Quantum error correction under numerically exact open-quantum-system dynamics

Abstract

The known quantum error-correcting codes are typically built on approximative open-quantum-system models such as Born--Markov master equations. However, it is an open question how such codes perform in actual physical systems that, to some extent, necessarily exhibit phenomena beyond the limits of these models. To this end, we employ numerically exact open-quantum-system dynamics to analyze the performance of a five-qubit error correction code where each qubit is coupled to its own bath. We first focus on the performance of a single error correction cycle covering time scales beyond that of Born--Markov models. Namely, we observe distinct power law behavior of the channel infidelity $\propto t^{2a}$: $a\lesssim 2$ in the ultrashort times $t<3/{\omega }_{\mathrm{c}}$ and $a\approx 1/2$ in the short-time range $3/{\omega }_{\mathrm{c}}<t<30/{\omega }_{\mathrm{c}}$, where ${\omega }_{\mathrm{c}}$ is the cutoff angular frequency of the bath. Importantly, the five-qubit quantum-error correction code suppresses all single errors, including those arising from the ultrashort and short-time evolution, which are peculiar to the exact evolution. Interestingly, we demonstrate the breaking points of the five-qubit error correction code and the Born--Markov models for repeated error correction when the repetition rate exceeds $2\pi /\omega$ or the coupling strength $\kappa \gtrsim 0.1\omega$, where $\omega$ is the angular frequency of the qubit. Our results pave the way for applying numerically exact open-quantum-system models for the studies of QECs beyond simple error models.

References in corpus (8)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Surface codes: Towards practical large-scale quantum computation
• Quantum computational advantage using photons
• Strong quantum computational advantage using a superconducting quantum processor
• Suppressing quantum errors by scaling a surface code logical qubit
• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment
• State leakage during fast decay and control of a superconducting transmon qubit

Cited by in corpus (8)

• Gate Operations for Superconducting Qubits and Non-Markovianity
• Modeling error correction with Lindblad dynamics and approximate channels
• Impact of time-retarded noise on dynamical decoupling schemes for qubits
• Noise-adapted Quantum Error Correction for Non-Markovian Noise
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Simulation of open quantum systems on universal quantum computers
• Environment-Mediated Long-Ranged Correlations in Many-Body System
• Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects