# Convergence condition of simulated quantum annealing for closed and open systems

@article{Kimura2022ConvergenceCO, title={Convergence condition of simulated quantum annealing for closed and open systems}, author={Yusuke Kimura and Hidetoshi Nishimori}, journal={Physical Review A}, year={2022} }

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…

## One Citation

### Convergence condition of simulated quantum annealing with a non-stoquastic catalyst

- Mathematics
- 2023

. The Ising model with a transverse ﬁeld and an antiferromagnetic transverse interaction is represented as a matrix in the computational basis with non-zero oﬀ-diagonal elements with both positive…

## References

SHOWING 1-10 OF 42 REFERENCES

### Mathematical foundation of quantum annealing

- Physics
- 2008

Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantum…

### Comparative study of the performance of quantum annealing and simulated annealing.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

It is pointed out that the present mapping can be extended to accommodate explicit time dependence of temperature, which is used to justify the quantum-mechanical analysis of simulated annealing by Somma, Batista, and Ortiz.

### Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics(General)

- Physics
- 2007

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or…

### Simulated quantum annealing as a simulator of nonequilibrium quantum dynamics

- PhysicsPhysical Review A
- 2021

Simulated quantum annealing based on the path-integral Monte Carlo is one of the most common tools to simulate quantum annealing on classical hardware. Nevertheless, it is in principle highly…

### Quantum and classical annealing in a continuous space with multiple local minima

- PhysicsPhysical Review A
- 2022

Abstract The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The…

### Quantum annealing in the transverse Ising model

- Physics
- 1998

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between…

### Convergence theorems for quantum annealing

- Mathematics, Physics
- 2006

We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular, the…

### Rigorous convergence condition for adiabatic and diabatic quantum annealing

- Physics, Mathematics
- 2022

. We derive a generic bound on the rate of decrease of transverse ﬁeld for adiabatic and diabatic quantum annealing to converge to the ground state of a generic Ising model when quantum annealing is…

### Study of Optimization Problems by Quantum Annealing

- Physics
- 2002

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. The idea is tested by the two models, the…

### Quantum approach to classical statistical mechanics.

- PhysicsPhysical review letters
- 2007

A new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d- dimensional quantum model, which allows the scope of standard optimization methods by unifying them under a general framework.