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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · QuantumLegos.jl</title><meta name="title" content="Home · QuantumLegos.jl"/><meta property="og:title" content="Home · QuantumLegos.jl"/><meta property="twitter:title" content="Home · QuantumLegos.jl"/><meta name="description" content="Documentation for QuantumLegos.jl."/><meta property="og:description" content="Documentation for QuantumLegos.jl."/><meta property="twitter:description" content="Documentation for QuantumLegos.jl."/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" 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src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>QuantumLegos.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li class="toplevel"><a class="tocitem" href="#Example"><span>Example</span></a></li><li><a class="tocitem" href="#CheckMatrix-and-defining-Lego"><span>CheckMatrix and defining Lego</span></a></li><li><a class="tocitem" href="#Defining-and-Updating-State"><span>Defining and Updating State</span></a></li><li><a class="tocitem" href="#2-Lego-1-edge-state"><span>2 Lego 1 edge state</span></a></li><li class="toplevel"><a class="tocitem" href="#Internal(how-it-works)"><span>Internal(how it works)</span></a></li><li><a class="tocitem" href="#Notes-on-Overall-flow"><span>Notes on Overall flow</span></a></li><li class="toplevel"><a class="tocitem" href="#API"><span>API</span></a></li></ul></li><li><a class="tocitem" href="pauliops/">PauliOps</a></li><li><a class="tocitem" href="checkmatrix/">Details on check matrix operations</a></li><li><a class="tocitem" href="distance/">How to calculate code distance from the state.</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/qwjyh/QuantumLegos.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/qwjyh/QuantumLegos.jl/blob/main/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="QuantumLegos"><a class="docs-heading-anchor" href="#QuantumLegos">QuantumLegos</a><a id="QuantumLegos-1"></a><a class="docs-heading-anchor-permalink" href="#QuantumLegos" title="Permalink"></a></h1><p>Documentation for QuantumLegos.</p><p>All contents:</p><ul><li><a href="checkmatrix/#Details-on-check-matrix-operations">Details on check matrix operations</a></li><li class="no-marker"><ul><li><a href="checkmatrix/#Basic-features-of-check-matrix">Basic features of check matrix</a></li><li><a href="checkmatrix/#Construction-of-check-matrices-and-retrieving-features">Construction of check matrices and retrieving features</a></li><li><a href="checkmatrix/#Direct-sum">Direct sum</a></li><li><a href="checkmatrix/#Self-tracing">Self-tracing</a></li></ul></li><li><a href="distance/#How-to-calculate-code-distance-from-the-state.">How to calculate code distance from the state.</a></li><li class="no-marker"><ul><li><a href="distance/#Definition-of-code-distance.">Definition of code distance.</a></li><li><a href="distance/#Classification-of-the-stabilizers.">Classification of the stabilizers.</a></li><li><a href="distance/#Calculating-code-distance-from-the-check-matrix.">Calculating code distance from the check matrix.</a></li><li><a href="distance/#Examples">Examples</a></li></ul></li><li><a href="#QuantumLegos">QuantumLegos</a></li><li><a href="#Example">Example</a></li><li class="no-marker"><ul><li><a href="#CheckMatrix-and-defining-Lego">CheckMatrix and defining Lego</a></li><li><a href="#Defining-and-Updating-State">Defining and Updating State</a></li><li><a href="#2-Lego-1-edge-state">2 Lego 1 edge state</a></li></ul></li><li><a href="#Internal(how-it-works)">Internal(how it works)</a></li><li class="no-marker"><ul><li><a href="#Notes-on-Overall-flow">Notes on Overall flow</a></li></ul></li><li><a href="#API">API</a></li><li><a href="pauliops/#PauliOps">PauliOps</a></li><li class="no-marker"><ul><li><a href="pauliops/#Example">Example</a></li><li><a href="pauliops/#API">API</a></li></ul></li></ul><h1 id="Example"><a class="docs-heading-anchor" href="#Example">Example</a><a id="Example-1"></a><a class="docs-heading-anchor-permalink" href="#Example" title="Permalink"></a></h1><h2 id="CheckMatrix-and-defining-Lego"><a class="docs-heading-anchor" href="#CheckMatrix-and-defining-Lego">CheckMatrix and defining Lego</a><a id="CheckMatrix-and-defining-Lego-1"></a><a class="docs-heading-anchor-permalink" href="#CheckMatrix-and-defining-Lego" title="Permalink"></a></h2><pre><code class="language-julia-repl hljs">julia> using QuantumLegos
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julia> stabilizers = pauliop.(["IIXXXX", "IIZZZZ", "ZIZZII", "IZZIZI", "IXXXII", "XIXIXI"])
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6-element Vector{StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}}:
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pauliop("IIXXXX")
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pauliop("IIZZZZ")
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pauliop("ZIZZII")
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pauliop("IZZIZI")
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pauliop("IXXXII")
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pauliop("XIXIXI")
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julia> cmat = checkmatrix(stabilizers)
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CheckMatrix with 6 generators, 6 legs:
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0 0 1 1 1 1 | 0 0 0 0 0 0
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0 0 0 0 0 0 | 0 0 1 1 1 1
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0 0 0 0 0 0 | 1 0 1 1 0 0
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0 0 0 0 0 0 | 0 1 1 0 1 0
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0 1 1 1 0 0 | 0 0 0 0 0 0
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1 0 1 0 1 0 | 0 0 0 0 0 0
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julia> cmat.nlegs
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6
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julia> cmat.ngens
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6
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julia> cmat.cmat
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6×12 Matrix{Bool}:
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0 0 1 1 1 1 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 1 1 1 1
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0 0 0 0 0 0 1 0 1 1 0 0
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0 0 0 0 0 0 0 1 1 0 1 0
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0 1 1 1 0 0 0 0 0 0 0 0
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1 0 1 0 1 0 0 0 0 0 0 0
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julia> # define lego
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julia> lego = Lego(stabilizers)
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Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")])
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julia> lego.stabgens |> checkmatrix
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CheckMatrix with 6 generators, 6 legs:
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0 0 1 1 1 1 | 0 0 0 0 0 0
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0 0 0 0 0 0 | 0 0 1 1 1 1
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0 0 0 0 0 0 | 1 0 1 1 0 0
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0 0 0 0 0 0 | 0 1 1 0 1 0
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0 1 1 1 0 0 | 0 0 0 0 0 0
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1 0 1 0 1 0 | 0 0 0 0 0 0
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</code></pre><ul><li><a href="pauliops/#QuantumLegos.PauliOps.pauliop-Tuple{AbstractString}"><code>pauliop</code></a></li><li><a href="checkmatrix/#QuantumLegos.checkmatrix"><code>checkmatrix</code></a> and <a href="checkmatrix/#QuantumLegos.CheckMatrix"><code>CheckMatrix</code></a></li><li><a href="#QuantumLegos.Lego"><code>Lego</code></a></li></ul><h2 id="Defining-and-Updating-State"><a class="docs-heading-anchor" href="#Defining-and-Updating-State">Defining and Updating State</a><a id="Defining-and-Updating-State-1"></a><a class="docs-heading-anchor-permalink" href="#Defining-and-Updating-State" title="Permalink"></a></h2><pre><code class="language-julia-repl hljs">julia> using QuantumLegos
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julia> stabilizers = pauliop.(["IIXXXX", "IIZZZZ", "ZIZZII", "IZZIZI", "IXXXII", "XIXIXI"])
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6-element Vector{StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}}:
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pauliop("IIXXXX")
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pauliop("IIZZZZ")
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pauliop("ZIZZII")
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pauliop("IZZIZI")
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pauliop("IXXXII")
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pauliop("XIXIXI")
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julia> lego = Lego(stabilizers)
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Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")])
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julia> # state with 1 lego, 0 leg
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julia> st = State([lego, ], Tuple{LegoLeg, LegoLeg}[])
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State(Lego[Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")])], Tuple{LegoLeg, LegoLeg}[], CheckMatrix(Bool[0 0 … 0 0; 0 0 … 1 1; … ; 0 1 … 0 0; 1 0 … 0 0], 6, 6))
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julia> st.cmat.cmat
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6×12 Matrix{Bool}:
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0 0 1 1 1 1 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 1 1 1 1
