dorsal/arxiv
View SchemaSimplifying Quantum Circuits via Circuit Invariants and Dressed CNOTs
| Authors | Robert R. Tucci |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606061 |
| URL | https://arxiv.org/abs/quant-ph/0606061 |
Abstract
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary matrix into a SEO, and some of these decompositions have shorter length (are more efficient) than others. Finding an optimum (shortest) decomposition is a very hard task, and is not our intention here. A less ambitious, more doable task is to find methods for optimizing small segments of a SEO. Call these methods piecewise optimizations. Piecewise optimizations involve replacing a small quantum circuit by an equivalent one with fewer CNOTs. Two circuits are said to be equivalent if one of them multiplied by some external local operations equals the other. This equivalence relation between circuits has its own class functions, which we call circuit invariants. Dressed CNOTs are a simple yet very useful generalization of standard CNOTs. After discussing circuit invariants and dressed CNOTs, we give some methods for simplifying 2-qubit and 3-qubit circuits. We include with this paper software (written in Octave/Matlab) that checks many of the algorithms proposed in the paper.
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"abstract": "Quantum Compiling Algorithms decompose (exactly, without approximations) an\narbitrary $2^\\nb$ unitary matrix acting on $\\nb$ qubits, into a sequence of\nelementary operations (SEO). There are many possible ways of decomposing a\nunitary matrix into a SEO, and some of these decompositions have shorter length\n(are more efficient) than others. Finding an optimum (shortest) decomposition\nis a very hard task, and is not our intention here. A less ambitious, more\ndoable task is to find methods for optimizing small segments of a SEO. Call\nthese methods piecewise optimizations. Piecewise optimizations involve\nreplacing a small quantum circuit by an equivalent one with fewer CNOTs. Two\ncircuits are said to be equivalent if one of them multiplied by some external\nlocal operations equals the other. This equivalence relation between circuits\nhas its own class functions, which we call circuit invariants. Dressed CNOTs\nare a simple yet very useful generalization of standard CNOTs. After discussing\ncircuit invariants and dressed CNOTs, we give some methods for simplifying\n2-qubit and 3-qubit circuits. We include with this paper software (written in\nOctave/Matlab) that checks many of the algorithms proposed in the paper.",
"arxiv_id": "quant-ph/0606061",
"authors": [
"Robert R. Tucci"
],
"categories": [
"quant-ph"
],
"title": "Simplifying Quantum Circuits via Circuit Invariants and Dressed CNOTs",
"url": "https://arxiv.org/abs/quant-ph/0606061"
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