Continuous quantum error correction for non-Markovian decoherence

TL;DR

This paper investigates how continuous quantum error correction affects non-Markovian decoherence, revealing a quadratic reduction in decoherence rate due to the Zeno effect, unlike the linear reduction in Markovian noise.

Contribution

It demonstrates that continuous error correction can significantly suppress non-Markovian decoherence through a quadratic scaling effect, highlighting the role of the Zeno regime.

Findings

Quadratic decrease in effective coupling constant with error correction rate

Difference between Markovian and non-Markovian decoherence suppression

Extension of results to general quantum error correction codes

Abstract

We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.