Non-Stoquastic Interactions in Quantum Annealing via the Aharonov-Anandan Phase

Abstract

We argue that a complete description of quantum annealing (QA) implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquastic terms in the effective quantum Ising Hamiltonians that are typically used to describe QA with flux-qubits. We explicitly demonstrate the effect of these geometric interactions when QA is performed with a system of one and two coupled flux-qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases QA with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well-known that the direct implementation of non-stoquastic interactions with flux-qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquastic interactions via geometric phases that can be exploited for computational purposes.

12 pages, 7 figures

References in corpus (12)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• How Powerful is Adiabatic Quantum Computation?
• Consistency Tests of Classical and Quantum Models for a Quantum Annealer
• Reexamining classical and quantum models for the D-Wave One processor
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• Shortcuts to adiabaticity for quantum annealing
• Adiabatic optimization versus diffusion Monte Carlo
• Geometric quantum gates with superconducting qubits
• Polynomial-time classical simulation of quantum ferromagnets
• Exact sampling hardness of Ising spin models

Cited by in corpus (29)

• Superconducting Qubits: Current State of Play
• Quantum Annealing for Industry Applications: Introduction and Review
• Digitized-counterdiabatic quantum approximate optimization algorithm
• SU(2) lattice gauge theory on a quantum annealer
• Demonstration of nonstoquastic Hamiltonian in coupled superconducting flux qubits
• Portfolio Optimization with Digitized-Counterdiabatic Quantum Algorithms
• Digitized-Counterdiabatic Quantum Optimization
• Electronic structure with direct diagonalization on a D-Wave quantum annealer
• Why and when is pausing beneficial in quantum annealing?
• Accelerated Quantum Monte Carlo with Probabilistic Computers
• Digitized Adiabatic Quantum Factorization
• Steering random spin systems to speed up the quantum adiabatic algorithm
• De-Signing Hamiltonians for Quantum Adiabatic Optimization
• Effective Hamiltonians for interacting superconducting qubits -- local basis reduction and the Schrieffer-Wolff transformation
• Testing a quantum annealer as a quantum thermal sampler
• Lower Bounds on Quantum Annealing Times
• Using Quantum Annealers to Calculate Ground State Properties of Molecules
• Parity-Engineered Light-Matter Interaction
• Nonpairwise interactions induced by virtual transitions in four coupled artificial atoms
• Customized quantum annealing schedules
• Superconducting qubit circuit emulation of a vector spin-1/2
• Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians
• Efficient numerical simulation of complex Josephson quantum circuits
• Theoretical survey of unconventional quantum annealing methods applied to adifficult trial problem
• Dynamic Asset Allocation with Expected Shortfall via Quantum Annealing
• Substochastic Monte Carlo Algorithms
• The anomalously slow dynamics of inhomogeneous quantum annealing
• Hyperspectral image segmentation with a machine learning model trained using quantum annealer
• Embodied observations from an intrinsic perspective can entail quantum dynamics