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

TL;DR

This paper demonstrates that nested quantum annealing correction effectively reduces errors and thermal fluctuations in all-to-all coupled Ising models, potentially improving quantum annealing performance.

Contribution

It provides an analytical demonstration that nested quantum annealing correction can suppress errors and phase transitions in infinite-range Ising models.

Findings

Nested correction weakens or removes first-order phase transitions.

It reduces the effective temperature, suppressing thermal fluctuations.

Error suppression is effective in ferromagnetic and antiferromagnetic 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.