Continuous quantum correction on Markovian and Non-Markovian models

Abstract

We investigate continuous quantum error correction, comparing performance under a Markovian error model to two distinct non-Markovian models. The first non-Markovian model involves an interaction Hamiltonian between the system and an environmental qubit via an X-X coupling, with a "cooling" bath acting on the environment qubit. This model is known to exhibit abrupt transitions between Markovian and non-Markovian behavior. The second non-Markovian model uses the post-Markovian master equation (PMME), which represents the bath correlation through a memory kernel; we consider an exponentially decaying kernel and both underdamped and overdamped dynamics. We systematically compare these non-Markovian error models against the Markovian case and against each other, for a variety of different codes. We start with a single qubit, which can be solved analytically. We then consider the three-qubit repetition code and the five-qubit "perfect" code. In all cases, we find that the fidelity decays more rapidly in the Markovian case than in either non-Markovian model, suggesting that continuous quantum error correction has enhanced performance against non-Markovian noise. We attribute this difference to the presence of a quantum Zeno regime in both non-Markovian models.

21 pages, 15 figures; fixed grant number and a few minor typos, added a few references

References in corpus (33)

• To catch and reverse a quantum jump mid-flight
• Continuous quantum error correction via quantum feedback control
• Foundations and Measures of Quantum Non-Markovianity
• Implementation of the Five Qubit Error Correction Benchmark
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
• Suppression of crosstalk in superconducting qubits using dynamical decoupling
• Dynamical decoupling for superconducting qubits: a performance survey
• A practical scheme for error control using feedback
• Reversing quantum trajectories with analog feedback
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
• Experimental demonstration of continuous quantum error correction
• Quantum simulation of the spin-boson model with a microwave circuit
• Continuous quantum error correction by cooling
• Continuous quantum error correction for non-Markovian decoherence
• Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics
• Predicting non-Markovian superconducting qubit dynamics from tomographic reconstruction
• Error suppression for Hamiltonian-based quantum computation using subsystem codes
• Quantum Simulation of Spin-Boson Models with Structured Bath
• Entanglement assisted probe of the non-Markovian to Markovian transition in open quantum system dynamics
• HOQST: Hamiltonian Open Quantum System Toolkit
• Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
• Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity
• Method for quantum-jump continuous-time quantum error correction
• Non-Markovianity of the Post Markovian Master Equation
• Continuous quantum error detection and suppression with pairwise local interactions
• Parametric approximation as open quantum systems problem
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Continuous monitoring can improve indistinguishability of a single-photon source
• Noise-adapted Quantum Error Correction for Non-Markovian Noise
• Markovian and non-Markovian dynamics induced by a generic environment
• Improving quantum dot based single-photon source with continuous measurements
• Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes