https://pennylane.ai/component---src-templates-glossary-glossary-t…swap-gate-index-mdx-c3c0c0c436442142aa01.js

1"use strict";
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3(self.webpackChunkpennylane_website=self.webpackChunkpennylane_website||[]).push([[8062],{211:function(e,t,a){a.r(t),a.d(t,{Head:function(){return v},default:function(){return y}});var n=a(2784),s=a(45392);function l(e){const t=Object.assign({p:"p",strong:"strong",hr:"hr",div:"div",em:"em",a:"a",code:"code"},(0,s.ah)(),e.components);return n.createElement(n.Fragment,null,n.createElement(t.p,null,"The ",n.createElement(t.strong,null,"SWAP gate")," is a gate in quantum computing that swaps the states of two qubits."),"\n",n.createElement(t.hr),"\n",n.createElement(t.p,null,"The diagram below shows how a SWAP gate is represented in quantum circuits."),"\n",n.createElement(t.p,null,n.createElement(t.div,{dangerouslySetInnerHTML:{__html:'<span\n      class="gatsby-resp-image-wrapper"\n      style="position: relative; display: block; margin-left: auto; margin-right: auto; max-width: 630px; "\n    >

3\n      <span\n    class="gatsby-resp-image-background-image"\n    style="padding-bottom: 45.56962025316456%; position: relative; bottom: 0; left: 0; background-image: url(\'data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAJCAYAAAAywQxIAAAACXBIWXMAABJ0AAASdAHeZh94AAAAnUlEQVQoz51SSQoEIQzs/3/Tkyh6cMclQ8lkcLbGbiEklCapSjzoecYYdOd85h0r2HunlNL0wODZaq3TVozz4Dl+KxhCICEElVKotUY552kopJQia+2Mcc/4z4I7klEErC5JZpncce3MrFdGfyXvMGR5lxgiCXNieesigDvnvvDTpWDDUsrX0L3302KMpLUmY8yMsTzgeHdb8u4/fAD7Gcg5mAbXpQAAAABJRU5ErkJggg==\'); background-size: cover; display: block;"\n  ></span>\n  <img\n        class="gatsby-resp-image-image"\n        alt="swap-gate-symbol"\n        title="swap-gate-symbol"\n        src="/static/bd19562d24111b3b6b83cfdd9955b5a9/f058b/swap-gate-symbol.png"\n        srcset="/static/bd19562d24111b3b6b83cfdd9955b5a9/c26ae/swap-gate-symbol.png 158w,\n/static/bd19562d24111b3b6b83cfdd9955b5a9/6bdcf/swap-gate-symbol.png 315w,\n/static/bd19562d24111b3b6b83cfdd9955b5a9/f058b/swap-gate-symbol.png 630w,\n/static/bd19562d24111b3b6b83cfdd9955b5a9/e1031/swap-gate-symbol.png 803w"\n        sizes="(max-width: 630px) 100vw, 630px"\n        style="width:100%;height:100%;margin:0;vertical-align:middle;position:absolute;top:0;left:0;"\n        loading="lazy"\n        decoding="async"\n      />\n    </span>'}})),"\n",n.createElement(t.p,null,"It can also be represented as"),"\n",n.createElement(t.p,null,n.createElement(t.div,{dangerouslySetInnerHTML:{__html:'<span\n      class="gatsby-resp-image-wrapper"\n      style="position: relative; display: block; margin-left: auto; margin-right: auto; max-width: 630px; "\n    >

