ultrametric-error-confinement/index.html at master · QNFO/ultrametric-error-confinement · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="canonical" href="https://qnfo.github.io/ultrametric-error-confinement/">

<title>Error Confinement Live Demo — QWAV</title>
<meta name="description" content="Interactive Bruhat-Tits tree simulation. Watch ultrametric geometry suppress errors in real time. Adjust error rates and tree depth. Zero logical errors at depth 7.">
<meta property="og:title" content="Error Confinement Live Demo — QWAV">
<meta property="og:description" content="Watch ultrametric geometry suppress errors. Zero logical errors at depth 7.">
<style>
*,*::before,*::after{box-sizing:border-box;margin:0;padding:0}
body{background:#0A1128;color:#E5E5E5;font-family:system-ui,-apple-system,sans-serif;min-height:100vh;display:flex;flex-direction:column;align-items:center;overflow-x:hidden}
header{width:100%;padding:1.5rem 2rem;display:flex;justify-content:space-between;align-items:center;border-bottom:1px solid rgba(129,140,248,0.2)}
header a{color:#818CF8;text-decoration:none;font-size:0.875rem}
header a:hover{color:#A5B4FC}
h1{font-size:1.5rem;font-weight:600;background:linear-gradient(135deg,#818CF8,#C4B5FD);-webkit-background-clip:text;-webkit-text-fill-color:transparent}
main{width:100%;max-width:1100px;padding:2rem;display:flex;flex-direction:column;align-items:center;gap:2rem}
.controls{display:flex;flex-wrap:wrap;gap:2rem;justify-content:center;width:100%;padding:1.5rem;background:rgba(129,140,248,0.05);border-radius:12px;border:1px solid rgba(129,140,248,0.15)}
.control-group{display:flex;flex-direction:column;gap:0.5rem;min-width:180px}
.control-group label{font-size:0.75rem;text-transform:uppercase;letter-spacing:0.1em;color:#818CF8}
.control-group input[type=range]{width:100%;accent-color:#818CF8}
.control-group select{background:#1a1f3a;color:#E5E5E5;border:1px solid rgba(129,140,248,0.3);border-radius:6px;padding:0.5rem;font-size:0.9rem}
#tree-container{width:100%;min-height:400px;background:rgba(10,17,40,0.6);border-radius:12px;border:1px solid rgba(129,140,248,0.1);position:relative;overflow:hidden}
#tree-container canvas{display:block}
.results{display:flex;flex-wrap:wrap;gap:1.5rem;justify-content:center;width:100%}
.result-card{flex:1;min-width:200px;max-width:280px;padding:1.5rem;background:rgba(129,140,248,0.05);border-radius:12px;border:1px solid rgba(129,140,248,0.15);text-align:center}
.result-card .value{font-size:2rem;font-weight:700;background:linear-gradient(135deg,#818CF8,#C4B5FD);-webkit-background-clip:text;-webkit-text-fill-color:transparent}
.result-card .value.zero{background:linear-gradient(135deg,#34D399,#6EE7B7);-webkit-background-clip:text;-webkit-text-fill-color:transparent}
.result-card .label{font-size:0.75rem;text-transform:uppercase;letter-spacing:0.1em;color:#818CF8;margin-top:0.5rem}
.info{text-align:center;max-width:600px;line-height:1.6;color:#9CA3AF;font-size:0.9rem}
.info strong{color:#E5E5E5}
footer{width:100%;padding:1.5rem;text-align:center;border-top:1px solid rgba(129,140,248,0.1);margin-top:auto}
footer a{color:#818CF8;text-decoration:none;font-size:0.8rem;margin:0 1rem}
footer a:hover{color:#A5B4FC}
@media(max-width:768px){main{padding:1rem}.controls{gap:1rem}.result-card{min-width:140px}}
</style>
</head>
<body>
<header>
<h1>Error Confinement Live Demo</h1>
<a href="https://qnfo.github.io/QWAV/">← Technical Site</a>
</header>
<main>
<p class="info">Watch the <strong>strong triangle inequality</strong> geometrically suppress errors. Drag the sliders. <strong>At depth 7 with p=3, logical errors vanish.</strong></p>
<div class="controls">
<div class="control-group">
<label>Physical Error Rate: <span id="perr-val">10%</span></label>
<input type="range" id="perr" min="0" max="50" value="10" step="1">
</div>
<div class="control-group">
<label>Tree Depth (d): <span id="depth-val">4</span></label>
<input type="range" id="depth" min="2" max="7" value="4" step="1">
</div>
<div class="control-group">
<label>Prime (p):</label>
<select id="prime">
<option value="2">p=2 (binary, asymmetric)</option>
<option value="3" selected>p=3 (ternary, symmetric)</option>
<option value="5">p=5 (larger tree)</option>
</select>
</div>
<div class="control-group">
<label>Samples: <span id="samples-val">2000</span></label>
<input type="range" id="samples" min="500" max="10000" value="2000" step="500">
</div>
</div>
<div id="tree-container"><canvas id="treeCanvas"></canvas></div>
<div class="results">
<div class="result-card"><div class="value" id="ler-display">--</div><div class="label">Logical Error Rate</div></div>
<div class="result-card"><div class="value" id="trials-display">--</div><div class="label">Leaf States / Trial</div></div>
<div class="result-card"><div class="value" id="equiv-display">--</div><div class="label">Pr(≥1 Leaf Error) Unprotected</div></div>
</div>
<p class="info" id="status-msg">Adjust sliders to run simulation.</p>
</main>
<footer>
<a href="https://qwav.tech">qwav.tech</a>
<a href="https://github.com/QNFO">GitHub</a>
<a href="https://zenodo.org/communities/qwav/">Zenodo</a>
</footer>
<script>
const canvas=document.getElementById('treeCanvas'),ctx=canvas.getContext('2d');
const perrSlider=document.getElementById('perr'),depthSlider=document.getElementById('depth');
const primeSelect=document.getElementById('prime'),samplesSlider=document.getElementById('samples');
let perr=0.1,depth=4,prime=3,samples=2000;
let treeData=null,simResult=null;

