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arXiv:quant-ph/0411008

Quantum error correction fails for Hamiltonian models

Robert Alicki

Published Nov 1, 2004• 7 citations
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Abstract

It is argued that the existing schemes of fault-tolerant quantum computation designed for discrete-time models and based on quantum error correction fail for continuous-time Hamiltonian models even with Markovian noise.
DOI
10.48550/arxiv.quant-ph/0411008

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One reason why building large-scale quantum computers will be particularly challenging is that quantum computers are far more susceptible to making errors than conventional digital computers. I will explain the principles of quantum error correction and fault-tolerant quantum computation, which can enable a properly designed quantum computer with imperfect components to achieve good reliability. Some recent developments in the theory of quantum fault tolerance will be reviewed, including quantum error-correcting codes for systems described by continuous quantum variables, robust storage of quantum information based on topological principles, and applications of quantum error-correcting codes to quantum cryptography.
Abstract As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design, test, and optimize fault-tolerant protocols tailored to the noise processes of the hardware. Our argument is essentially a critical analysis of the current methods envisioned to optimize fault-tolerant schemes, which rely on hardware characterization, noise modeling, and numerical simulations. We show that, even within a very restricted set of noise models, error-correction protocols depend strongly on the details of the noise model. Combined to the intrinsic difficulty of hardware characterization and of numerical simulations of fault-tolerant protocols, we arrive at the conclusion that the currently envisioned optimization cycle is of very limited scope. On the other hand, the direct characterization of a fault-tolerant scheme on a small quantum computer bypasses these difficulties, and could provide a bootstrapping path to full-scale fault-tolerant quantum computation.