3\n      <span\n    class="gatsby-resp-image-background-image"\n    style="padding-bottom: 42.405063291139236%; position: relative; bottom: 0; left: 0; background-image: url(\'data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAICAYAAAD5nd/tAAAACXBIWXMAABJ0AAASdAHeZh94AAAAkUlEQVQoz4VR2w4FEQz0/3/KGyHuuhlJpWs5Z5JJaWv0osYYBAK1VmqtzXvv/WUZtxhbJZO11uScm6I558UY43wAP84yBt9LUP58Ax6llJbwDulTsmU+7wRQOQRPeZ8K9xntwGy5Qsztb4UMYwxZa6mUQt57CiEsAhCTPhCfHZcCi6DcIPO05T12bfkGOa9fLT9CmXlnLLzR1AAAAABJRU5ErkJggg==\'); background-size: cover; display: block;"\n  ></span>\n  <img\n        class="gatsby-resp-image-image"\n        alt="swap-gate-alternate-symbol"\n        title="swap-gate-alternate-symbol"\n        src="/static/e44243c3f1f478400b899708afe2397f/f058b/swap-gate-alternate-symbol.png"\n        srcset="/static/e44243c3f1f478400b899708afe2397f/c26ae/swap-gate-alternate-symbol.png 158w,\n/static/e44243c3f1f478400b899708afe2397f/6bdcf/swap-gate-alternate-symbol.png 315w,\n/static/e44243c3f1f478400b899708afe2397f/f058b/swap-gate-alternate-symbol.png 630w,\n/static/e44243c3f1f478400b899708afe2397f/8b69f/swap-gate-alternate-symbol.png 912w"\n        sizes="(max-width: 630px) 100vw, 630px"\n        style="width:100%;height:100%;margin:0;vertical-align:middle;position:absolute;top:0;left:0;"\n        loading="lazy"\n        decoding="async"\n      />\n    </span>'}})),"\n",n.createElement(t.p,null,"The SWAP gate can be decomposed into three CNOT gates, as shown below."),"\n",n.createElement(t.p,null,n.createElement(t.div,{dangerouslySetInnerHTML:{__html:'<span\n      class="gatsby-resp-image-wrapper"\n      style="position: relative; display: block; margin-left: auto; margin-right: auto; max-width: 630px; "\n    >

3\n      <span\n    class="gatsby-resp-image-background-image"\n    style="padding-bottom: 44.30379746835443%; position: relative; bottom: 0; left: 0; background-image: url(\'data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAJCAYAAAAywQxIAAAACXBIWXMAABJ0AAASdAHeZh94AAAAzUlEQVQoz51SSQqEQAz0/3dvvsGrf/DqH8QFFNxo1xqqINIzo8ygEFLdSSqVtAEAHMche/r5tYF/2LZNZg3mecY4jorRT9MkPAwDlmV5E2L+JNz3HUVRKHldV92laYooioSrqkJd18JhGCLLMmESXxJejeycOxWykY+p/nZkn9Q/s7spIIFhepvia+Q7dZ8KSWAkPxXaDsuyRNd1SuYDcKd5nqsgjmMkSaI83jGXOUZ8uUMG+cosolFd3/eKNU2Dtm2F2ZRklvf3yE/+wxdIZ8FnttcypAAAAABJRU5ErkJggg==\'); background-size: cover; display: block;"\n  ></span>\n  <img\n        class="gatsby-resp-image-image"\n        alt="making-a-swap-gate-from-cnot-gates"\n        title="making-a-swap-gate-from-cnot-gates"\n        src="/static/51a7a86b53b9abf0d6ba8827c2402108/f058b/making-a-swap-gate-from-cnot-gates.png"\n        srcset="/static/51a7a86b53b9abf0d6ba8827c2402108/c26ae/making-a-swap-gate-from-cnot-gates.png 158w,\n/static/51a7a86b53b9abf0d6ba8827c2402108/6bdcf/making-a-swap-gate-from-cnot-gates.png 315w,\n/static/51a7a86b53b9abf0d6ba8827c2402108/f058b/making-a-swap-gate-from-cnot-gates.png 630w,\n/static/51a7a86b53b9abf0d6ba8827c2402108/6029f/making-a-swap-gate-from-cnot-gates.png 906w"\n        sizes="(max-width: 630px) 100vw, 630px"\n        style="width:100%;height:100%;margin:0;vertical-align:middle;position:absolute;top:0;left:0;"\n        loading="lazy"\n        decoding="async"\n      />\n    </span>'}})),"\n",n.createElement(t.p,null,"Thus, the SWAP gate can be thought of as a convenient shorthand for this sequence of CNOT gates."),"\n",n.createElement(t.p,null,"Mathematically, the SWAP gate's action on a quantum state is"),"\n",n.createElement(t.p,null,"$$\n\\text{SWAP} (|\\phi_{1}\\rangle \\otimes |\\phi_{2}\\rangle) = |\\phi_{2}\\rangle \\otimes |\\phi_{1}\\rangle.