dorsal/arxiv
View SchemaRecognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates
| Authors | Vivek V. Shende, Stephen S. Bullock, Igor L. Markov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308045 |
| URL | https://arxiv.org/abs/quant-ph/0308045 |
| DOI | 10.1103/PhysRevA.70.012310 |
| Journal | Physical Review A 70, 012310 (2004) |
Abstract
This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-not (CNOT) gates and all other gates being one-qubit. We give an algorithm for synthesizing two-qubit circuits with optimal number of CNOT gates, and illustrate it on operators appearing in quantum algorithms by Deutsch-Josza, Shor and Grover. In another application, our explicit numerical tests allow timing a given Hamiltonian to compute a CNOT modulo one-qubit gates, when this is possible.
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"abstract": "This work proposes numerical tests which determine whether a two-qubit\noperator has an atypically simple quantum circuit. Specifically, we describe\nformulae, written in terms of matrix coefficients, characterizing operators\nimplementable with exactly zero, one, or two controlled-not (CNOT) gates and\nall other gates being one-qubit. We give an algorithm for synthesizing\ntwo-qubit circuits with optimal number of CNOT gates, and illustrate it on\noperators appearing in quantum algorithms by Deutsch-Josza, Shor and Grover. In\nanother application, our explicit numerical tests allow timing a given\nHamiltonian to compute a CNOT modulo one-qubit gates, when this is possible.",
"arxiv_id": "quant-ph/0308045",
"authors": [
"Vivek V. Shende",
"Stephen S. Bullock",
"Igor L. Markov"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.012310",
"journal_ref": "Physical Review A 70, 012310 (2004)",
"title": "Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates",
"url": "https://arxiv.org/abs/quant-ph/0308045"
},
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