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0 0 0 0 0 0 1 0 1 1 0 0
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0 0 0 0 0 0 0 1 1 0 1 0
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0 1 1 1 0 0 0 0 0 0 0 0
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1 0 1 0 1 0 0 0 0 0 0 0
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julia> add_lego!(st, lego)
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State(Lego[Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")]), Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")])], Tuple{LegoLeg, LegoLeg}[], CheckMatrix(Bool[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], 12, 12))
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julia> st.cmat.cmat
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12×24 Matrix{Bool}:
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0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0
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0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0
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0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
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julia> # state with 2 legos, 0 leg
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julia> st2 = State([lego, lego], Tuple{LegoLeg, LegoLeg}[])
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State(Lego[Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")]), Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")])], Tuple{LegoLeg, LegoLeg}[], CheckMatrix(Bool[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], 12, 12))
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julia> st == st2
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true</code></pre><h2 id="2-Lego-1-edge-state"><a class="docs-heading-anchor" href="#2-Lego-1-edge-state">2 Lego 1 edge state</a><a id="2-Lego-1-edge-state-1"></a><a class="docs-heading-anchor-permalink" href="#2-Lego-1-edge-state" title="Permalink"></a></h2><pre><code class="language-julia-repl hljs">julia> using QuantumLegos
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julia> stabilizers = pauliop.(["IIXXXX", "IIZZZZ", "ZIZZII", "IZZIZI", "IXXXII", "XIXIXI"])
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6-element Vector{StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}}:
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pauliop("IIXXXX")
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pauliop("IIZZZZ")
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pauliop("ZIZZII")
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pauliop("IZZIZI")
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pauliop("IXXXII")
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pauliop("XIXIXI")
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julia> lego = Lego(stabilizers)
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Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")])
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julia> state = State([lego, lego], edge.([((1, 3), (2, 3))]))
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State(Lego[Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")]), Lego{6}(6, StaticArraysCore.SVector{6, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("IIXXXX"), pauliop("IIZZZZ"), pauliop("ZIZZII"), pauliop("IZZIZI"), pauliop("IXXXII"), pauliop("XIXIXI")])], Tuple{LegoLeg, LegoLeg}[(LegoLeg(1, 3), LegoLeg(2, 3))], CheckMatrix(Bool[1 0 … 0 0; 0 1 … 0 0; … ; 0 0 … 1 1; 0 0 … 0 1], 10, 10))
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julia> state.cmat
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CheckMatrix with 10 generators, 10 legs:
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1 0 1 0 1 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0
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0 1 0 1 1 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 1 0 1 0 1 | 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 1 0 1 1 | 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 | 1 0 0 1 1 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 1 1 1
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0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 0 0 1 1
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0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 1 0 1
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julia> pg = state.cmat |> generators |> GeneratedPauliGroup
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GeneratedPauliGroup{10}(StaticArraysCore.SVector{10, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("XIXIXIIIII"), pauliop("IXIXXIIIII"), pauliop("IIXXXIIXXX"), pauliop("IIIIIXIXIX"), pauliop("IIIIIIXIXX"), pauliop("ZIIZZIIIII"), pauliop("IZZIZIIIII"), pauliop("IIZZZIIZZZ"), pauliop("IIIIIZIIZZ"), pauliop("IIIIIIZZIZ")], IterTools.Subsets{Vector{StaticArraysCore.SVector{N, QuantumLegos.PauliOps.SinglePauliOp} where N}}(StaticArraysCore.SVector{N, QuantumLegos.PauliOps.SinglePauliOp} where N[pauliop("XIXIXIIIII"), pauliop("IXIXXIIIII"), pauliop("IIXXXIIXXX"), pauliop("IIIIIXIXIX"), pauliop("IIIIIIXIXX"), pauliop("ZIIZZIIIII"), pauliop("IZZIZIIIII"), pauliop("IIZZZIIZZZ"), pauliop("IIIIIZIIZZ"), pauliop("IIIIIIZZIZ")]))
