","CA-AB");
clring(64,"PE","CA-PE");
clring(72,"QC","CA-QC path");
clring(80,"NU","CA-NU path");
clring(88,"NT","CA-NT path");
clring(136,"NB","CA-NB");
clring(144,"NS","CA-NS path");
clring(160,"BC","CA-BC path");
clring(216,"YT","CA-YT");

kT=kT*cl;

if(kT<kTF){
var date = new Date($.now());
$('#cd').append("finish at "+date+" , E = "+E+"<br>");    
stopAnnealing();
run = 0;
return false;
};

This code is free to use to understand quantum computation.

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