Scaling and diabatic effects in quantum annealing with a D-Wave device

Abstract

We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on $L\times L$ lattices with $L\le 32$. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal $L$ dependent annealing rate $v$ for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of $v$ and $L$-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when $v$ is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.

arXiv comment12 pages, 9 figures

References in corpus (71)

• A variational eigenvalue solver on a quantum processor
• Quantum Simulation
• Nonequilibrium dynamics of closed interacting quantum systems
• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Quantum computing with trapped ions
• An Open-System Quantum Simulator with Trapped Ions
• The cold atom Hubbard toolbox
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Effective quantum spin systems with ion traps
• Dynamics of a Quantum Phase Transition
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Quantum Annealing and Analog Quantum Computation
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Quantum Search by Local Adiabatic Evolution
• Defining and detecting quantum speedup
• Quantum dynamics of cold trapped ions, with application to quantum computation
• Quantum transport simulations in a programmable nanophotonic processor
• Universal adiabatic dynamics across a quantum critical point
• Mathematical Foundation of Quantum Annealing
• Quantum Boltzmann Machine
• Realizing the $XY$ Hamiltonian in polariton simulators
• Quantum simulations and many-body physics with light
• Experimental Investigation of an Eight Qubit Unit Cell in a Superconducting Optimization Processor
• What is the Computational Value of Finite Range Tunneling?
• Anderson localization casts clouds over adiabatic quantum optimization
• Quench dynamics near a quantum critical point
• Quantum Simulation with Interacting Photons
• Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning
• Quantum Optimization of Fully-Connected Spin Glasses
• Quantum versus Classical Annealing of Ising Spin Glasses
• Experimental Demonstration of a Robust and Scalable Flux Qubit
• Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise
• Searching for quantum speedup in quasistatic quantum annealers
• Non-equilibrium dynamic critical scaling of the quantum Ising chain
• Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines
• Adiabatic dynamics in open quantum critical many-body systems
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Universal nonequilibrium quantum dynamics in imaginary time
• Effects of dissipation on a quantum critical point with disorder
• Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field
• Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
• Theory of smeared quantum phase transitions
• Residual Energies after Slow Quantum Annealing
• Unraveling Quantum Annealers using Classical Hardness
• Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model
• Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
• 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
• Dissipative Landau-Zener problem and thermally assisted Quantum Annealing
• Thermalization, freeze-out and noise: deciphering experimental quantum annealers
• Quantum annealing via environment-mediated quantum diffusion
• Quasi-adiabatic quantum Monte Carlo algorithm for quantum evolution in imaginary time
• Practical engineering of hard spin-glass instances
• Microscopic theory of non-adiabatic response in real and imaginary time
• Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems
• On the optimal working point in dissipative quantum annealing
• Quantum annealing speedup over simulated annealing on random Ising chains
• Open system quantum annealing in mean field models with exponential degeneracy
• Interacting lattice systems with quantum dissipation: a quantum Monte Carlo study
• Dynamic scaling of topological ordering in classical systems
• Quantum Register Physics
• A Random Matrix Model of Adiabatic Quantum Computing
• Dynamics following a linear ramps in the $O(N)$ model: dynamical transition and statistics of excitations
• Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures
• Heat transport in an open transverse-field Ising chain
• Dynamic scaling in the 2D Ising spin glass with Gaussian couplings
• Experimental Freezing of mid-Evolution Fluctuations with a Programmable Annealer

Cited by in corpus (63)

• Quantum critical dynamics in a 5000-qubit programmable spin glass
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Quantum Annealing: An Overview
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Beyond-classical computation in quantum simulation
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
• Coherent and dissipative dynamics at quantum phase transitions
• Qubit spin ice
• Basic Elements for Simulations of Standard Model Physics with Quantum Annealers: Multigrid and Clock States
• Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling
• Shortcuts to Adiabaticity in Krylov Space
• NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems
• GPU-accelerated simulations of quantum annealing and the quantum approximate optimization algorithm
• Quantum annealing simulation of out-of-equilibrium magnetization in a spin-chain compound
• Mean field analysis of reverse annealing for code-division multiple-access multiuser detection
• Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics
• Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism
• Integrated probabilistic computer using voltage-controlled magnetic tunnel junctions as its entropy source
• Scaling Advantage in Approximate Optimization with Quantum Annealing
• Understanding domain-wall encoding theoretically and experimentally
• Experimentally verifying anti-Kibble-Zurek behavior in a quantum system under noisy control field
• Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition
• Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition
• Varying quench dynamics in the transverse Ising chain: the Kibble-Zurek, saturated, and pre-saturated regimes
• Driven quantum spin chain in the presence of noise: Anti-Kibble-Zurek behavior
• Benchmarking quantum annealing dynamics: the spin-vector Langevin model
• Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
• Breakdown of the weak coupling limit in quantum annealing
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Large Deviations Beyond the Kibble-Zurek Mechanism
• Kink correlations, domain size distribution, and the emptiness formation probability after the Kibble-Zurek quench in the quantum Ising chain
• 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
• Classical simulation and theory of quantum annealing in a thermal environment
• Interferometry based on quantum Kibble-Zurek mechanism
• Suppression of Spontaneous Defect Formation in Inhomogeneous Bose Gases
• Driven one-dimensional noisy Kitaev chain
• Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions
• Dual dynamic scaling in deconfined quantum criticality
• Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate
• Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model
• Navigating the noise-depth tradeoff in adiabatic quantum circuits
• Kibble-Zurek scaling immune to anti-Kibble-Zurek behavior in driven open systems at the limit of loss difference
• Convergence condition of simulated quantum annealing for closed and open systems
• Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• From Classical to quantum stochastic process
• Advantages of fixing spins in quantum annealing
• Universal Critical Holography and Domain Wall Formation
• Imaginary-time relaxation quantum critical dynamics in two-dimensional dimerized Heisenberg model
• Annealing Dynamics of Regular Rotor Networks: Universality and Its Breakdown
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Topological Defects from Quantum Reset Dynamics
• Learning topological defects formation with neural networks in a quantum phase transition
• Persistent oscillation of a Cooper-pair condensate of topological defects in a nonintegrable quantum Ising chain
• Dynamics of the order parameter in symmetry breaking phase transitions
• Digitized counterdiabatic quantum critical dynamics
• Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior
• Deconstructing symmetry breaking dynamics
• A graphene edge-mediated quantum gate
• Quantum annealing and condensed matter physics