A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

Abstract

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.

15 pages, 6 figures, email correspondence to [email protected] ; a shorter version of this article appeared in the April 20, 2001 issue of Science; see http://www.sciencemag.org/cgi/content/full/292/5516/472

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• Almost exact state transfer in a spin chain via pulse control
• Adiabatic evolution under quantum control
• Nested Quantum Annealing Correction at Finite Temperature: $p$-spin models
• Adiabatic landscape and optimal paths in ergodic systems
• Quantum state preparation for coupled period tripling oscillators
• Generalized transitionless quantum driving for open quantum systems
• Fast Quantum Methods for Optimization
• Demonstration of low-overhead quantum error correction codes
• Not-so-adiabatic quantum computation for the shortest vector problem
• Quantum thermodynamics in adiabatic open systems and its trapped-ion experimental realization
• An adiabatic Leakage Elimination Operator in experimental framework
• Optimal working point in digitized quantum annealing
• Using thermal boundary conditions to engineer the quantum state of a bulk magnet
• Circumventing superexponential runtimes for hard instances of quantum adiabatic optimization
• Non-adiabatic Fast Control of Mixed States based on Lewis-Riesenfeld Invariant
• Adiabatic Quantum Optimization for Associative Memory Recall
• Perturbative Formulation and Non-adiabatic Corrections in Adiabatic Quantum Computing Schemes
• Benchmarking quantum annealing dynamics: the spin-vector Langevin model
• A Quantum Annealing Approach for Dynamic Multi-Depot Capacitated Vehicle Routing Problem
• Assessment of Quantum Annealing for the Construction of Satisfiability Filters
• Extending relax-and-round combinatorial optimization solvers with quantum correlations
• Interface dynamics in the two-dimensional quantum Ising model
• Adiabatic topological quantum computing
• Greedy parameter optimization for diabatic quantum annealing
• Elimination of Perturbative Crossings in Adiabatic Quantum Optimization
• Certification of quantum states with hidden structure of their bitstrings
• Quantum Error Mitigation Relying on Permutation Filtering
• Quantum heuristic algorithm for traveling salesman problem
• Floquet resonances close to the adiabatic limit and the effect of dissipation
• New anatomy of quantum holonomy
• Rapid mixing and stability of quantum dissipative systems
• Testing a quantum annealer as a quantum thermal sampler
• Quantum gates by inverse engineering of a Hamiltonian
• Many-body localization enables iterative quantum optimization
• Adiabatic Quantum Kitchen Sinks for Learning Kernels Using Randomized Features
• Density functional theory and quantum computation
• Adiabatic theorem for closed quantum systems initialized at finite temperature
• Ferromagnetically shifting the power of pausing
• Ground state cooling of quantum systems via a one-shot measurement
• Implementation of controlled phase shift gates and Collins version of Deutsch-Jozsa algorithm on a quadrupolar spin-7/2 nucleus using non-adiabatic geometric phases
• Quantum Correlations in the Kerr Ising Model
• Singularity of Berry Connections Inhibits the Accuracy of Adiabatic Approximation
• Quantum algorithms for scientific computing
• Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms
• A comparative study of universal quantum computing models: towards a physical unification
• Local Hamiltonians in Quantum Computation
• Quantum independent set problem and non-abelian adiabatic mixing
• Dynamics of the quantum search and quench-induced first-order phase transitions
• Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits
• Superconducting Quantum Annealing Architecture with LC Resonators
• Experimental and Theoretical Study of Thermodynamic Effects in a Quantum Annealer
• Quantum variational approach to lattice gauge theory at nonzero density
• Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study
• A Random Matrix Model of Adiabatic Quantum Computing
• Quantum Register Physics
• Breakdown of the weak coupling limit in quantum annealing
• Continuous-Time Quantum Algorithms for Unstructured Problems
• Improved Bounds for Eigenpath Traversal
• Fault-tolerant Holonomic Quantum Computation in Surface Codes
• Knapsack Problem variants of QAOA for battery revenue optimisation
• Adiabatic quantum optimization in presence of discrete noise: Reducing the problem dimensionality
• Error suppression in adiabatic quantum computing with qubit ensembles
• Improving performance of logical qubits by parameter tuning and topology compensation
• The adiabatic theorem in the presence of noise
• Anomalous behavior of the energy gap in the one-dimensional quantum XY model
• Optimization by Decoded Quantum Interferometry
• Quantum Simulation of Klein Gordon Equation and Observation of Klein Paradox in IBM Quantum Computer
• Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations
• Kibble-Zurek mechanism in a Dissipative Transverse Ising Chain
• Environment-assisted analog quantum search
• Synchronization of Multiple Coupled rf-SQUID Flux Qubits
• Heterogeneous Quantum Computing for Satellite Constellation Optimization: Solving the Weighted K-Clique Problem
• Fair sampling of ground-state configurations of binary optimization problems
• Quantum phase transition with inhomogeneous driving in the Lechner-Hauke-Zoller model
• Fast, Lifetime-Preserving Readout for High-Coherence Quantum Annealers
• Towards Large-Scale Quantum Computation
• Controlling and reversing the transition from classical diffusive to quantum ballistic transport in a quantum walk by driving the coin
• Decoherence induced deformation of the ground state in adiabatic quantum computation
• Controlling open quantum systems using fast transitions
• Theorem on the existence of a nonzero energy gap in adiabatic quantum computation
• Simulating long-distance entanglement in quantum spin chains by superconducting flux qubits
• Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems
• Quantum Programming of the Satisfiability Problem with Rydberg Atom Graphs
• Diabatic Quantum Annealing for the Frustrated Ring Model
• Quantum and classical annealing in a continuous space with multiple local minima
• Quantum Computing by Cooling
• Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
• Estimating the Density of States of Frustrated Spin Systems
• Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
• Viewing Vanilla Quantum Annealing Through Spin Glasses
• Thermalization of noninteracting quantum systems coupled to blackbody radiation: A Lindblad-based analysis
• Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures
• Quantum search by partial adiabatic evolution
• The Phase Transition in Exact Cover
• Quantum Adiabatic Algorithm and Large Spin Tunnelling
• Quantum simulator for the $\f{O(3)}$ nonlinear sigma model
• Dynamic-ADAPT-QAOA: An algorithm with shallow and noise-resilient circuits
• Universal Quantum Optimization with Cold Atoms in an Optical Cavity
• Speedup of the Quantum Adiabatic Algorithm using Delocalization Catalysis
• Pattern-recalling processes in quantum Hopfield networks far from saturation
• ON-OFF Neuromorphic ISING Machines using Fowler-Nordheim Annealers
• Hilbert Space Fragmentation and Ashkin-Teller Criticality in Fluctuation Coupled Ising Models
• Success of digital adiabatic simulation with large Trotter step
• Fidelity-optimized quantum state estimation
• Counterdiabatic optimized driving in quantum phase sensitive models
• Experimental realization of noise-induced adiabaticity in nuclear magnetic resonance
• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Parity Quantum Optimization: Encoding Constraints
• Quantum entangling power of adiabatically connected hamiltonians
• Geometric phase of a two-level system in a dissipative environment
• Exponential capacity of associative memories under quantum annealing recall
• Few-body spin couplings and their implications for universal quantum computation
• Optimizing QAOA: Success Probability and Runtime Dependence on Circuit Depth
• Realization of a classical counterpart of a scalable design for adiabatic quantum computation
• A Fault-Tolerant Scheme of Holonomic Quantum Computation on Stabilizer Codes with Robustness to Low-weight Thermal Noise
• Quantum Computational Method of Finding the Ground State Energy and Expectation Values
• Adiabatic optical entanglement between electron spins in separate quantum dots
• Nonpairwise interactions induced by virtual transitions in four coupled artificial atoms
• Optimizing adiabatic quantum pathways via a learning algorithm
• Thermal, quantum and simulated quantum annealing: analytical comparisons for simple models
• Variational quantum iterative power algorithms for global optimization
• A Quantum-Inspired Method for Three-Dimensional Ligand-Based Virtual Screening
• Patch-planting spin-glass solution for benchmarking
• Quantum Langevin Dynamics for Optimization
• Entanglement and level crossings in frustrated ferromagnetic rings
• Ergodic and localized regions in quantum spin glasses on the Bethe lattice
• On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks
• A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization
• Stochastic learning control of adiabatic speedup in a non-Markovian open qutrit system
• Dual time scales in simulated annealing of a two-dimensional Ising spin glass
• Effectiveness of quantum annealing for continuous-variable optimization
• Quantum annealing for hard 2-SAT problems : Distribution and scaling of minimum energy gap and success probability
• Adiabatic quantum dynamics under decoherence in a controllable trapped-ion setup
• Non-Markovian incoherent quantum dynamics of a two-state system
• Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
• Monte Carlo simulation of stoquastic Hamiltonians
• Variations on the adiabatic invariance: the Lorentz pendulum
• Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere
• Quantum adiabatic optimization and combinatorial landscapes
• Diagonal Catalysts in Quantum Adiabatic Optimization
• A hybrid scheme for prime factorization and its experimental implementation using IBM quantum processor
• Quantum Annealing for Dirichlet Process Mixture Models with Applications to Network Clustering
• Accelerated quantum control in a three-level system by jumping along the geodesics
• Mediator assisted cooling in quantum annealing
• Classical simulation and theory of quantum annealing in a thermal environment
• Making Classical Ground State Spin Computing Fault-Tolerant
• Quantum adiabatic optimization with Rydberg arrays: localization phenomena and encoding strategies
• Fast quantum algorithms for traversing paths of eigenstates
• External-level assisted cooling by measurement
• Exploiting In-Constraint Energy in Constrained Variational Quantum Optimization
• Operational geometric phase for mixed quantum states
• A Quantized Inter-level Character in Quantum Systems
• Quantum annealing and the Schrödinger-Langevin-Kostin equation
• Dynamical quantum phase transitions
• Quantum information processing: The case of vanishing interaction energy
• Leveraging Analog Quantum Computing with Neutral Atoms for Solvent Configuration Prediction in Drug Discovery
• Realization of programmable Ising models in a trapped-ion quantum simulator
• Collective dynamics of phase-repulsive oscillators solves graph coloring problem
• Hybrid annealing using a quantum simulator coupled to a classical computer
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Optimization by a quantum reinforcement algorithm
• Disorder-assisted graph coloring on quantum annealers
• On the dynamics of Simulated Quantum Annealing in random Ising chains
• Preparing ground states of the XXZ model using the quantum annealing with inductively coupled superconducting flux qubits
• VanQver: The Variational and Adiabatically Navigated Quantum Eigensolver
• Ising Machines for Diophantine Problems in Physics
• A Quantum Extension of Variational Bayes Inference
• Quantum annealing with twisted fields
• Accuracy of the adiabatic-impulse approximation for closed and open quantum systems
• Cyclic Quantum Annealing: Searching for Deep Low-Energy States in 5000-Qubit Spin Glass
• Quantum Atom Optics: Theory and Applications to Quantum Technology
• Adiabatic quantum algorithm for artificial graphene
• Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo
• How Fast Can Quantum Annealers Count?
• Quantum search algorithms
• Quantum accelerated approach to the thermal state of classical spin systems with applications to pattern-retrieval in the Hopfield neural network
• Digitized Counterdiabatic Quantum Algorithms for Logistics Scheduling
• Secular master equation for adiabatically time dependent systems
• Advantage of pausing: parameter setting for quantum annealers
• Design Optimization of Noise Filter using Quantum Annealer
• Sensitivity of quantum speedup by quantum annealing to a noisy oracle
• Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries
• Optimizing Quantum Adiabatic Algorithm
• Simulations of the adiabatic quantum optimization for the Set Partition Problem
• Effects of non-Markovian squeezed bath on the dynamics of open systems
• Eigenstates Transition Without Undergoing an Adiabatic Process
• A Class of Time-Energy Uncertainty Relations for Time-dependent Hamiltonians
• On the quantum spin glass transition on the Bethe lattice
• Adiabatic dynamics in a spin-1 chain with uniaxial single-spin anisotropy
• Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians
• Quantum search using non-Hermitian adiabatic evolution
• Non-Hermitian Quantum Annealing in the Ferromagnetic Ising Model
• Non-Adiabatic Quantum Dynamics of Grover's Adiabatic Search Algorithm
• Quantum approximate algorithm for NP optimization problems with constraints
• Coherent Control with User-Defined Passage
• A Novel Algebraic Geometry Compiling Framework for Adiabatic Quantum Computations
• Probabilistic Eigensolver with a Trapped-Ion Quantum Processor
• Performance enhancement of quantum annealing under the Lechner-Hauke-Zoller scheme by non-linear driving of the constraint term
• GPU Based Parallel Ising Computing for Combinatorial Optimization Problems in VLSI Physical Design
• Sufficient conditions for adiabaticity in open quantum systems
• Quantum Vertex Model for Reversible Classical Computing
• Why the Quantitative Condition Fails to Reveal Quantum Adiabaticity
• Quantum Portfolios
• Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer
• Quantum annealing approach to Ionic Diffusion in Solid
• Quantum annealing in spin-boson model: from a perturbative to a ultrastrong mediated coupling
• Quantum adiabatic cycles and their breakdown
• A small-world search for quantum speedup: How small-world interactions can lead to improved quantum annealer designs
• Robust quantum searching with spontaneously decaying qubits
• Localization transition induced by programmable disorder
• Feeding the multitude: A polynomial-time algorithm to improve sampling
• Solving systems of Boolean multivariate equations with quantum annealing
• Measuring adiabaticity in non-equilibrium quantum systems
• Duality in Quantum Quenches and Classical Approximation Algorithms: Pretty Good or Very Bad
• Deterministic Quantum Annealing Expectation-Maximization Algorithm
• Adiabatic quantum computation along quasienergies
• Hybrid adiabatic quantum computing for tomographic image reconstruction -- opportunities and limitations
• Robustness of controlled Hamiltonian approaches to unitary quantum gates
• Multi-nucleon structure and dynamics via quantum computing
• New Developments in Quantum Algorithms
• Measurement-Based Quantum Computation on Two-Body Interacting Qubits with Adiabatic Evolution
• A Quantum Algorithm for Model-Independent Searches for New Physics
• Floating block method for quantum Monte Carlo simulations
• Classical and Quantum Annealing in the Median of Three Satisfiability
• Cavity-assisted Dynamical Quantum Phase Transition at Bifurcation Points
• Enhancing quantum annealing performance by a degenerate two-level system
• Adiabatic graph-state quantum computation
• Adiabatic evolution of a coupled-qubit Hamiltonian
• Non-monotonic Dynamics in Frustrated Ising Model with Time-Dependent Transverse Field
• Quantum annealing speedup of embedded problems via suppression of Griffiths singularities
• Lossy compression of statistical data using quantum annealer
• Semiclassical approach to finite temperature quantum annealing with trapped ions
• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Landau-Zener-Stückelberg Spectroscopy of a Superconducting Flux Qubit
• Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits
• Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts
• Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain
• Ion native variational ansatz for quantum approximate optimization
• How Quantum is the Speedup in Adiabatic Unstructured Search?
• Simple derivation of the Weyl and Dirac quantum cellular automata
• Nonvolatile bistable memory and Ising machine based on Micro-Electro-Mechanical Systems
• Hamiltonian quantum computer in one dimension
• Two-photon-transition superadiabatic passage in an nitrogen-vacancy center in diamond
• Formal Methods for Quantum Programs: A Survey
• Speeding up quantum adiabatic processes with dynamical quantum geometric tensor
• On models of nonlinear evolution paths in adiabatic quantum algorithms
• Highly Versatile FPGA-Implemented Cyber Coherent Ising Machine
• Realizable Quantum Adiabatic Search
• Digital-analog quantum learning on Rydberg atom arrays
• On complexity of the quantum Ising model
• Measurement-induced cooling of a qubit in structured environments
• Enhancing the efficiency of quantum annealing via reinforcement: A path-integral Monte Carlo simulation of the quantum reinforcement algorithm
• Low-temperature coherence properties of Z_2 quantum memory
• Benchmarking Quantum Optimization for the Maximum-Cut Problem on a Superconducting Quantum Computer
• Obstacles to quantum annealing in a planar embedding of XORSAT
• A Spin Hall Ising Machine
• Subspace projection method for unstructured searches with noisy quantum oracles using a signal-based quantum emulation device
• PyQUBO: Python Library for Mapping Combinatorial Optimization Problems to QUBO Form
• Resonant Quantum Search with Monitor Qubits
• Petri Net Modeling for Ising Model Formulation in Quantum Annealing
• The quantum annealing gap and quench dynamics in the exact cover problem
• Why adiabatic quantum annealing is unlikely to yield speed-up
• Oscillating potential well in complex plane and the adiabatic theorem
• Probing nonlinear adiabatic paths with a universal integrator
• Dissipative failure of adiabatic quantum transport as a dynamical phase transition
• Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing
• Preparing Greenberger-Horne-Zeilinger state on ground levels of neutral atoms
• Quantum algorithm for spectral projection by measuring an ancilla iteratively
• Quantum Chaos in Random Ising Networks
• Counterdiabatic Driving with Performance Guarantees
• Pulsed quantum annealing
• Critical properties of dissipative quantum spin systems in finite dimensions
• Robust Preparation of Many-body Ground States in Jaynes-Cummings Lattices
• The relationship between minimum gap and success probability in adiabatic quantum computing
• Quadratic unconstrained binary optimization formulation for rectified-linear-unit-type functions
• Localization in the constrained quantum annealing of graph coloring
• Analytical results for the Quantum Alternating Operator Ansatz with Grover Mixer
• Simulated Quantum Computation of Global Minima
• Quantum Monte Carlo Annealing with Multi-Spin Dynamics
• Characterizing Adiabaticity in Quantum Many-Body Systems at Finite Temperature
• Solving Satisfiability Problems by the Ground-State Quantum Computer
• Unraveling Reverse Annealing: A Study of D-Wave Quantum Annealers
• Quantum optimization with linear Ising penalty functions for customer data science
• Symmetry constraints on temporal order in measurement-based quantum computation
• Quantum search in many-body interacting system with long-range interaction
• Minimal action control method in quantum critical models
• Determination of Molecular Energies via Quantum Imaginary Time Evolution in a Superconducting Qubit System
• Variational Phase Estimation with Variational Fast Forwarding
• Quantum circuit compilation with quantum computers
• Universal Quantum Computation by Scattering in the Fermi-Hubbard Model
• A classical limit of Grover's algorithm induced by dephasing: Coherence vs entanglement
• Hard instance learning for quantum adiabatic prime factorization
• Infinite-range transverse field Ising models and quantum computation
• Optimized QUBO formulation methods for quantum computing
• How do higher-order interactions shape the energy landscape?
• Quantum Annealing and Graph Neural Networks for Solving TSP with QUBO
• A necessary condition for quantum adiabaticity applied to the adiabatic Grover search
• Entanglement Generation by Communication using Phase-Squeezed Light with Photon Loss
• Surface Entanglement in Quantum Spin Networks
• Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing
• Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model
• On the efficiency of Hamiltonian-based quantum computation for low-rank matrices
• Energy Landscape Structure of Small Graph Isomorphism Under Variational Optimization
• Quantum annealing with a nonvanishing final value of the transverse field
• Mapping NP-hard and NP-complete optimisation problems to Quadratic Unconstrained Binary Optimisation problems
• Path-Integral Quantum Monte Carlo simulation with Open-Boundary Conditions
• Red-QAOA: Efficient Variational Optimization through Circuit Reduction
• Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
• Quantum Algorithm to Solve Satisfiability Problems
• Avoid First Order Quantum Phase Transition by Changing Problem Hamiltonians
• Totally Corrective Boosting with Cardinality Penalization
• Dynamics of strongly coupled disordered dissipative spin-boson systems
• Excited state search using quantum annealing
• Bifurcation-based quantum annealing with nested spins
• Validation of Quantum Adiabaticity through Non-Inertial Frames and Its Trapped-Ion Realization
• Improving nonstoquastic quantum annealing with spin-reversal transformations
• Counterdiabatic Hamiltonians for multistate Landau-Zener problem
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation
• Quantum annealing with pairs of ${}^2\Sigma$ molecules as qubits
• Quantum annealing sampling with a bias field
• Convergence condition of simulated quantum annealing for closed and open systems
• Analysis of the shortest vector problems with the quantum annealing to search the excited states
• Effects of low-lying excitations on ground-state energy and energy gap of Sherrington-Kirkpatrick model in transverse field
• Quantum Information Aspects on Bulk and Nano Interacting Fermi System: Spin-Space Density Matrix Approach
• State Preparation in a Jaynes-Cummings Lattice with Quantum Optimal Control
• Quantum techniques for eigenvalue problems
• Connection between single-layer Quantum Approximate Optimization Algorithm interferometry and thermal distributions sampling
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
• Hierarchical Theory of Quantum Adiabatic Evolution
• Implementing transferable annealing protocols for combinatorial optimisation on neutral atom quantum processors: a case study on smart-charging of electric vehicles
• An approximate diagonalization method for large scale Hamiltonians
• QUBO Decision Tree: Annealing Machine Extends Decision Tree Splitting
• Quantum sampling for the Euclidean path integral of lattice gauge theory
• Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method
• Bounds for nonadiabatic transitions
• The speed of Markovian relaxation towards the ground state
• Exact expression of the energy gap at first-order quantum phase transitions of a non-stoquastic Hamiltonian
• A Quantum Walk Enhanced Grover Search Algorithm for Global Optimization
• The Fundamental Gap for a Class of Schrödinger Operators on Path and Hypercube Graphs
• Performance of Equal Phase-Shift Search for One Iteration
• Approximating satisfiability transition by suppressing fluctuations
• Adiabatic Computation - A Toy Model
• Statistical Mechanics of the Quantum K-Satisfiability problem
• Decoherence Rates in Large Scale Quantum Computers and Macroscopic Systems
• Employing feedback in adiabatic quantum dynamics
• Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO($n$)
• Adiabatic Control of the Electron Phase in a Quantum Dot
• Upper bounds for relative entropy of entanglement based on active learning
• Performance of quantum annealing for 2-SAT problems with multiple satisfying assignments
• Homological Description of the Quantum Adiabatic Evolution With a View Toward Quantum Computations
• A Factorisation Algorithm in Adiabatic Quantum Computation
• BBGKY chain and kinetic equations for the level dynamics in an externally perturbed quantum system
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations
• Tunneling time from spin fluctuations in Larmor clock
• Investigating the potential for a limited quantum speedup on protein lattice problems
• Physical consequences of P$\ne$NP and the DMRG-annealing conjecture
• Scalable Parity Architecture With a Shuttling-Based Spin Qubit Processor
• Quantum Adiabatic Computation and the Travelling Salesman Problem
• The effect of quantum fluctuations on the coloring of random graphs
• Singular-value decomposition using quantum annealing
