# Fault-tolerant quantum computation with constant error

@inproceedings{Aharonov1997FaulttolerantQC,
title={Fault-tolerant quantum computation with constant error},
author={Dorit Aharonov and Michael Ben-Or},
booktitle={STOC '97},
year={1997}
}
• Published in STOC '97 14 November 1996
• Mathematics, Computer Science, Physics
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, q, is smaller than some constant threshold, q.. The cost is polylogarithmic in time and space, and no…
563 Citations
Fault-Tolerant Quantum Computation with Constant Error Rate
• Computer Science, Physics
SIAM J. Comput.
• 2008
This paper provides a self-contained and complete proof of universal fault-tolerant quantum computation in the presence of local noise, and shows that local noise is in principle not an obstacle for scalable quantum computation.
Novel Methods in Quantum Error Correction
This thesis proposes new schemes for universal fault-tolerant quantum computation in both the concatenated and topological code settings and presents a new class of private quantum channels, expanding the existing class beyond a seemingly fundamental restriction.
QUIC-97-004 A Theory of Fault-Tolerant Quantum Computation
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some
Ju l 2 00 0 Toward fault-tolerant quantum computation without concatenation
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold.
Thresholds for Universal Concatenated Quantum Codes.
• Computer Science, Medicine
Physical review letters
• 2016
It is shown that while the level-1 pseudothreshold for the concatenated scheme is limited by the logical Hadamard gate, the error suppression of the logical cnot gates allows for the asymptotic threshold to increase by orders of magnitude at higher levels.
New methods in quantum error correction and fault-tolerant quantum computing
A new decoding algorithm is proposed which can optimize threshold values of error correcting codes under different noise models and is shown that for certain noise models, logical Clifford corrections can further improve a code’s threshold value if the code obeys certain symmetries.
Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes
It is shown that transversal gates have a restricted form and prove that some important families of them cannot be quantum universal, strong evidence that so-called quantum software is necessary to achieve universality, and fault-tolerant quantum computer architecture is fundamentally different from classical computer architecture.
Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code
• Computer Science, Mathematics
Quantum Inf. Comput.
• 2012
This work provides two simplified circuits for fault-tolerant preparation of Golay code-encoded ancillas, reducing the overhead by roughly a factor of four compared to standard encoding circuits and proves a threshold above 1.32×10-3 noise per gate.
Efficient fault-tolerant quantum computing
• A. Steane
• Physics, Computer Science
Nature
• 1999
The recovery operation is adapted to simultaneously correct errors and perform a useful measurement that drives the computation, which means that the difficulty of realizing a useful quantum computer need be only an order of magnitude larger than the logic device contained within it.

## References

SHOWING 1-10 OF 80 REFERENCES
Theory of fault-tolerant quantum computation
In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a
Good quantum error-correcting codes exist.
• Physics, Medicine
Physical review. A, Atomic, molecular, and optical physics
• 1996
The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.
Polynomial simulations of decohered quantum computers
• Physics, Computer Science
Proceedings of 37th Conference on Foundations of Computer Science
• 1996
This work presents a simulation of decohered sequential quantum computers, on a classical probabilistic Turing machine, and proves that the expected slowdown of this simulation is polynomial in time and space of the quantum computation, for any non zero decoherence rate.
Quantum circuits with mixed states
• Mathematics, Computer Science
STOC '98
• 1998
A solution for the subroutine problem: the general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations.
Oracle Quantum Computing
• Mathematics
Workshop on Physics and Computation
• 1992
This paper continues the study of the power of oracles to separate quantum com.plexity classes from classical (including probabilistic and nondeterministic) complexity classes, which we initiated in
Threshold Accuracy for Quantum Computation
• Mathematics, Physics
• 1996
We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has error
Quantum Computers, Factoring, and Decoherence
• Computer Science, Physics
Science
• 1995
Here it is shown how the decoherence process degrades the interference pattern that emerges from the quantum factoring algorithm, a problem of practical significance for cryptographic applications.
Theory of quantum error-correcting codes
• Physics
• 1997
Quantum error correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of
Two-bit gates are universal for quantum computation.
• DiVincenzo
• Physics, Medicine
Physical review. A, Atomic, molecular, and optical physics
• 1995
A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The
Algorithms for quantum computation: discrete logarithms and factoring
• P. Shor
• Mathematics, Computer Science
Proceedings 35th Annual Symposium on Foundations of Computer Science
• 1994
Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.