Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model

Abstract

Introducing a nonstoquastic catalyst is a promising avenue to improve quantum annealing with the transverse field. In the present paper, we propose a nonstoquastic catalyst for bifurcation-based quantum annealing described by the spin-1 operators to improve the efficiency of a ground-state search. To investigate the effect of the nonstoquastic catalyst, we study the ferromagnetic $p$-spin model, which has difficulty with finding the ground state due to the first-order phase transition for quantum annealing. A semiclassical analysis shows that the problematic first-order phase transition can be eliminated by introducing the proposed nonstoquastic catalyst with the appropriate amplitude. We also numerically calculate the minimum energy gap for a finite-size system by diagonalizing the Hamiltonian. We find that while the energy gap decreases exponentially with increasing system size for the original Hamiltonian, it decreases polynomially against the system size for the Hamiltonian with the nonstoquastic catalyst. This result implies that the proposed nonstoquastic catalyst has the potential to improve the performance of bifurcation-based quantum annealing.

11 pages, 11 figures

References in corpus (22)

• Universal dynamical decoupling of a single solid-state spin from a spin bath
• Strong Coupling of a Spin Ensemble to a Superconducting Resonator
• Mathematical Foundation of Quantum Annealing
• Bounds for the adiabatic approximation with applications to quantum computation
• Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Quantum annealing with antiferromagnetic fluctuations
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Generalized spin mapping for quantum-classical dynamics
• Radio-frequency magnetometry using a single electron spin
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• Reverse quantum annealing of the $p$-spin model with relaxation
• Two-parameter counter-diabatic driving in quantum annealing
• Optimal quantum annealing: A variational shortcut to adiabaticity approach
• Quantum annealing with capacitive-shunted flux qubits
• Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
• Polynomial scaling enhancement in ground-state preparation of Ising spin models via counter-diabatic driving
• Preparing ground states of the XXZ model using the quantum annealing with inductively coupled superconducting flux qubits
• Effective spin models of Kerr-nonlinear parametric oscillators for quantum annealing
• Exact expression of the energy gap at first-order quantum phase transitions of a non-stoquastic Hamiltonian

Cited by in corpus (2)

• How to experimentally evaluate the adiabatic condition for quantum annealing
• Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy