Quantum Annealing: An Overview

Abstract

In this review, after providing the basic physical concept behind quantum annealing (or adiabatic quantum computation), we present an overview of some recent theoretical as well as experimental developments pointing to the issues which are still debated. With a brief discussion on the fundamental ideas of continuous and discontinuous quantum phase transitions, we discuss the Kibble-Zurek scaling of defect generation following a ramping of a quantum many body system across a quantum critical point. In the process, we discuss associated models, both pure and disordered, and shed light on implementations and some recent applications of the quantum annealing protocols. Furthermore, we discuss the effect of environmental coupling on quantum annealing. Some possible ways to speed up the annealing protocol in closed systems are elaborated upon: We especially focus on the recipes to avoid discontinuous quantum phase transitions occurring in some models where energy gaps vanish exponentially with the system size.

arXiv commentPhil.Trans. R. Soc. A 381, 20210417

References in corpus (96)

• Nonequilibrium dynamics of closed interacting quantum systems
• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Efficient simulation of one-dimensional quantum many-body systems
• Adiabatic Quantum Computing
• Real time evolution using the density matrix renormalization group
• Continuous Quantum Phase Transitions
• Shortcuts to adiabaticity: concepts, methods, and applications
• Quantum annealing with more than one hundred qubits
• Dynamics of a Quantum Phase Transition
• Theory of Quantum Annealing of an Ising Spin Glass
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Quantum Annealing and Analog Quantum Computation
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Perspectives of quantum annealing: Methods and implementations
• Universal adiabatic dynamics across a quantum critical point
• The iTEBD algorithm beyond unitary evolution
• Mathematical Foundation of Quantum Annealing
• Strong disorder RG approach of random systems
• The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
• Infinite-randomness quantum Ising critical fixed points
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Massively Parallel Probabilistic Computing with Sparse Ising Machines
• Defect production in non-linear quench across a quantum critical point
• Quantum Optimization of Fully-Connected Spin Glasses
• Quantum annealing of the Traveling Salesman Problem
• First order phase transition in the Quantum Adiabatic Algorithm
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Searching for quantum speedup in quasistatic quantum annealers
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Optimal non-linear passage through a quantum critical point
• Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
• Dynamics after a sweep through a quantum critical point
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
• Quantum annealing with antiferromagnetic fluctuations
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Thermally assisted adiabatic quantum computation
• Adiabatic dynamics in open quantum critical many-body systems
• Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
• Dynamics of a quantum phase transition in the random Ising model
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
• First-order transitions and the performance of quantum algorithms in random optimization problems
• Strong Disorder RG approach - a short review of recent developments
• Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains
• Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field
• Scaling and diabatic effects in quantum annealing with a D-Wave device
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
• Multivariable Optimization: Quantum Annealing & Computation
• Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• On quantum mean-field models and their quantum annealing
• Adequacy of Si:P Chains as Fermi-Hubbard Simulators
• Residual Energies after Slow Quantum Annealing
• Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model
• Quantum annealing of the $p$-spin model under inhomogeneous transverse field driving
• Parallel Quantum Annealing
• New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
• Random quantum magnets with broad disorder distribution
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions
• Quantum Kibble-Zurek physics in the presence of spatially-correlated dissipation
• Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability
• Universal anti-Kibble-Zurek scaling in fully-connected systems
• Study of Optimization Problems by Quantum Annealing
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
• Quantum Annealing in a Kinetically Constrained System
• Calculation of molecular vibrational spectra on a quantum annealer
• Mean Field Analysis of Quantum Annealing Correction
• Quantum annealing simulation of out-of-equilibrium magnetization in a spin-chain compound
• Stability of the quantum Sherrington-Kirkpatrick spin glass model
• Cooling dynamics of pure and random Ising chains
• On the optimal working point in dissipative quantum annealing
• Existence of replica-symmetry breaking in quantum glasses
• Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions
• A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
• Nested Quantum Annealing Correction at Finite Temperature: $p$-spin models
• A quantum Monte Carlo algorithm realizing an intrinsic relaxation
• Optimal working point in digitized quantum annealing
• Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model
• Dynamical generation of Majorana edge correlations in a ramped Kitaev chain coupled to nonthermal dissipative channels
• Possible Ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing
• Kibble-Zurek mechanism in a Dissipative Transverse Ising Chain
• Critical and Griffiths-McCoy singularities in quantum Ising spin-glasses on d-dimensional hypercubic lattices: A series expansion study
• Quantum annealing of pure and random Ising chains coupled to a bosonic environment
• Observing the fate of the false vacuum with a quantum laboratory
• Classical simulation and theory of quantum annealing in a thermal environment
• Unconventional critical activated scaling of two-dimensional quantum spin-glasses
• A comparison between D-wave and a classical approximation algorithm and a heuristic for computing the ground state of an Ising spin glass
• Quantum annealing speedup of embedded problems via suppression of Griffiths singularities
• Unraveling the origin of higher success probabilities in quantum versus semi-classical annealing
• Quantum Annealing search of Ising spin glass ground state(s) with tunable transverse & longitudinal fields