• Experimental Determination of Electronic States via Digitized Shortcut-to-Adiabaticity and Sequential Digitized Adiabaticity
• High-dimensional counterdiabatic quantum computing
• Limitations of some simple adiabatic quantum algorithms
• Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer
• Digital simulation of zero-temperature spontaneous symmetry breaking in a superconducting lattice processor
• Metropolis-style random sampling of quantum gates for the estimation of low-energy observables
• Highly parallel algorithm for the Ising ground state searching problem
• Effect of Constraint Relaxation on the Minimum Vertex Cover Problem in Random Graphs
• The Role of Quantum Computing in Advancing Scientific High-Performance Computing: A perspective from the ADAC Institute
• Minimizing polynomial functions on quantum computers
• Imaginary Hamiltonian variational ansatz for combinatorial optimization problems
• Lower bounds for adiabatic quantum algorithms by quantum speed limits
• Quantum Advantage in Variational Bayes Inference
• A proposal of noise suppression for quantum annealing
• Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Spectroscopic estimation of the photon number for superconducting Kerr parametric oscillators
• Semiclassical quantization of nonadiabatic systems with hopping periodic orbits
• Quantum Integer Programming (QuIP) 47-779: Lecture Notes
• Quantum annealing of Cayley-tree Ising spins at small scales
• Approximating maximum independent set on Rydberg atom arrays using local detunings
• Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
• Phase transitions and gaps in quantum random energy models
• Out-of-equilibrium dynamics of Bose-Bose mixtures in optical lattices
• Quantum Shortcut to Adiabaticity for State Preparation in a Finite-Sized Jaynes-Cummings Lattice
• Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis-Hastings Warm-Starting Algorithm
• Adiabatic evolution on a spatial-photonic Ising machine
• Quantum Annealing for Prime Factorization
• Enhancing Quantum Annealing in Digital-Analog Quantum Computing
• Quantum Phase Transition in Fully-Connected Quantum Wajnflasz-Pick Model
• Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy
• Computational Bottlenecks of Quantum Annealing
• Evaluating the Practicality of Quantum Optimization Algorithms for Prototypical Industrial Applications
• Typical case behaviour of spin systems in random graph and composite ensembles
• Necessity of integral formalism
• Using copies to improve precision in continuous-time quantum computing
• Efficiency of Ground State Quantum Computer
• Flux Qubit Readout in the Persistent Current Basis at arbitrary Bias Points
• Error-run-time trade-off in the adiabatic approximation beyond scaling relations
• Emergent Quantumness in Neural Networks
• Deep Unfolded Local Quantum Annealing
• Analysis of the Hopfield Model with Discrete Coupling
• Validating a Two Qubit Non-Stoquastic Hamiltonian in Quantum Annealing
• Interpolation Approach to Hamiltonian-varying Quantum Systems and the Adiabatic Theorem
• Optimization via Quantum Preconditioning
• Solving tiling puzzles with quantum annealing
• Adiabatic Quantum Programming: Minor Embedding With Hard Faults
• Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
• Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise
• A Quantum Monte Carlo Method at Fixed Energy
• Enhancing the efficiency of adiabatic quantum computations
• A quantum algorithm for solving some discrete mathematical problems by probing their energy spectra
• Classical simulation of dissipative fermionic linear optics
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
• Recursive simulation of quantum annealing
• Accelerating quantum adiabatic evolution with $\pi$-pulse sequences
• Approximate combinatorial optimization with Rydberg atoms: the barrier of interpretability
• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Accelerating an adiabatic process by nonlinear sweeping
• Variational quantum compiling for three-qubit gates design in quantum dots
• Folding lattice proteins confined on minimal grids using a quantum-inspired encoding
• Quantum simulations of complex systems
• Machine-learning-inspired quantum control in many-body dynamics
• Decoherence of a tunable capacitively shunted flux qubit
• Efficient correlation-based discretization of continuous variables for annealing machines
• Analytic approach to the Landau-Zener problem in bounded parameter space
• Bounds on Effective Hamiltonians for Stabilizer Codes
• Parent Hamiltonian Reconstruction via Inverse Quantum Annealing
• Quantum Approximation for Wireless Scheduling
• Escaping Local Minima with Quantum Coherent Cooling
• Coarsening of Disordered Quantum Rotors under a Bias Voltage
• The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion
• Reliability of digitized quantum annealing and the decay of entanglement
• A Thermodynamic Turing Machine: Artificial Molecular Computing Using Classical Reversible Logic Switching Networks
• Spintronics for neuromorphic computing
• Development of research network on Quantum Annealing Computation and Information using Google Scholar data
• Superposition of Macroscopically Distinct States in Adiabatic Quantum Computation
• Bayesian Networks based Hybrid Quantum-Classical Machine Learning Approach to Elucidate Gene Regulatory Pathways
• A measurement driven analog of adiabatic quantum computation for frustration-free Hamiltonians
• Non-classical Role of Potential Energy in Adiabatic Quantum Annealing
• Non-Hermitian Adiabatic Quantum Optimization
• Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing
• Derivation of QUBO formulations for sparse estimation
• An Overview of Approaches to Modernize Quantum Annealing Using Local Searches
• Geometric Phases for Classical and Quantum Dynamics: Hannay angle and Berry Phase for Loops on a Torus
• Absence of small-world effects at the quantum level and stability of the quantum critical point
• Quantum Field Induced Orderings in Fully Frustrated Ising Spin Systems
• Eigenlevel statistics of the quantum adiabatic algorithm
• Fast-forward of quantum adiabatic dynamics in electro-magnetic field
• Investigating the Performance of an Adiabatic Quantum Optimization Processor
• Statistical mechanics of classical and quantum computational complexity
• StoqMA vs. MA: the power of error reduction
• Quantum hypercomputation based on the dynamical algebra su(1,1)
• Iterative classical superadiabatic algorithm for combinatorial optimization
• Time-resolved tomography of a driven adiabatic quantum simulation
• Reduction of the energy-gap scaling by coherent catalysis in models of quantum annealing
• A possible hypercomputational quantum algorithm
• Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem
• Atom Cavity Encoding for NP-Complete Problems
• Hardness-dependent quantum adiabatic schedules for the maximum-independent-set problem
• Quantum Annealing and Computation: A Brief Documentary Note
• Unstructured Adiabatic Quantum Optimization: Optimality with Limitations
• Minimizing minor embedding energy: an application in quantum annealing
• Enhancing Multiple Object Tracking Accuracy via Quantum Annealing
• The Perturbed Ferromagnetic Chain: A Tuneable Test of Quantum Hardness in the Transverse-Field Ising Model
• Classical Simulation of Quantum Adiabatic Algorithms using Mathematica on GPUs
• Excited-State Adiabatic Quantum Computation Started with Vacuum States
• Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem
• Classical Simulated Annealing Using Quantum Analogues
• Hardware-efficient quantum annealing with error mitigation via classical shadow
• Spin-Boson Model to Demonstrate Quantum Tunneling in Biomolecules using IBM Quantum Computer
• Relation of classical non-equilibrium dynamics and quantum annealing
• Characterization of Locality in Spin States and Forced Moves for Optimizations
• Optimization of Robot Trajectory Planning with Nature-Inspired and Hybrid Quantum Algorithms
• Convergence condition of simulated quantum annealing with a non-stoquastic catalyst
• The Human Group Optimizer (HGO): Mimicking the collective intelligence of human groups as an optimization tool for combinatorial problems
• Analytical shortcuts to adiabaticity of weakly driven processes
• Charge-Density-Wave Oscillator Networks for Solving Combinatorial Optimization Problems
• Solving Set Cover with Pairs Problem Using Quantum Annealing
• Relaxation of the EM Algorithm via Quantum Annealing for Gaussian Mixture Models
• Geometric Floquet Condition for Quantum Adiabaticity
• Approaches to Quantum Error Correction
• Subsampling Factorization Machine Annealing
• Entanglement and Quantum Phase Transitions via Adiabatic Quantum Computation
• Applying computational complexity to the emergence of classicality
• The quantum version of the shifted power method and its application in quadratic binary optimization
• Relaxation of the EM Algorithm via Quantum Annealing
• Robust preparation of ground state phases under noisy imaginary time evolution
• Energy Spectrum and Exact Cover in an Extended Quantum Ising Model
• Optimal Quantum Likelihood Estimation
• A journey into localization, integrability and thermalization
• The anomalously slow dynamics of inhomogeneous quantum annealing
• Quantum annealing in capacitively coupled Kerr parametric oscillators using frequency-chirped drives
• Quantum sequel of neural network training
• Digitized Counter-Diabatic Quantum Optimization for Bin Packing Problem
• On fixed-gap adiabatic quantum computation
• Adiabatic theorem for classical stochastic processes
• Hard combinatorial problems and minor embeddings on lattice graphs
• Validity condition for high-fidelity Digitized Quantum Annealing
• Signatures of quantum chaos and complexity in the Ising model on random graphs
• Koopman analysis of combinatorial optimization problems with replica exchange Monte Carlo method
• Accelerating Quantum Eigensolver Algorithms With Machine Learning
• Counterdiabatic ADAPT-VQE for molecular simulation
• Effect of Quantum Statistics on Computational Power of Atomic Quantum Annealers
• Graph Coloring via Quantum Optimization on a Rydberg-Qudit Atom Array
• Adiabatic state preparation from general initial states
• Benchmarking a heuristic Floquet adiabatic algorithm for the Max-Cut problem
• A Novel AQC Factoring Algorithm
• Adiabatic Quantum Computing
• Structured beam controlled super-resolution in quantum dots via rapid adiabatic passage
• Quantum Auctions using Adiabatic Evolution: The Corrupt Auctioneer and Circuit Implementations
• Improving adiabatic quantum factorization via chopped random-basis optimization
• The Rise of Quantum Computing -- Take a BITE for Built Environment and Urban Microclimate Research
• Variational Quantum Algorithm for Constrained Combinatorial Optimization Problems
• Quantum information and statistical mechanics: an introduction to frontier
• Trajectory-independent speed limits for controlled open quantum systems
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Hamiltonian Transformability, Fast Adiabatic Dynamics and Hidden Adiabaticity
• Resource-Efficient Quantum Optimization via Higher-Order Encoding
• The Rayleigh-Lorentz Invariant and Optimal Adiabatic Qubit-Information Detection for Superconducting Qubit Resonators
• Hybrid Real-Imaginary Time Evolution for Low-Depth Hamiltonian Simulation in Quantum Optimization
• Bounding Run-Times of Local Adiabatic Algorithms
• Relating computational complexity and quantum spectral complexity
• Quantum speed-up for solving the one-dimensional Hubbard model using quantum annealing
• Degeneracy Engineering for Classical and Quantum Annealing: A Case Study of Sparse Linear Regression in Collider Physics
• Role of overparametrization in quantum approximate optimization
• Sequences of selective rotation operators to engineer interactions for quantum annealing on three qutrits
• Two geometric phases can dramatically differ from each other even if their evolution paths are sufficiently close in a pointwise manner
• Renormalization method for proving frustration-free local spin chains are gapped
• Reflection-Based Adiabatic State Preparation
• A digital quantum simulator in the presence of a bath
• Dipolar optimal control of entangled current states
• Realistic cost for the model of coherent computing
• Femtosecond Photo-Induced Multiphoton Analog Computation for Symmetry-Based Pattern Classification
• Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results
• Computational solution to quantum foundational problems
• Comparison of spin-qubit architectures for quantum error-correcting codes
• Optimal Shortcuts to Adiabaticity for a Quantum Piston
• Quantum Computation
• Weyl's Relations, Integrable Matrix Models and Quantum Computation
• Curve fitting on a quantum annealer for an advanced navigation method
• Robust phase estimation of the ground-state energy without controlled time evolution on a quantum device
• Statistical Analysis of Quantum Annealing
• A strong-driving toolkit for topological Floquet energy pumps with superconducting circuits
• Monte Carlo Quantum Computing
• Generation of all-to-all connections in a two-dimensional qubit array with two-body interactions
• Programming tools for Analogue Quantum Computing in the High-Performance Computing Context -- A Review
• One-in-Two-Matching Problem is NP-complete
• Multi-step quantum algorithm for solving the 3-bit exact cover problem
• QUBO-inspired Molecular Fingerprint for Chemical Property Prediction
• Shortcuts to adiabaticity and applications to Quantum Computation
• Treating the Independent Set Problem by 2D Ising Interactions with Adiabatic Quantum Computing
• 2D implementation of quantum annealing algorisms for fourth order binary optimization problems
• Quantum-inspired search method for low-energy states of classical Ising Hamiltonians
• Lie transformation on shortcut to adiabaticity in parametric driving quantum system
• Solving the Turbine Balancing Problem using Quantum Annealing
• Quantum imaginary time evolution and UD-MIS problem
• Experiments with Probabilistic Quantum Auctions
• Experimental verification of the inertial theorem control protocols
• Upper bound inequality for calculation time in simulated annealing analogous to adiabatic theorem in quantum systems
• An Adiabatic Quantum Algorithm for Determining Gracefulness of A Graph
• Adiabatic Dynamics and Shortcuts to Adiabaticity: Fundamentals and Applications