BBGKY hierarchy for quantum error mitigation

Abstract

Mitigation of quantum errors is critical for current NISQ devices. In the present work, we address this task by treating the execution of quantum algorithms as the time evolution of an idealized physical system. We use knowledge of its physics to assist the mitigation of the quantum noise produced on the real device. In particular, the time evolution of the idealized system obeys a corresponding BBGKY hierarchy of equations. This is the basis for the novel error mitigation scheme that we propose. Specifically, we employ a subset of the BBGKY hierarchy as supplementary constraints in the ZNE method for error mitigation. We ensure that the computational cost of the scheme scales polynomially with the system size. We test our method on digital quantum simulations of the lattice Schwinger model under noise levels mimicking realistic quantum hardware. We demonstrate that our scheme systematically improves the error mitigation for the measurements of the particle number and the charge within this system. Relative to ZNE we obtain an average reduction of the error by $(18.2\pm 0.5)\%$ and $(52.8\pm 6.3)\%$ for the respective above observables. We propose further applications of the BBGKY hierarchy for quantum error mitigation.

11 pages, 8 figures, 1 table. Updated 3 figures, added 1 figure, extended discussion of results

References in corpus (22)

• Error mitigation for short-depth quantum circuits
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Efficient variational quantum simulator incorporating active error minimisation
• Noise tailoring for scalable quantum computation via randomized compiling
• Practical Quantum Error Mitigation for Near-Future Applications
• Low-cost error mitigation by symmetry verification
• Finding Exponential Product Formulas of Higher Orders
• Model-free readout-error mitigation for quantum expectation values
• Fundamental limits of quantum error mitigation
• Dynamical decoupling for superconducting qubits: a performance survey
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition
• Mitigating Coherent Noise Using Pauli Conjugation
• Universal Sampling Lower Bounds for Quantum Error Mitigation
• Simulation of Quantum Spin Dynamics by Phase Space Sampling of BBGKY Trajectories
• Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term
• First-Order Phase Transition of the Schwinger Model with a Quantum Computer
• A simplified BBGKY hierarchy for correlated fermionic systems from a Stochastic Mean-Field approach
• Equilibration in long-range quantum spin systems from a BBGKY perspective
• Partitioned Density Matrices and Entanglement Correlators
• Toward dense QCD in quantum computers
• Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model