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julia> pauliop("XIIXIXIIXI") in pg
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true
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</code></pre><h1 id="Internal(how-it-works)"><a class="docs-heading-anchor" href="#Internal(how-it-works)">Internal(how it works)</a><a id="Internal(how-it-works)-1"></a><a class="docs-heading-anchor-permalink" href="#Internal(how-it-works)" title="Permalink"></a></h1><h2 id="Notes-on-Overall-flow"><a class="docs-heading-anchor" href="#Notes-on-Overall-flow">Notes on Overall flow</a><a id="Notes-on-Overall-flow-1"></a><a class="docs-heading-anchor-permalink" href="#Notes-on-Overall-flow" title="Permalink"></a></h2><p>Details on <sup class="footnote-reference"><a id="citeref-1" href="#footnote-1">[1]</a></sup></p><ul><li>state is translated to a single check matrix<ul><li>the size is ≤ <span>$N \times 2N$</span> where <span>$N$</span> is maximum number of lego logs.</li></ul></li><li>any contraction can be performed on this single check matrix</li><li>if the check matrix can be represented as direct sum of matrices with <span>$k N$</span> columns where <span>$k ∈ ℕ$</span>, then they are not contracted</li></ul><h3 id="Construction-of-State"><a class="docs-heading-anchor" href="#Construction-of-State">Construction of State</a><a id="Construction-of-State-1"></a><a class="docs-heading-anchor-permalink" href="#Construction-of-State" title="Permalink"></a></h3><p>Construction of <code>State</code> is completed by calling <code>State</code> constructor recursively.</p><ol><li>Construct <code>State</code> without edge. Just adding legos. Checkmatrix is just a direct sum of each lego's checkmatrix</li><li>Concatenate each edges. During this operation, self tracing of checkmatrix is evaluated.</li></ol><p>Each constructor calls action function (which is a map from <code>State</code> to <code>State</code>). Therefore, action functions can be used both for direct construction of <code>State</code> and action application to <code>State</code> during the game.</p><h1 id="API"><a class="docs-heading-anchor" href="#API">API</a><a id="API-1"></a><a class="docs-heading-anchor-permalink" href="#API" title="Permalink"></a></h1><ul><li><a href="pauliops/#QuantumLegos.PauliOps"><code>QuantumLegos.PauliOps</code></a></li><li><a href="checkmatrix/#QuantumLegos.CheckMatrix"><code>QuantumLegos.CheckMatrix</code></a></li><li><a href="#QuantumLegos.Lego"><code>QuantumLegos.Lego</code></a></li><li><a href="#QuantumLegos.LegoLeg"><code>QuantumLegos.LegoLeg</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.GeneratedPauliGroup"><code>QuantumLegos.PauliOps.GeneratedPauliGroup</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.PauliOp"><code>QuantumLegos.PauliOps.PauliOp</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.SinglePauliOp"><code>QuantumLegos.PauliOps.SinglePauliOp</code></a></li><li><a href="#QuantumLegos.State"><code>QuantumLegos.State</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.pauliop-Tuple{AbstractString}"><code>QuantumLegos.PauliOps.pauliop</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.single_pauliop-Tuple{Char}"><code>QuantumLegos.PauliOps.single_pauliop</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.weight"><code>QuantumLegos.PauliOps.weight</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.xweight"><code>QuantumLegos.PauliOps.xweight</code></a></li><li><a href="pauliops/#QuantumLegos.PauliOps.zweight"><code>QuantumLegos.PauliOps.zweight</code></a></li><li><a href="#QuantumLegos._naive_distance-Tuple{State}"><code>QuantumLegos._naive_distance</code></a></li><li><a href="#QuantumLegos.add_edge!-Tuple{State, LegoLeg, LegoLeg}"><code>QuantumLegos.add_edge!</code></a></li><li><a href="#QuantumLegos.add_lego!-Tuple{State, Lego}"><code>QuantumLegos.add_lego!</code></a></li><li><a href="checkmatrix/#QuantumLegos.align_row!"><code>QuantumLegos.align_row!</code></a></li><li><a href="checkmatrix/#QuantumLegos.checkmatrix"><code>QuantumLegos.checkmatrix</code></a></li><li><a href="#QuantumLegos.cmat_index-Tuple{State, LegoLeg}"><code>QuantumLegos.cmat_index</code></a></li><li><a href="checkmatrix/#QuantumLegos.direct_sum"><code>QuantumLegos.direct_sum</code></a></li><li><a href="#QuantumLegos.distance-Tuple{State}"><code>QuantumLegos.distance</code></a></li><li><a href="#QuantumLegos.edge-Union{Tuple{T}, NTuple{4, T}} where T<:Integer"><code>QuantumLegos.edge</code></a></li><li><a href="#QuantumLegos.edge-Union{Tuple{Tuple{T, T}}, Tuple{T}} where T<:Tuple{Integer, Integer}"><code>QuantumLegos.edge</code></a></li><li><a href="#QuantumLegos.edge-Union{Tuple{NTuple{4, T}}, Tuple{T}} where T<:Integer"><code>QuantumLegos.edge</code></a></li><li><a href="#QuantumLegos.edge"><code>QuantumLegos.edge</code></a></li><li><a href="checkmatrix/#QuantumLegos.eliminate_column!"><code>QuantumLegos.eliminate_column!</code></a></li><li><a href="checkmatrix/#QuantumLegos.eliminate_dependent_row!"><code>QuantumLegos.eliminate_dependent_row!</code></a></li><li><a href="checkmatrix/#QuantumLegos.generators"><code>QuantumLegos.generators</code></a></li><li><a href="#QuantumLegos.is_connected_to_firstlego-Tuple{State}"><code>QuantumLegos.is_connected_to_firstlego</code></a></li><li><a href="checkmatrix/#QuantumLegos.ref!"><code>QuantumLegos.ref!</code></a></li><li><a href="checkmatrix/#QuantumLegos.self_trace!"><code>QuantumLegos.self_trace!</code></a></li><li><a href="checkmatrix/#QuantumLegos.xpart"><code>QuantumLegos.xpart</code></a></li><li><a href="checkmatrix/#QuantumLegos.zpart"><code>QuantumLegos.zpart</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.Lego" href="#QuantumLegos.Lego"><code>QuantumLegos.Lego</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Quantum lego with <code>N</code> legs.</p><p><strong>Fields</strong></p><ul><li><code>nlegs::Int64</code>: number of legs, equals <code>N</code></li><li><code>stabgens::SVector{N, PauliOp{N}}</code>: stabilizer generators. vector of <a href="pauliops/#QuantumLegos.PauliOps.PauliOp"><code>PauliOp</code></a></li></ul><p><strong>Constructor</strong></p><pre><code class="nohighlight hljs">Lego([nlegs::Integer], stabgens::AbstractVector{PauliOp{N}})</code></pre><p>Constructor for <a href="#QuantumLegos.Lego"><code>Lego</code></a>. <code>nlegs</code> is optional (default is length of the first stabilizer generator).</p><p><strong>Example</strong></p><pre><code class="language-julia-repl hljs">julia> stabgens = pauliop.(["II", "XX"])
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2-element Vector{StaticArraysCore.SVector{2, QuantumLegos.PauliOps.SinglePauliOp}}:
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pauliop("II")
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pauliop("XX")
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julia> Lego(stabgens)
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Lego{2}(2, StaticArraysCore.SVector{2, QuantumLegos.PauliOps.SinglePauliOp}[pauliop("II"), pauliop("XX")])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L8-L31">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.LegoLeg" href="#QuantumLegos.LegoLeg"><code>QuantumLegos.LegoLeg</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">mutable struct State</code></pre><p>To be used in <a href="#QuantumLegos.State"><code>State</code></a>.</p><p><strong>Fields</strong></p><ul><li><code>lego_id::Int64</code>: index in <code>legos</code> in <code>State</code></li><li><code>edge_id::Int64</code>: index in <code>Lego</code> in <code>legos</code> in <code>State</code>. No validation check included in <code>LegoLeg</code>.</li></ul><p><strong>Example</strong></p><pre><code class="language-julia-repl hljs">julia> x = LegoLeg.([(2, 1), (1, 1), (1, 0)])
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3-element Vector{LegoLeg}:
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LegoLeg(2, 1)
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LegoLeg(1, 1)
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LegoLeg(1, 0)
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julia> sort(x)
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3-element Vector{LegoLeg}:
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LegoLeg(1, 0)
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LegoLeg(1, 1)
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LegoLeg(2, 1)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L50-L73">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.State" href="#QuantumLegos.State"><code>QuantumLegos.State</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">mutable struct State</code></pre><p>State (in p.4)</p><p><strong>Fields</strong></p><ul><li><code>legos</code>: <code>Vector{Lego}</code></li><li><code>edges</code>: Vector of ((<code>lego_i, leg_n</code>), (<code>lego_j, leg_m</code>)). Each element is sorted (i.e. <code>lego_i < lego_j</code> or <code>lego_i == lego_j && leg_n < leg_m</code>). This feature is used in <a href="#QuantumLegos.is_connected_to_firstlego-Tuple{State}"><code>is_connected_to_firstlego</code></a>.</li><li><code>cmat::CheckMatrix</code>: CheckMatrix</li></ul><p><strong>Constructor</strong></p><pre><code class="nohighlight hljs">State(legos::Vector{Lego{N}}, edges::Vector{Tuple{LegoLeg, LegoLeg}})</code></pre><p><strong>Methods with</strong></p><ul><li><a href="#QuantumLegos.add_lego!-Tuple{State, Lego}"><code>add_lego!</code></a></li><li><a href="#QuantumLegos.add_edge!-Tuple{State, LegoLeg, LegoLeg}"><code>add_edge!</code></a></li></ul><p><strong>Example</strong></p><p>TODO</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L115-L136">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos._naive_distance-Tuple{State}" href="#QuantumLegos._naive_distance-Tuple{State}"><code>QuantumLegos._naive_distance</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Calculate distance. Use minimum distance of all generated normalizers.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L261-L264">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.add_edge!-Tuple{State, LegoLeg, LegoLeg}" href="#QuantumLegos.add_edge!-Tuple{State, LegoLeg, LegoLeg}"><code>QuantumLegos.add_edge!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">add_edge!(state::State, leg_1::LegoLeg, leg_2::LegoLeg)::State</code></pre><p>Add a new edge between <code>leg_1</code> and <code>leg_2</code>, updating <code>state</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L209-L213">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.add_lego!-Tuple{State, Lego}" href="#QuantumLegos.add_lego!-Tuple{State, Lego}"><code>QuantumLegos.add_lego!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">add_lego!(state::State, lego::Lego) -> State</code></pre><p>Add a new lego, updating <code>state</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L171-L175">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.cmat_index-Tuple{State, LegoLeg}" href="#QuantumLegos.cmat_index-Tuple{State, LegoLeg}"><code>QuantumLegos.cmat_index</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">cmat_index(state::State, leg::LegoLeg)::Int64</code></pre><p>Get column index corresponds to <code>leg</code> in check matrix of <code>state</code>. If given <code>leg</code> is already connected, it throws <code>ArgumentError</code>. If given <code>lego_id</code> of <code>leg</code> is out of <code>state.legos</code>, throws <code>ArgumentError</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L183-L189">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.distance-Tuple{State}" href="#QuantumLegos.distance-Tuple{State}"><code>QuantumLegos.distance</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">distance(state::State) -> Int</code></pre><p>Calculate code distance when the first leg of <code>state</code> is assigned as logical.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L253-L257">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.edge" href="#QuantumLegos.edge"><code>QuantumLegos.edge</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Helper function to create <code>Tuple{LegoLeg, LegoLeg}</code> to represent edge.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L81-L83">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.edge-Union{Tuple{NTuple{4, T}}, Tuple{T}} where T<:Integer" href="#QuantumLegos.edge-Union{Tuple{NTuple{4, T}}, Tuple{T}} where T<:Integer"><code>QuantumLegos.edge</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">edge(t::Tuple{T, T, T, T}) where {T <: Integer}</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L93-L95">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.edge-Union{Tuple{Tuple{T, T}}, Tuple{T}} where T<:Tuple{Integer, Integer}" href="#QuantumLegos.edge-Union{Tuple{Tuple{T, T}}, Tuple{T}} where T<:Tuple{Integer, Integer}"><code>QuantumLegos.edge</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">edge(t::Tuple{T, T}) where {T <: Tuple{Integer, Integer}}</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L86-L88">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.edge-Union{Tuple{T}, NTuple{4, T}} where T<:Integer" href="#QuantumLegos.edge-Union{Tuple{T}, NTuple{4, T}} where T<:Integer"><code>QuantumLegos.edge</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">edge(x::T, y::T, z::T, w::T) where {T <: Integer}</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L100-L102">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="QuantumLegos.is_connected_to_firstlego-Tuple{State}" href="#QuantumLegos.is_connected_to_firstlego-Tuple{State}"><code>QuantumLegos.is_connected_to_firstlego</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">is_connected_to_firstlego(state::State)::BitVector</code></pre><p>Returns vector which stores whether each lego is connected to the first lego.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/qwjyh/QuantumLegos.jl/blob/fda016f02dad2c2600c16e88335a3733b9e1c284/src/game.jl#L228-L232">source</a></section></article><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><a href="https://doi.org/10.1007/JHEP05(2021)127">C. Cao and B. Lackey, ‘Approximate Bacon-Shor code and holography’, J. High Energ. Phys., vol. 2021, no. 5, p. 127, May 2021, doi: 10.1007/JHEP05(2021)127.</a></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="pauliops/">PauliOps »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Tuesday 7 May 2024 02:53">Tuesday 7 May 2024</span>. 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