Quantum annealing (QA) is a promising quantum computing paradigm for solving optimization problems. However, the performance of QA is often limited by issues such as slow convergence rates and sensitivity to parameter settings. This paper presents a novel optimization method designed to address these limitations. The approach introduces refined parameters and an adaptive strategy to enhance the algorithm's convergence speed and solution accuracy. We explore the application of this optimized QA method to complex problems, demonstrating its potential for improved performance. The core of the optimization lies in modifying the annealing schedule and incorporating a dynamic adjustment of the magnetic field strength, denoted as $H(t)$ , where $t$ represents time. The objective function to be minimized is typically represented as $E[s]$ , where $s$ is the state vector of the quantum annealer. We introduce a variance reduction technique, denoted as $\sigma(t)$ , which is dynamically adjusted based on the error estimates of the current state. The overall optimization process can be summarized as: $\min_{s} E[s] \quad \text{subject to} \quad \frac{dS}{dt} = - \beta(t) E[s] - \gamma(t) H(t)s$ where $\beta(t)$ is the annealing rate and $\gamma(t)$ is the magnetic field strength. The adaptive strategy involves updating $\beta(t)$ and $\gamma(t)$ based on the error in the current solution, aiming to reduce the variance $\sigma(t)$ and improve the convergence. The theoretical analysis suggests that this approach can significantly reduce the computational cost and improve the solution quality compared to traditional QA methods. Furthermore, we investigate the impact of different parameter settings on the algorithm's performance, highlighting the importance of careful tuning for optimal results. The results demonstrate a notable improvement in solution quality and convergence speed across various benchmark problems.Quantum annealing (QA) is a promising quantum computing paradigm for solving optimization problems. However, the performance of QA is often limited by issues such as slow convergence rates and sensitivity to parameter settings. This paper presents a novel optimization method designed to address these limitations. The approach introduces refined parameters and an adaptive strategy to enhance the algorithm's convergence speed and solution accuracy. We explore the application of this optimized QA method to complex problems, demonstrating its potential for improved performance. The core of the optimization lies in modifying the annealing schedule and incorporating a dynamic adjustment of the magnetic field strength, denoted as $H(t)$, where $t$ represents time. The objective function to be minimized is typically represented as $E[s]$, where $s$ is the state vector of the quantum annealer. We introduce a variance reduction technique, denoted as $\sigma(t)$, which is dynamically adjusted based on the error estimates of the current state. The overall optimization process can be summarized as: $\min_{s} E[s] \quad \text{subject to} \quad \frac{dS}{dt} = - \beta(t) E[s] - \gamma(t) H(t)s$ where $\beta(t)$ is the annealing rate and $\gamma(t)$ is the magnetic field strength. The adaptive strategy involves updating $\beta(t)$ and $\gamma(t)$ based on the error in the current solution, aiming to reduce the variance $\sigma(t)$ and improve the convergence. The theoretical analysis suggests that this approach can significantly reduce the computational cost and improve the solution quality compared to traditional QA methods. Furthermore, we investigate the impact of different parameter settings on the algorithm's performance, highlighting the importance of careful tuning for optimal results. The results demonstrate a notable improvement in solution quality and convergence speed across various benchmark problems.

