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.
Highlights
High-quality physical qubits with long coherence times that allow one to reliably store fragile quantum states form the backbone of currently developed quantum processors [18, 26]
We illustrated that simple physical noise models can lead to non-trivial dynamics of logical qubits, which are not captured by usual relaxation time scales
As shown by the examples explored in this work, deviations from simple exponential decay dynamics of logical qubits are possible even in Markovian systems
Summary
High-quality physical qubits with long coherence times that allow one to reliably store fragile quantum states form the backbone of currently developed quantum processors [18, 26]. Widespread and popular figures of merit are the longitudinal and transverse relaxation time scales, known as T1 and T2 They were originally introduced in the field of nuclear magnetic resonance, describing a simple exponential decay dynamics of spin states [1, 26]. We are witnessing enormous efforts to build and reliably control increasingly larger quantum processors - often termed noisy intermediatescale quantum (NISQ) devices [35] These devices are used to implement low-distance quantum error correcting codes [5, 10, 15, 23, 27, 36, 39, 44], which allow one to encode and protect quantum information in so-called logical qubits formed of entangled ensembles of physical qubits [20, 26, 43]. We foresee that awareness of these effects and the efficient characterisation tools used in this work will guide the development and optimisation of logical qubits
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
