Mapping State Transition Susceptibility in Quantum Annealing

Abstract

Quantum annealing is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. Quantum annealing in the transverse field Ising model, implemented on D-Wave devices, works by applying a time dependent transverse field, which puts all qubits into a uniform state of superposition, and then applying a Hamiltonian over time which describes a user programmed Ising problem. We present a method which utilizes two control features of D-Wave quantum annealers, reverse annealing and an h-gain schedule, to quantify the susceptibility, or the distance, between two classical states of an Ising problem. The starting state is encoded using reverse annealing, and the second state is encoded on the linear terms of problem Hamiltonian. An h-gain schedule is specified which incrementally increases the strength of the linear terms, thus allowing a quantification of the h-gain strength required to transition the anneal into a specific state at the final measurement. By the nature of quantum annealing, the state tends towards global minima and therefore we restrict the second classical state to a minimum solution of the given Ising problem. This susceptibility mapping, when enumerated across all initial states, shows in detail the behavior of the quantum annealer during reverse annealing. The procedure is experimentally demonstrated on three small test Ising's which were embedded in parallel on the D-Wave Advantage_system4.1. Analysis of the state transition mapping shows detailed characteristics of the reverse annealing process including intermediate state transition paths, which are visually represented as state transition networks.

Typo fixes and updated figures

References in corpus (20)

• Mathematical Foundation of Quantum Annealing
• Quantum Annealing for Industry Applications: Introduction and Review
• Warm-starting quantum optimization
• Quantum annealing correction for random Ising problems
• A Quantum Annealing Approach for Fault Detection and Diagnosis of Graph-Based Systems
• Parallel Quantum Annealing
• 3-Regular 3-XORSAT Planted Solutions Benchmark of Classical and Quantum Heuristic Optimizers
• Scaling overhead of embedding optimization problems in quantum annealing
• Quantum annealing simulation of out-of-equilibrium magnetization in a spin-chain compound
• Fair Sampling by Simulated Annealing on Quantum Annealer
• Understanding domain-wall encoding theoretically and experimentally
• Experimental Realization of Classical ${\mathbb{Z}}_2$ Spin Liquids in a Programmable Quantum Device
• Standard quantum annealing outperforms adiabatic reverse annealing with decoherence
• Quantum Annealing Algorithms for Boolean Tensor Networks
• Signatures of Open and Noisy Quantum Systems in Single-Qubit Quantum Annealing
• A double-slit proposal for quantum annealing
• Fair sampling of ground-state configurations of binary optimization problems
• Customized quantum annealing schedules
• Perils of Embedding for Quantum Sampling
• The Perturbed Ferromagnetic Chain: A Tuneable Test of Quantum Hardness in the Transverse-Field Ising Model

Cited by in corpus (1)

• Frustration Elimination and Excited State Search in Coherent Ising Machines