Error Mitigation of BQP Computations using Measurement-Based Verification

Abstract

We present a modular error mitigation protocol for running $\mathsf{BQP}$ computations on a quantum computer with time-dependent noise. Utilising existing tools from quantum verification and measurement-based quantum computation, our protocol interleaves standard computation rounds alongside test rounds for noise sampling and inherits an exponential bound (in the number of circuit runs) on the probability that a returned classical output is correct. We introduce a post-selection technique called \textit{basketing} to address time-dependent noise and reduce overhead. The result is an error mitigation protocol which requires minimal noise assumptions, making it straightforwardly implementable on existing, NISQ devices. We perform a demonstration of the protocol using classical noisy simulation, presenting a universal measurement pattern which directly maps to (and can be tiled on) the heavy-hex layout of current IBM hardware.

14 pages, 5 figures

References in corpus (27)

• Measurement-based quantum computation with cluster states
• Error mitigation for short-depth quantum circuits
• Efficient variational quantum simulator incorporating active error minimisation
• Practical Quantum Error Mitigation for Near-Future Applications
• Hybrid quantum-classical algorithms and quantum error mitigation
• Fluctuations of Energy-Relaxation Times in Superconducting Qubits
• Decoherence benchmarking of superconducting qubits
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Fundamental limits of quantum error mitigation
• Resource Efficient Zero Noise Extrapolation with Identity Insertions
• Qutrit randomized benchmarking
• Determinism in the one-way model
• Exponential Error Suppression for Near-Term Quantum Devices
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels
• Universal Sampling Lower Bounds for Quantum Error Mitigation
• Dual-state purification for practical quantum error mitigation
• Randomized Benchmarking with Restricted Gate Sets
• Estimating the fidelity of T gates using standard interleaved randomized benchmarking
• Analyzing the impact of time-correlated noise on zero-noise extrapolation
• Randomized Benchmarking under Different Gatesets
• Multi-qubit time-varying quantum channels for NISQ-era superconducting quantum processors
• Mitigating errors by quantum verification and post-selection
• Detection of temporal fluctuation in superconducting qubits for quantum error mitigation
• Virtual distillation with noise dilution
• Study of noise in virtual distillation circuits for quantum error mitigation