Modeling error correction with Lindblad dynamics and approximate channels

Abstract

We analyze the performance of a quantum error correction code subject to physically motivated noise modeled by a Lindblad master equation. We consider dissipative and coherent single-qubit terms and two-qubit crosstalk, studying how different approximations of the noise capture the success rate of a code. Focusing on the five-qubit code and adapting it to partially correct two-qubit errors in relevant parameter regimes according to the noise model, we find that a composite-channel approximation where every noise term is considered separately captures the behavior in many physical cases up to long timescales, eventually failing due to the effect of noncommuting terms. In contrast, we find that single-qubit approximations do not properly capture the error correction dynamics with two-qubit noise, even for short times. A Pauli approximation going beyond a single-qubit channel is sensitive to the details of the noise, state, and decoder, and succeeds at short timescales relative to the noise strength, beyond which it fails. Furthermore, we point out a mechanism for a Pauli model failure where it underestimates the failure rate of a code even with frequent syndrome projection and correction cycles. These results shed light on the performance of error correction in the presence of realistic noise and can advance the ongoing efforts towards useful quantum error correction.

References in corpus (31)

• 14-qubit entanglement: creation and coherence
• Suppressing quantum errors by scaling a surface code logical qubit
• Logical quantum processor based on reconfigurable atom arrays
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• High-threshold and low-overhead fault-tolerant quantum memory
• Demonstration of fault-tolerant universal quantum gate operations
• Low-distance Surface Codes under Realistic Quantum Noise
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• The XZZX Surface Code
• Encoding a magic state with beyond break-even fidelity
• Efficient Long-Range Entanglement using Dynamic Circuits
• Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment
• Realizing coherently convertible dual-type qubits with the same ion species
• Exact solutions of interacting dissipative systems via weak symmetries
• Comparison of a quantum error correction threshold for exact and approximate errors
• Bias-tailored quantum LDPC codes
• Predicting non-Markovian superconducting qubit dynamics from tomographic reconstruction
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• Exact solution of the infinite-range dissipative transverse-field Ising model
• Correcting non-independent and non-identically distributed errors with surface codes
• Dissipative Dynamics of Graph-State Stabilizers with Superconducting Qubits
• Characterizing non-Markovian Off-Resonant Errors in Quantum Gates
• Effective qubit dephasing induced by spectator-qubit relaxation
• Improved quantum error correction with randomized compiling
• Comparing Two-Qubit and Multi-Qubit Gates within the Toric Code
• Optimized noise-assisted simulation of the Lindblad equation with time-dependent coefficients on a noisy quantum processor
• Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Adaptive variational low-rank dynamics for open quantum systems
• Quantum error correction under numerically exact open-quantum-system dynamics
• Decoherence Limits the Cost to Simulate an Anharmonic Oscillator
• A solvable model for graph state decoherence dynamics

Cited by in corpus (5)

• Efficient Lindblad synthesis for noise model construction
• Generalizing the matching decoder for the Chamon code
• Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations
• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
• Feedforward suppression of readout-induced faults in quantum error correction