STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Can complex structures be generically stable in a noisy world?
IBM Journal of Research and Development
Fault-Tolerant Quantum Computation with Constant Error Rate
SIAM Journal on Computing
The capacity of the quantum depolarizing channel
IEEE Transactions on Information Theory
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The ability to protect quantum information from the effect of noise is one of the majorgoals of quantum information processing. In this article, we study limitations on theasymptotic stability of quantum information stored in passive N-qubit systems. Weconsider the effect of small imperfections in the implementation of the protecting Hamil-tonian in the form of perturbations or weak coupling to a ground state environment.We thus depart from the usual Markovian approximation for a thermal bath by concen-trating on models for which part of the evolution can be calculated exactly. We provethat, regardless of the protecting Hamiltonian, there exists a perturbed evolution thatnecessitates a final error correcting step for the state of the memory to be read. Suchan error correction step is shown to require a finite error threshold, the lack thereofbeing exemplified by the 3D XZ-compass model [1]. We go on to present explicit weakHamiltonian perturbations which destroy the logical information stored in the 2D toriccode in a time O(log(N)).