dorsal/arxiv
View SchemaQuantum Compiling with Approximation of Multiplexors
| Authors | Robert R. Tucci |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412072 |
| URL | https://arxiv.org/abs/quant-ph/0412072 |
Abstract
A quantum compiling algorithm is an algorithm for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose $U_{in}$ is an $\nb$-bit unstructured unitary matrix (a unitary matrix with no special symmetries) that we wish to compile. For $\nb>10$, expressing $U_{in}$ as a SEO requires more than a million CNOTs. This calls for a method for finding a unitary matrix that: (1)approximates $U_{in}$ well, and (2) is expressible with fewer CNOTs than $U_{in}$. The purpose of this paper is to propose one such approximation method. Various quantum compiling algorithms have been proposed in the literature that decompose an arbitrary unitary matrix into a sequence of U(2)-multiplexors, each of which is then decomposed into a SEO. Our strategy for approximating $U_{in}$ is to approximate these intermediate U(2)-multiplexors. In this paper, we will show how one can approximate a U(2)-multiplexor by another U(2)-multiplexor that is expressible with fewer CNOTs.
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"abstract": "A quantum compiling algorithm is an algorithm for decomposing (\"compiling\")\nan arbitrary unitary matrix into a sequence of elementary operations (SEO).\nSuppose $U_{in}$ is an $\\nb$-bit unstructured unitary matrix (a unitary matrix\nwith no special symmetries) that we wish to compile. For $\\nb\u003e10$, expressing\n$U_{in}$ as a SEO requires more than a million CNOTs. This calls for a method\nfor finding a unitary matrix that: (1)approximates $U_{in}$ well, and (2) is\nexpressible with fewer CNOTs than $U_{in}$. The purpose of this paper is to\npropose one such approximation method. Various quantum compiling algorithms\nhave been proposed in the literature that decompose an arbitrary unitary matrix\ninto a sequence of U(2)-multiplexors, each of which is then decomposed into a\nSEO. Our strategy for approximating $U_{in}$ is to approximate these\nintermediate U(2)-multiplexors. In this paper, we will show how one can\napproximate a U(2)-multiplexor by another U(2)-multiplexor that is expressible\nwith fewer CNOTs.",
"arxiv_id": "quant-ph/0412072",
"authors": [
"Robert R. Tucci"
],
"categories": [
"quant-ph"
],
"title": "Quantum Compiling with Approximation of Multiplexors",
"url": "https://arxiv.org/abs/quant-ph/0412072"
},
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