Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9705031 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Reliable quantum computers

John P. Preskill

Published Jan 8, 1998• 993 citations
arXivHTMLPDF

Abstract

The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 106 qubits, with a probability of error per quantum gate of order 10–6, would be a formidable factoring engine. Even a smaller less–accurate quantum computer would be able to perform many useful tasks. This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15 to 18 December 1996.

DOI
10.1098/rspa.1998.0167

Related papers

FAULT-TOLERANT QUANTUM COMPUTATION

John P. Preskill

The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.

arXiv:quant-ph/9712048•WORLD SCIENTIFIC eBooks•Oct 1, 1998•478 citations

Quantum computing: pro and con

John P. Preskill

I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault–tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high–precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfil their destiny as the world's fastest computing devices. This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, December 1996.

arXiv:quant-ph/9705032•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Jan 8, 1998•128 citations

Introduction to quantum fault tolerance

Panos Aliferis

One of the applications of quantum error correction is protecting quantum computers from noise. Certainly, there is nothing particularly quantum mechanical in the idea of protecting information by encoding it. Even ordinary digital computers use various fault tolerance methods at the software level to correct errors during the storage or the transmission of information; e.g., the integrity of the bits stored in hard disks is verified by using parity checks (checksums). In addition, for critical computing systems such as those inside airplanes or nuclear reactors, software fault tolerance methods are also applied during the processing of information; e.g., airplane control computers compare the results from multiple parallel processors to detect faults. In general, however, the hardware of modern computers is remarkably robust to noise, so that for most applications the processing of information can be executed with high reliability without using software error correction. In contrast to the ease and robustness with which classical information can be processed, the processing of quantum information appears at present to be much more challenging. Although constructing reliable quantum computing hardware is certainly a daunting task, we have nevertheless strong hopes that large-scale quantum computers, able to implement useful long computations, can in fact be realized. This optimism is founded on methods of quantum fault tolerance , which show that scalable quantum computation is, in principle, possible against a variety of noise processes.

Cambridge University Press eBooks•Sep 5, 2013•5 citations

Experimental Quantum Error Correction

Raymond Laflamme

The Achilles' heel of quantum information processors is the fragility of quantum states and processes. Without a method to control imperfection and imprecision of quantum devices, the probability that a quantum computation succeed will decrease exponentially in the number of gates it requires. In the last fifteen years, building on the discovery of quantum error correction, accuracy threshold theorems were proved showing that error can be controlled using a reasonable amount of resources as long as the error rate is smaller than a certain threshold. We thus have a scalable theory describing how to control quantum systems. The next step is to turn this theory into practice. I will give an overview of some of the progress towards the implmentation of quantum error correction around the world with a focus on results since the last Quantum Error Correction conference at USC. I will compare the various achievements and point towards what still need to be done to get robust quantum information processors.

APS•Feb 6, 2008•0 citations

Resilient Quantum Computation: Error Models and Thresholds

Knill, E H, Laflamme, R, Zurek, W H

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.

•Jan 1, 1997•287 citations

Resilient quantum computation: error models and thresholds

Emanuel Knill, Raymond Laflamme, Wojciech H. Zurek

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error–correction, fault–tolerant state recovery, fault–tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.

arXiv:quant-ph/9702058•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Jan 8, 1998•344 citations
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 106 qubits, with a probability of error per quantum gate of order 10–6, would be a formidable factoring engine. Even a smaller less–accurate quantum computer would be able to perform many useful tasks. This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15 to 18 December 1996.
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.
I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault–tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high–precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfil their destiny as the world's fastest computing devices. This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, December 1996.
One of the applications of quantum error correction is protecting quantum computers from noise. Certainly, there is nothing particularly quantum mechanical in the idea of protecting information by encoding it. Even ordinary digital computers use various fault tolerance methods at the software level to correct errors during the storage or the transmission of information; e.g., the integrity of the bits stored in hard disks is verified by using parity checks (checksums). In addition, for critical computing systems such as those inside airplanes or nuclear reactors, software fault tolerance methods are also applied during the processing of information; e.g., airplane control computers compare the results from multiple parallel processors to detect faults. In general, however, the hardware of modern computers is remarkably robust to noise, so that for most applications the processing of information can be executed with high reliability without using software error correction. In contrast to the ease and robustness with which classical information can be processed, the processing of quantum information appears at present to be much more challenging. Although constructing reliable quantum computing hardware is certainly a daunting task, we have nevertheless strong hopes that large-scale quantum computers, able to implement useful long computations, can in fact be realized. This optimism is founded on methods of quantum fault tolerance , which show that scalable quantum computation is, in principle, possible against a variety of noise processes.
The Achilles' heel of quantum information processors is the fragility of quantum states and processes. Without a method to control imperfection and imprecision of quantum devices, the probability that a quantum computation succeed will decrease exponentially in the number of gates it requires. In the last fifteen years, building on the discovery of quantum error correction, accuracy threshold theorems were proved showing that error can be controlled using a reasonable amount of resources as long as the error rate is smaller than a certain threshold. We thus have a scalable theory describing how to control quantum systems. The next step is to turn this theory into practice. I will give an overview of some of the progress towards the implmentation of quantum error correction around the world with a focus on results since the last Quantum Error Correction conference at USC. I will compare the various achievements and point towards what still need to be done to get robust quantum information processors.
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error–correction, fault–tolerant state recovery, fault–tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.