Convergence condition of simulated quantum annealing for closed and open systems
arXiv:2209.15523 · doi:10.1103/PhysRevA.106.062614
Abstract
Simulated quantum annealing is a generic classical protocol to simulate some aspects of quantum annealing and is sometimes regarded as a classical alternative to quantum annealing in finding the ground state of a classical Ising model. We derive a generic condition for simulated quantum annealing to converge to thermal equilibrium at a given, typically low, temperature. Both closed and open systems are treated. We rewrite the classical master equation for simulated quantum annealing into an imaginary-time Schrödinger equation, to which we apply the imaginary-time variant of asymptotic adiabatic condition to deduce the convergence condition. The result agrees qualitatively with a rigorous convergence condition of simulated quantum annealing for closed systems, which was derived from the theory of inhomogeneous Markov process. Also observed is qualitative agreement with a rigorous convergence condition of quantum annealing for closed systems under the real-time Schrödinger dynamics. This coincidence of convergence conditions for classical stochastic processes for simulated quantum annealing and the real-time quantum dynamics for quantum annealing is highly non-trivial and calls for further scrutiny.
arXiv comment10 pages. Added references
References in corpus (28)
- Quantum Annealing in the Transverse Ising Model
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Adiabatic Quantum Computing
- Theory of Quantum Annealing of an Ising Spin Glass
- Quantum Annealing and Analog Quantum Computation
- Perspectives of quantum annealing: Methods and implementations
- Mathematical Foundation of Quantum Annealing
- Observation of topological phenomena in a programmable lattice of 1,800 qubits
- Quantum Adiabatic Markovian Master Equations
- Coherent quantum annealing in a programmable 2000-qubit Ising chain
- Quantum versus Classical Annealing of Ising Spin Glasses
- Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
- Prospects for Quantum Enhancement with Diabatic Quantum Annealing
- From quantum mechanics to classical statistical physics: generalized Rokhsar-Kivelson Hamiltonians and the "Stochastic Matrix Form" decomposition
- Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
- From classical to quantum dynamics at Rokhsar-Kivelson points
- A Quantum Approach to Classical Statistical Mechanics
- Scaling and diabatic effects in quantum annealing with a D-Wave device
- Convergence theorems for quantum annealing
- Quantum Computing for Quantum Tunnelling
- Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics
- Comparative Study of the Performance of Quantum Annealing and Simulated Annealing
- Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics
- Relaxation vs. adiabatic quantum steady state preparation: which wins?
- Quantum Optimisation of Complex Systems with a Quantum Annealer
- Griffiths-McCoy singularity on the diluted Chimera graph: Monte Carlo simulations and experiments on the quantum hardware
- Quantum and classical annealing in a continuous space with multiple local minima
- Rigorous convergence condition for quantum annealing