dorsal/arxiv
View SchemaParallel Quantum Computation and Quantum Codes
| Authors | Cristopher Moore, Martin Nilsson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9808027 |
| URL | https://arxiv.org/abs/quant-ph/9808027 |
Abstract
We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or more generally any circuit consisting of controlled-not gates, controlled pi-shifts, and Hadamard gates. Finally, while we note the Quantum Fourier Transform can be parallelized to linear depth, we conjecture that an even simpler `staircase' circuit cannot be parallelized to less than linear depth, and might be used to prove that QNC < QP.
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"abstract": "We propose a definition of QNC, the quantum analog of the efficient parallel\nclass NC. We exhibit several useful gadgets and prove that various classes of\ncircuits can be parallelized to logarithmic depth, including circuits for\nencoding and decoding standard quantum error-correcting codes, or more\ngenerally any circuit consisting of controlled-not gates, controlled pi-shifts,\nand Hadamard gates. Finally, while we note the Quantum Fourier Transform can be\nparallelized to linear depth, we conjecture that an even simpler `staircase\u0027\ncircuit cannot be parallelized to less than linear depth, and might be used to\nprove that QNC \u003c QP.",
"arxiv_id": "quant-ph/9808027",
"authors": [
"Cristopher Moore",
"Martin Nilsson"
],
"categories": [
"quant-ph",
"math.QA"
],
"title": "Parallel Quantum Computation and Quantum Codes",
"url": "https://arxiv.org/abs/quant-ph/9808027"
},
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