dorsal/arxiv
View SchemaFault-Tolerant Quantum Computation With Constant Error Rate
| Authors | Dorit Aharonov, Michael Ben-Or |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906129 |
| URL | https://arxiv.org/abs/quant-ph/9906129 |
Abstract
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very general, not necessarily probabilistic noise model, for quantum particles with any number of states, and is also generalized to one dimensional quantum computers with only nearest neighbor interactions. No measurements, or classical operations, are required during the quantum computation. The proceeding version was very succinct, and here we fill all the missing details, and elaborate on many parts of the proof. In particular, we devote a section for a discussion of universality issues and proofs that the sets of gates that we use are universal. Another section is devoted to a rigorous proof that fault tolerance can be achieved in the presence of general non probabilistic noise. The systematic structure of the fault tolerant procedures for polynomial codes is explained in length. The proof that the concatenation scheme works is written in a clearer way. The paper also contains new and significantly simpler proofs for most of the known results which we use. For example, we give a simple proof that it suffices to correct bit and phase flips, we significantly simplify Calderbank and Shor's original proof of the correctness of CSS codes. We also give a simple proof of the fact that two-qubit gates are universal. The paper thus provides a self contained and complete proof for universal fault tolerant quantum computation.
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"abstract": "This paper proves the threshold result, which asserts that quantum\ncomputation can be made robust against errors and inaccuracies, when the error\nrate, $\\eta$, is smaller than a constant threshold, $\\eta_c$. The result holds\nfor a very general, not necessarily probabilistic noise model, for quantum\nparticles with any number of states, and is also generalized to one dimensional\nquantum computers with only nearest neighbor interactions. No measurements, or\nclassical operations, are required during the quantum computation. The\nproceeding version was very succinct, and here we fill all the missing details,\nand elaborate on many parts of the proof. In particular, we devote a section\nfor a discussion of universality issues and proofs that the sets of gates that\nwe use are universal. Another section is devoted to a rigorous proof that fault\ntolerance can be achieved in the presence of general non probabilistic noise.\nThe systematic structure of the fault tolerant procedures for polynomial codes\nis explained in length. The proof that the concatenation scheme works is\nwritten in a clearer way. The paper also contains new and significantly simpler\nproofs for most of the known results which we use. For example, we give a\nsimple proof that it suffices to correct bit and phase flips, we significantly\nsimplify Calderbank and Shor\u0027s original proof of the correctness of CSS codes.\nWe also give a simple proof of the fact that two-qubit gates are universal. The\npaper thus provides a self contained and complete proof for universal fault\ntolerant quantum computation.",
"arxiv_id": "quant-ph/9906129",
"authors": [
"Dorit Aharonov",
"Michael Ben-Or"
],
"categories": [
"quant-ph"
],
"title": "Fault-Tolerant Quantum Computation With Constant Error Rate",
"url": "https://arxiv.org/abs/quant-ph/9906129"
},
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