Analysis of the quantum Zeno effect for quantum control and computation

TL;DR

This paper investigates the quantum Zeno effect as a method for quantum control and error correction, demonstrating that weak measurements can effectively protect quantum states from environmental decoherence.

Contribution

It introduces open-loop protocols using stabilizer codes and derives bounds showing weak measurements can realize the Zeno effect for quantum state protection.

Findings

Weak measurements can induce the quantum Zeno effect.

Protocols can protect arbitrary quantum states against environment.

Rigorous bounds demonstrate effectiveness under certain conditions.

Abstract

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 [G. A. Paz-Silva et al., Phys. Rev. Lett. 108, 080501 (2012), arXiv:1104.5507], 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.