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Journal of Optics B Quantum and Semiclassical Optics

Coherence protection by random coding

E. Brion, V. M. Akulin, Ilya I. Dumer, G. Harel, Gershon Kurizki

Published Sep 21, 2005• 2 citations
Publisher

Abstract

We show that multidimensional Zeno effect combined with non-holonomic control allows to efficiently protect quantum systems from decoherence by a method similar to classical coding.Contrary to the conventional approach, our method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems.We also propose algorithms of finding encoding that approaches the Hamming upper bound along with methods of practical realizations of the encodings.Two new codes protecting 2 information qubits out of 7 and 4 information qubits out of 9 against a single error with arbitrarily small probability of failure are constructed as an example.

DOI
10.1088/1464-4266/7/10/022

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We show that multidimensional Zeno effect combined with non-holonomic control allows to efficiently protect quantum systems from decoherence by a method similar to classical coding.Contrary to the conventional approach, our method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems.We also propose algorithms of finding encoding that approaches the Hamming upper bound along with methods of practical realizations of the encodings.Two new codes protecting 2 information qubits out of 7 and 4 information qubits out of 9 against a single error with arbitrarily small probability of failure are constructed as an example.
We show that multidimensional Zeno effect allows one to efficiently protect quantum systems from coherence loss by a method similar to classical coding. Contrary to the conventional approach, our method is applicable to arbitrary error-induced Hamiltonians and general quantum systems. We propose algorithms for finding the coherence-protecting codes along with a method of practical encoding by non-holonomic control. Two new single-error–correcting codes are constructed that surpass the bounds valid for classical quantum codes.
Within quantum information, many methods have been proposed to avoid or correct the deleterious effects of the environment on a system of interest. In this work, expanding on our earlier paper (Paz-Silva et al 2012 Phys. Rev. Lett. 108 080501), we evaluate the applicability of the quantum Zeno effect as one such method. Using the algebraic structure of stabilizer quantum error correction codes as a unifying framework, two open-loop protocols are described which involve frequent non-projective (i.e. weak) measurement of either the full stabilizer group or a minimal generating set thereof. The effectiveness of the protocols is measured by the distance between the final state under the protocol and the final state of an idealized evolution in which system and environment do not interact. Rigorous bounds on this metric are derived which demonstrate that, under certain assumptions, a Zeno effect may be realized with arbitrarily weak measurements, and that this effect can protect an arbitrary, unknown encoded state against the environment arbitrarily well.
Within quantum information, many methods have been proposed to avoid or correct the deleterious effects of the environment on a system of interest. In this work, expanding on our earlier paper (Paz-Silva et al 2012 Phys. Rev. Lett. 108 080501), we evaluate the applicability of the quantum Zeno effect as one such method. Using the algebraic structure of stabilizer quantum error correction codes as a unifying framework, two open-loop protocols are described which involve frequent non-projective (i.e. weak) measurement of either the full stabilizer group or a minimal generating set thereof. The effectiveness of the protocols is measured by the distance between the final state under the protocol and the final state of an idealized evolution in which system and environment do not interact. Rigorous bounds on this metric are derived which demonstrate that, under certain assumptions, a Zeno effect may be realized with arbitrarily weak measurements, and that this effect can protect an arbitrary, unknown encoded state against the environment arbitrarily well.