dorsal/arxiv
View SchemaFault Tolerant Quantum Computation with Constant Error
| Authors | Dorit Aharonov, Michael Ben-Or |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9611025 |
| URL | https://arxiv.org/abs/quant-ph/9611025 |
Abstract
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than some constant threshold. The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. The result holds also for quantum circuits which operate on nearest neighbors only. To achieve this noise resistance, we use concatenated quantum error correcting codes. The scheme presented is general, and works with all quantum codes that satisfy some restrictions, namely that the code is ``proper''. We present two explicit classes of proper quantum codes. The first example of proper quantum codes generalizes classical secret sharing with polynomials. The second uses a known class of quantum codes and converts it to a proper code. This class is defined over a field with p elements, so the elementary quantum particle is not a qubit but a ``qupit''. With our codes, the threshold is about 10^(-6). Hopefully, this paper motivates a search for proper quantum codes with higher thresholds, at which point quantum computation becomes practical.
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"abstract": "Recently Shor showed how to perform fault tolerant quantum computation when\nthe error probability is logarithmically small. We improve this bound and\ndescribe fault tolerant quantum computation when the error probability is\nsmaller than some constant threshold. The cost is polylogarithmic in time and\nspace, and no measurements are used during the quantum computation. The result\nholds also for quantum circuits which operate on nearest neighbors only. To\nachieve this noise resistance, we use concatenated quantum error correcting\ncodes. The scheme presented is general, and works with all quantum codes that\nsatisfy some restrictions, namely that the code is ``proper\u0027\u0027.\n We present two explicit classes of proper quantum codes. The first example of\nproper quantum codes generalizes classical secret sharing with polynomials. The\nsecond uses a known class of quantum codes and converts it to a proper code.\nThis class is defined over a field with p elements, so the elementary quantum\nparticle is not a qubit but a ``qupit\u0027\u0027. With our codes, the threshold is about\n10^(-6). Hopefully, this paper motivates a search for proper quantum codes with\nhigher thresholds, at which point quantum computation becomes practical.",
"arxiv_id": "quant-ph/9611025",
"authors": [
"Dorit Aharonov",
"Michael Ben-Or"
],
"categories": [
"quant-ph"
],
"title": "Fault Tolerant Quantum Computation with Constant Error",
"url": "https://arxiv.org/abs/quant-ph/9611025"
},
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