Mean Field Analysis of Quantum Annealing Correction

Abstract

Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error-correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the $p$-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for $p=2$, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For $p\ge 3$, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.

23 pages, 13 figures. v2: updated to published version

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Cited by in corpus (24)

• Quantum Annealing: An Overview
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Temperature scaling law for quantum annealing optimizers
• Quantum annealing of the $p$-spin model under inhomogeneous transverse field driving
• Nested Quantum Annealing Correction
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Performance of two different quantum annealing correction codes
• Improved Boltzmann machines with error corrected quantum annealing
• Scalable effective temperature reduction for quantum annealers via nested quantum annealing correction
• Nested Quantum Annealing Correction at Finite Temperature: $p$-spin models
• Error suppression in adiabatic quantum computing with qubit ensembles
• Error Suppression for Hamiltonian Quantum Computing in Markovian Environments
• Noise Dynamics of Quantum Annealers: Estimating the Effective Noise Using Idle Qubits
• Dynamics of Order Parameters of Non-stoquastic Hamiltonians in the Adaptive Quantum Monte Carlo Method
• Perils of Embedding for Quantum Sampling
• Balancing coherent and dissipative dynamics in a central-spin system
• Quantum annealing with a nonvanishing final value of the transverse field
• Bifurcation-based quantum annealing with nested spins
• Demonstration of error-suppressed quantum annealing via boundary cancellation
• Using copies to improve precision in continuous-time quantum computing
• Analog Errors in Quantum Annealing: Doom and Hope
• Effects of dynamical paths on the energy gap and the corrections to free energy in path integrals of mean-field quantum spin systems
• Structural Comparison of Error Mitigation Methods for Ising Machines: Penalty-Spin Model versus Stacked Model
• Frustration-enhanced quantum annealing correction models with additional inter-replica interactions