Cited by in corpus (40)

• A symbolic approach to discrete structural optimization using quantum annealing
• Quantum pricing-based column-generation framework for hard combinatorial problems
• A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems
• Cyclic Quantum Annealing: Searching for Deep Low-Energy States in 5000-Qubit Spin Glass
• Towards an Automatic Framework for Solving Optimization Problems with Quantum Computers
• Test Case Minimization with Quantum Annealers
• Topological Quantum Gates in Homotopy Type Theory
• Genuine Multipartite Entanglement in Quantum Optimization
• Optimized QUBO formulation methods for quantum computing
• A Quantum Annealing Protocol to Solve the Nuclear Shell Model
• A numerical approach for calculating exact non-adiabatic terms in quantum dynamics
• A Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem
• How to experimentally evaluate the adiabatic condition for quantum annealing
• General Oscillator-Based Ising Machine Models with Phase-Amplitude Dynamics and Polynomial Interactions
• A Decomposition Method for the Hybrid Quantum-Classical Solution of the Number Partitioning Problem
• Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer
• Boosting quantum annealing performance through direct polynomial unconstrained binary optimization
• Classical Criticality via Quantum Annealing
• A Lattice-Reduction Aided Vector Perturbation Precoder Relying on Quantum Annealing
• Quantum ergodicity and scrambling in quantum annealers
• Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model
• Learning-Driven Annealing with Adaptive Hamiltonian Modification for Solving Large-Scale Problems on Quantum Devices
• Quantum simulations of complex systems
• Topological Defects from Quantum Reset Dynamics
• Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point
• Annealing Dynamics of Regular Rotor Networks: Universality and Its Breakdown
• Approximate Quadratization of High-Order Hamiltonians for Combinatorial Quantum Optimization
• The anomalously slow dynamics of inhomogeneous quantum annealing
• Quantum Global Minimum Finder based on Variational Quantum Search
• Quantum Annealing in SK Model Employing Suzuki-Kubo-deGennes Quantum Ising Mean Field Dynamics
• Subsampling Factorization Machine Annealing
• Optimal Quantum Likelihood Estimation
• Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem
• Inference of maximum parsimony phylogenetic trees with model-based classical and quantum methods
• A Quantum Genetic Algorithm with application to Cosmological Parameters Estimation
• Leveraging Analog Neutral Atom Quantum Computers for Diversified Pricing in Hybrid Column Generation Frameworks
• Formulation and evaluation of ocean dynamics problems as optimization problems for quantum annealing machines
• Finite-rate quench in disordered Chern and $Z_2$ topological insulators
• A quantum wire approach to weighted combinatorial graph optimisation problems
• Programming tools for Analogue Quantum Computing in the High-Performance Computing Context -- A Review