\n$$"),"\n",n.createElement(t.p,null,"The SWAP gate can be represented in matrix form as"),"\n",n.createElement(t.p,null,"$$\n\\text{SWAP} \\equiv \\left[ \\begin{matrix}1 & 0 & 0 & 0 \\\\ 0 & 0 & 1 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\end{matrix} \\right].\n$$"),"\n",n.createElement(t.p,null,"The SWAP gate is extremely useful in hardware settings; if two qubits are not physically connected, we can simply ",n.createElement(t.em,null,"swap")," one of those qubits with another that ",n.createElement(t.em,null,"is")," physically connected to the other qubit. The SWAP gate may also appear as a necessary part in building the quantum Fourier transform or in other routines such as the SWAP test."),"\n",n.createElement(t.p,null,"The ",n.createElement(t.a,{href:"https://docs.pennylane.ai/en/stable/code/api/pennylane.SWAP.html"},"SWAP gate in PennyLane")," is available as ",n.createElement(t.code,null,"qml.SWAP"),". This gate is called ",n.createElement(t.a,{href:"https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.SwapGate"},n.createElement(t.code,null,"SwapGate")," in Qiskit"),"."))}var i=function(e){void 0===e&&(e={});const{wrapper:t}=Object.assign({},(0,s.ah)(),e.components);return t?n.createElement(t,e,n.createElement(l,e)):l(e)},o=a(56694),r=a(82256),c=a(28546),g=a(2409),m=a(76741),p=a(9619),d=a(86165),b=a(95692),A=a(19948),u=a(45051),h=a(52322);const f={Notes:d.Z,Footnotes:g.Z,MarkdownText:p.Z,PermaLink:A.Z,a:m.Z,p:b.Z};function w(e){let{data:t,children:a}=e;const{mdx:n}=t,l=null==n?void 0:n.frontmatter,i=null==n?void 0:n.tableOfContents;return(0,h.jsxs)(h.Fragment,{children:[(0,h.jsx)(o.Z,{pageTitle:(null==l?void 0:l.title)||""}),(0,h.jsx)(c.Z,{mainSection:(0,h.jsxs)("section",{className:"glossary-item-container w-[830px]",children:[(null==l?void 0:l.title)&&(0,h.jsxs)("h1",{children:[l.title," ",(0,h.jsx)(A.Z,{title:l.title})]}),(0,h.jsx)(s.Zo,{components:f,children:a})]}),sidebarSection:null!=i&&i.items&&i.items instanceof Array&&i.items.length>0?(0,h.jsx)(r.Z,{linksList:null==i?void 0:i.items,contentTitle:"Glossary"}):void 0})]})}function y(e){return n.createElement(w,e,n.createElement(i,e))}const v=e=>{var t,a,n,s,l,i,o,r,c,g;let{data:m}=e;return(0,h.jsx)(u.Z,{title:null!==(t=m.mdx)&&void 0!==t&&null!==(a=t.frontmatter)&&void 0!==a&&a.meta_title?m.mdx.frontmatter.meta_title:(null===(n=m.mdx)||void 0===n||null===(s=n.frontmatter)||void 0===s?void 0:s.title)||"",image:(null===(l=m.mdx)||void 0===l||null===(i=l.frontmatter)||void 0===i?void 0:i.meta_image)||"",description:(null===(o=m.mdx)||void 0===o||null===(r=o.frontmatter)||void 0===r?void 0:r.meta_description)||"",pathname:"/glossary/"+(null===(c=m.mdx)||void 0===c||null===(g=c.frontmatter)||void 0===g?void 0:g.slug)})}}}]);
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