Sep 3, 20260 citations

Beyond Standard Quantum Annealing

Tameem Albash

Bulletin of the American Physical SocietyMar 4, 20200 citations

Quantum annealing optimization and geophysical inverse method

Meigen Zhang

The idea of Quantum Annealing(QA),which is based on the mechanism of quantum transition tunneling effect and not same with the annealing theory of simulated thermal annealing,is a recent offspring of the celebrated simulated thermal annealing by Kirkpatrick.This paper,firstly,summarizes the basic differences between Quantum Annealing and Simulated Annealing;and then mainly addresses the attention to the practical developments of the application in optimization such as Ising spin glass,Traveling Salesman Problem,Boolean Satisfiability Problem and so on,discusses the details of the annealing process of Quantum Annealing and its compare with Simulated Annealing on test problems;subsequently,expatiates the geophysical inverse theory and method corresponding to Quantum Annealing,discusses the setting of parameters such as Temperature and Transverse field,compares the probabilities of being on configurations with different transverse fields and potential energies;finally briefly summarizes the prospects and the existent problems of using Quantum Annealing in geophysical inverse problem.The idea of Quantum Annealing(QA),which is based on the mechanism of quantum transition tunneling effect and not same with the annealing theory of simulated thermal annealing,is a recent offspring of the celebrated simulated thermal annealing by Kirkpatrick.This paper,firstly,summarizes the basic differences between Quantum Annealing and Simulated Annealing;and then mainly addresses the attention to the practical developments of the application in optimization such as Ising spin glass,Traveling Salesman Problem,Boolean Satisfiability Problem and so on,discusses the details of the annealing process of Quantum Annealing and its compare with Simulated Annealing on test problems;subsequently,expatiates the geophysical inverse theory and method corresponding to Quantum Annealing,discusses the setting of parameters such as Temperature and Transverse field,compares the probabilities of being on configurations with different transverse fields and potential energies;finally briefly summarizes the prospects and the existent problems of using Quantum Annealing in geophysical inverse problem.

Progress in geophysicsJan 1, 20072 citations

Greedy parameter optimization for diabatic quantum annealing

Tadashi Kadowaki, Hidetoshi Nishimori

A shorter processing time is desirable for quantum computation to minimize the effects of noise. We propose a simple procedure to variationally determine a set of parameters in the transverse-field Ising model for quantum annealing (QA) appended with a field along the [Formula: see text]-axis. The method consists of greedy optimization of the signs of coefficients of the [Formula: see text]-field term based on the outputs of short annealing processes. We test the idea in the ferromagnetic system with all-to-all couplings and spin-glass problems, and find that the method outperforms the traditional form of QA and simulated annealing in terms of the success probability and the time to solution, in particular, in the case of shorter annealing times, achieving the goal of improved performance while avoiding noise. The non-stoquastic [Formula: see text] term can be eliminated by a rotation in the spin space, resulting in a non-trivial diabatic control of the coefficients in the stoquastic transverse-field Ising model, which may be feasible for experimental realization. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.A shorter processing time is desirable for quantum computation to minimize the effects of noise. We propose a simple procedure to variationally determine a set of parameters in the transverse-field Ising model for quantum annealing (QA) appended with a field along the [Formula: see text]-axis. The method consists of greedy optimization of the signs of coefficients of the [Formula: see text]-field term based on the outputs of short annealing processes. We test the idea in the ferromagnetic system with all-to-all couplings and spin-glass problems, and find that the method outperforms the traditional form of QA and simulated annealing in terms of the success probability and the time to solution, in particular, in the case of shorter annealing times, achieving the goal of improved performance while avoiding noise. The non-stoquastic [Formula: see text] term can be eliminated by a rotation in the spin space, resulting in a non-trivial diabatic control of the coefficients in the stoquastic transverse-field Ising model, which may be feasible for experimental realization. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

arXiv:2111.13287Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesDec 4, 202215 citations

Error tolerance of quantum annealing

秀稔西森, Hidetoshi Nishimori

Jan 1, 20160 citations

H(t)

, where

t

represents time. The objective function to be minimized is typically represented as

E[s]

, where

s

is the state vector of the quantum annealer. We introduce a variance reduction technique, denoted as

\sigma(t)

, which is dynamically adjusted based on the error estimates of the current state. The overall optimization process can be summarized as:

\min_{s} E[s] \quad \text{subject to} \quad \frac{dS}{dt} = - \beta(t) E[s] - \gamma(t) H(t)s

where

\beta(t)

is the annealing rate and

\gamma(t)

is the magnetic field strength. The adaptive strategy involves updating

\beta(t)

and

\gamma(t)

based on the error in the current solution, aiming to reduce the variance

\sigma(t)

and improve the convergence. The theoretical analysis suggests that this approach can significantly reduce the computational cost and improve the solution quality compared to traditional QA methods. Furthermore, we investigate the impact of different parameter settings on the algorithm's performance, highlighting the importance of careful tuning for optimal results. The results demonstrate a notable improvement in solution quality and convergence speed across various benchmark problems.