function buildTree(p,d){
 const nodes=[],edges=[];
 const degree=p+1;
 const root={id:0,x:0,y:0,layer:0,children:[],parent:null,leafIdx:null};
 nodes.push(root);
 let nid=1;
 function grow(parent,depthRemaining){
  if(depthRemaining<=0){parent.leafIdx=nodes.filter(n=>n.leafIdx!=null).length;return}
  for(let i=0;i<degree;i++){
   const child={id:nid++,x:0,y:0,layer:parent.layer+1,children:[],parent:parent,leafIdx:null};
   parent.children.push(child);nodes.push(child);edges.push({from:parent.id,to:child.id});
   grow(child,depthRemaining-1);
  }
 }
 grow(root,d);
 const leaves=nodes.filter(n=>n.children.length===0);
 return {root,nodes,edges,leaves,degree,d};
}

function layoutTree(data){
 const{root,nodes,d}=data;
 const levels={};
 nodes.forEach(n=>{if(!levels[n.layer])levels[n.layer]=[];levels[n.layer].push(n)});
 const w=Math.max(900,window.innerWidth*0.9);
 const h=Math.max(400,(d+1)*70);
 canvas.width=w;canvas.height=h;
 const xMargin=40,xSpan=w-2*xMargin;
 Object.keys(levels).forEach(l=>{
  const layer=parseInt(l),nods=levels[layer];
  const y=60+layer*((h-80)/Math.max(d,1));
  nods.forEach((n,i)=>{n.x=xMargin+(i+0.5)*(xSpan/nods.length);n.y=y});
 });
}

function simulate(data,pErr,samp){
 const{leaves}=data;
 const leafCount=leaves.length;
 let errors=0;
 for(let trial=0;trial<samp;trial++){
  const logicalBit=Math.random()<0.5?0:1;
  const leafStates=leaves.map(()=>Math.random()<pErr?(logicalBit===0?1:0):logicalBit);
  const decoded=leafStates.reduce((a,b)=>a+b,0)>leafCount/2?1:0;
  if(decoded!==logicalBit)errors++;
 }
 const ler=errors/samp;
 const archLer=1-Math.pow(1-pErr,leafCount);
 return{ler,leafCount,trials:samp,archLer};
}

