The DOI matches its Crossref record; 61 of the 61 references it cites were found in a registry or an index.
Fault-tolerant quantum computation with constant error
Open accessAbstract
In the past year many developments have taken place in the area of quantum error corrections. Recently Shor showed how to perform fault tolerant quantum computation when, , the probability for a fault in one time step per qubit or per gate, is polylogarithmically small. This paper closes the gap and shows how to perform fault tolerant quantum computation when the error probability, , is smaller than some constant threshold, 0 . The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. The same result is shown also for quantum circuits which operate on nearest neighbors only.
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In the citing paper
“First, the choice to work with circuits which allow parallelism is necessary, because sequential quantum computation, such as quantum Turing machines, cannot be noise resistant[3], since error corrections cannot be applied fast enough to prevent accumulation of errors.”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [3]
In the citing paper
“In a previous paper, we have shown that quantum systems can be simulated efficiently by a classical Turing machine if the noise is large[3].”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [3]
In the citing paper
“In [3] it was shown that for a very high noise rate, the quantum circuit behaves in a classical way.”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [3]
In the citing paper
“Second, by considering more favorable schemes for Hamiltonian decomposition 256,257 , most modern-day simulation algorithms scale in terms of τ max = t ‖ H ‖ max instead of τ , where ‖ H ‖ max is the absolute value of the largest entry of H as a matrix in the computational basis.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [256]
In the citing paper
“In fact, arbitrarily large quantum computations can be performed with arbitrary accuracy, provided the error level of the elementary components of the quantum computer is below a certain threshold. This important result is called the threshold theorem of quantum computation 59-62”
From Measurement-based quantum computation (2009) · cites this paper as [60]
Citations
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Metadata
- Authors
- Aharonov, D., & Ben-Or, M.
- Affiliations
- Hebrew University of Jerusalem (IL)
- Venue
- Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97
- Publisher
- ACM Press
- Published
- 1997
- Pages
- 176-188
- OpenAlex
- W2052169397
- Cited by
- 631
- References
- 61
- Citations by year
- 2026: 25 · 2025: 44 · 2024: 29 · 2023: 18 · 2022: 17 · 2021: 26 · 2020: 29 · 2019: 21 · 2018: 18 · 2017: 19 · 2016: 19 · 2015: 23 · 2014: 19 · 2013: 16 · 2012: 20
- FWCI
- 16.52
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- ACM Symposium on Theory of Computing (STOC) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
- Keywords
- fault-tolerant quantum computing, quantum error correction, concatenated quantum codes, secret sharing
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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