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arXiv:quant-ph/0507158 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Non-holonomic control III: coherence protection by the quantum zeno effect and non-holonomic control

E. Brion, V. M. Akulin, D. Comparat, Ilya I. Dumer, V. Gershkovich, G. Harel, G. Kurizki, I. E. Mazets, P. Pillet

Published Jun 1, 2005• 0 citations
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Abstract

In this paper, we present a coherence protection method based upon a multidimensional generalization of the Quantum Zeno Effect, as well as ideas from the coding theory. The non-holonomic control technique is employed as a physical tool which allows its effective implementation. The two limiting cases of small and large quantum systems are considered.

DOI
10.1117/12.620468

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In this paper, we present a coherence protection method based upon a multidimensional generalization of the Quantum Zeno Effect, as well as ideas from the coding theory. The non-holonomic control technique is employed as a physical tool which allows its effective implementation. The two limiting cases of small and large quantum systems are considered.
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.
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.
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error correction (ancilla adding, coding and decoding) and the quantum Zeno effect. A demonstration of our method on a simple atomic system---namely, a rubidium isotope---is proposed.
The quantum Zeno effect is a distinctive phenomenon in quantum mechanics, describing the nontrivial effect of frequent projective measurements on hindering the evolution of a quantum system. However, when subjected to environmental noise, the quantum system may dissipate, and the quantum Zeno effect no longer works. This research starts from the physical mechanism for the decay of the quantum Zeno effect in the presence of noise and investigates the effect of coherent quantum controls on mitigating the decrease of the survival probability that the system stays in the initial state induced by the noise. We derive the decay rate of the survival probability with and without coherent quantum controls in general, and show that when the frequency of the projective measurements is large but finite, proper coherent controls by sufficiently strong Hamiltonians can be designed to decrease the decay rate of the survival probability. A two-level quantum system suffering from typical unitary and nonunitary noise is then considered to demonstrate the effect of the proposed coherent quantum control scheme in protecting the quantum Zeno effect against the noise. The decay rate of the survival probability is obtained in the presence of noise, and the control Hamiltonian is further optimized analytically to minimize the decay rate by a variational approach. The evolution paths of the quantum system with the optimal coherent controls are illustrated numerically for different scenarios to explicitly show how the coherent control scheme works in lowering the decay of survival probability.