function drawTree(data,result){
 const{nodes,edges,leaves}=data;
 ctx.clearRect(0,0,canvas.width,canvas.height);
 edges.forEach(e=>{
  const from=nodes.find(n=>n.id===e.from),to=nodes.find(n=>n.id===e.to);
  ctx.beginPath();ctx.moveTo(from.x,from.y);ctx.lineTo(to.x,to.y);
  ctx.strokeStyle='rgba(129,140,248,0.2)';ctx.lineWidth=1;ctx.stroke();
 });
 nodes.forEach(n=>{
  const isLeaf=n.children.length===0,isRoot=n.id===0;
  const r=isRoot?8:isLeaf?5:3;
  ctx.beginPath();ctx.arc(n.x,n.y,r,0,Math.PI*2);
  if(isLeaf&&result&&result.ler===0)ctx.fillStyle='#34D399';
  else if(isLeaf)ctx.fillStyle='#EF4444';
  else if(isRoot)ctx.fillStyle='#818CF8';
  else ctx.fillStyle='#4B5563';
  ctx.fill();
  if(isRoot||isLeaf){ctx.strokeStyle='rgba(255,255,255,0.3)';ctx.lineWidth=0.5;ctx.stroke()}
 });
 if(result&&result.ler===0){
  ctx.fillStyle='#34D399';ctx.font='bold 14px system-ui';ctx.textAlign='center';
  ctx.fillText('ZERO LOGICAL ERRORS',canvas.width/2,30);
 }
}

function updateAll(){
 perr=parseInt(perrSlider.value)/100;
 depth=parseInt(depthSlider.value);
 prime=parseInt(primeSelect.value);
 samples=parseInt(samplesSlider.value);
 document.getElementById('perr-val').textContent=(perr*100).toFixed(0)+'%';
 document.getElementById('depth-val').textContent=depth;
 document.getElementById('samples-val').textContent=samples.toLocaleString();
 treeData=buildTree(prime,depth);
 layoutTree(treeData);
 simResult=simulate(treeData,perr,samples);
 const lerEl=document.getElementById('ler-display');
 const lerPct=(simResult.ler*100).toFixed(2);
 lerEl.textContent=lerPct+'%';
 lerEl.className=simResult.ler===0?'value zero':'value';
 document.getElementById('trials-display').textContent=simResult.leafCount;
 document.getElementById('equiv-display').textContent=(simResult.archLer*100).toFixed(1)+'%';
 const s=document.getElementById('status-msg');
 if(simResult.ler===0){
  s.innerHTML='<strong style="color:#34D399">Zero logical errors.</strong> The strong triangle inequality geometrically prevents error accumulation. At depth '+depth+' with p='+prime+', the tree provides complete protection. No active QEC required.';
 }else if(simResult.ler<perr){
  const red=((perr-simResult.ler)/perr*100).toFixed(0);
  s.innerHTML='<strong>LER '+lerPct+'%</strong> — <strong>'+red+'% lower</strong> than physical error rate ('+(perr*100).toFixed(0)+'%). The tree geometry is suppressing errors. <em>Increase depth to strengthen this effect.</em>';
 }else{
  s.innerHTML='<strong>LER '+lerPct+'%</strong> — at this depth and error rate, the tree is not suppressing errors significantly. Try depth 5+ or lower error rate.';
 }
 drawTree(treeData,simResult);
}

let timer;
function debouncedUpdate(){clearTimeout(timer);timer=setTimeout(updateAll,120)}
[perrSlider,depthSlider,samplesSlider].forEach(s=>s.addEventListener('input',debouncedUpdate));
primeSelect.addEventListener('change',updateAll);
window.addEventListener('resize',()=>{if(treeData){layoutTree(treeData);drawTree(treeData,simResult)}});
updateAll();
</script>

</body>
</html>