Nested Quantum Annealing Correction at Finite Temperature: $p$-spin models

Abstract

Quantum annealing in a real device is necessarily susceptible to errors due to diabatic transitions and thermal noise. Nested quantum annealing correction is a method to suppress errors by using an all-to-all penalty coupling among a set of physical qubits representing a logical qubit. We show analytically that nested quantum annealing correction can suppress errors effectively in ferromagnetic and antiferromagnetic Ising models with infinite-range interactions. Our analysis reveals that the nesting structure can significantly weaken or even remove first-order phase transitions, in which the energy gap closes exponentially. The nesting structure also suppresses thermal fluctuations by reducing the effective temperature.

28 pages

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Cited by in corpus (14)

• Quantum Annealing: An Overview
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Counterdiabatic driving in the quantum annealing of the $p$-spin model: a variational approach
• Genetic optimization of quantum annealing
• Dissipative phase transitions in the fully-connected Ising model with $p$-spin interaction
• Improved Boltzmann machines with error corrected quantum annealing
• Error suppression in adiabatic quantum computing with qubit ensembles
• Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries
• Perils of Embedding for Quantum Sampling
• 4-clique Network Minor Embedding for Quantum Annealers
• Demonstration of error-suppressed quantum annealing via boundary cancellation
• Using copies to improve precision in continuous-time quantum computing
• 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