Relaxation times do not capture logical qubit dynamics

TL;DR

This paper demonstrates that traditional relaxation times are inadequate for characterizing logical qubit dynamics, emphasizing the need for new observables to understand their behavior under spatially correlated noise.

Contribution

The work introduces a new framework using specific observables to effectively track and characterize logical qubit dynamics, surpassing the limitations of relaxation times.

Findings

Relaxation times do not reflect logical qubit behavior.

Spatial noise correlations cause complex logical qubit dynamics.

New observables effectively characterize logical qubit evolution.

Abstract

Quantum error correction procedures have the potential to enable faithful operation of large-scale quantum computers. They protect information from environmental decoherence by storing it in logical qubits, built from ensembles of entangled physical qubits according to suitably tailored quantum error correcting encodings. To date, no generally accepted framework to characterise the behaviour of logical qubits as quantum memories has been developed. In this work, we show that generalisations of well-established figures of merit of physical qubits, such as relaxation times, to logical qubits fail and do not capture dynamics of logical qubits. We experimentally illustrate that, in particular, spatial noise correlations can give rise to rich and counter-intuitive dynamical behavior of logical qubits. We show that a suitable set of observables, formed by code space population and logical operators within the code space, allows one to track and characterize the dynamical behaviour of logical qubits. Awareness of these effects and the efficient characterisation tools used in this work will help to guide and benchmark experimental implementations of logical qubits.