Reliable Quantum Computers

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 10^6 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, 15-18 December 1996.)

24 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor corrections

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• A Theory of Fault-Tolerant Quantum Computation
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• Continuous Error Correction
• Parity Cross-Resonance: A Multiqubit Gate
• High fidelity universal set of quantum gates using non-adiabatic rapid passage
• On the query complexity of unitary channel certification
• Quantum Learning Algorithms and Post-Quantum Cryptography
• Error suppression in Hamiltonian based quantum computation using energy penalties
• Comparison of spin-qubit architectures for quantum error-correcting codes
• Practical implementation of Toffoli-based qubit rotation
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation
• Open n-Qubit System as a Quantum Computer with Four-Valued Logic
• A Theory of Physical Quantum Computation: The Quantum Computer Condition
• Operator Imprecision and Scaling of Shor's Algorithm