Ising machines as hardware solvers of combinatorial optimization problems (2204.00276v1)

Abstract: Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity class NP as an Ising problem with only polynomial overhead. A scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications for a wide variety of optimization problems. In this review, we survey the current status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors, and digital hardware accelerators; dynamical-systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses.

• The paper presents hardware implementations of Ising machines using classical thermal annealing, quantum tunneling, and dynamical system evolution.
• It compares success probabilities and time-to-solution metrics on benchmark problems such as MaxCut and the Sherrington-Kirkpatrick model.
• The study highlights challenges like connectivity and decoherence while identifying future research directions in hybrid and quantum-classical approaches.

Ising Machines: Hardware Solvers for Combinatorial Optimization Problems

The paper "Ising Machines: Hardware Solvers for Combinatorial Optimization Problems" authored by Naeimeh Mohseni, Peter L. McMahon, and Tim Byrnes, provides a comprehensive review of Ising machines, which are specialized hardware platforms designed for solving combinatorial optimization problems. The authors focus on the computational significance of the Ising model, which represents a class of problems that are NP-complete, meaning they encompass some of the most challenging problems within the NP complexity class. The paper highlights various strategies and technological approaches used to construct Ising machines, including traditional computational methodologies and emerging quantum and hybrid paradigms.

The authors categorize Ising machines based on three principal computational strategies: classical thermal annealing, quantum annealing, and dynamical system evolution. The classical thermal annealing approach leverages stochastic processes to simulate thermal equilibrium at low temperatures, traditionally implemented via Monte Carlo methods on digital computers, or through dedicated analog hardware exploiting physical parallelism and noisiness intrinsic to certain materials. Quantum annealing capitalizes on quantum superposition and tunneling, employing techniques such as the adiabatic theorem, which promises a potential quantum speed-up over classical annealing for specific problem instances.

Dynamical system solvers diverge from the equilibrium strategies, engaging with the system's dynamics to locate optimal solutions through analog means, such as neural networks or nonlinear oscillators, typified by coherent Ising machines.

To assess the efficacy of these machines, the paper compares numerical results, including success probabilities and time-to-solution metrics across different types of Ising machines. These assessments draw on experimentally tested systems and benchmark problems like the Sherrington-Kirkpatrick model and MaxCut problem instances.

Classical digital approaches, such as those implemented on FPGAs and ASICs, often demonstrate superior current performance due to their mature and highly-parallelizable architecture. Meanwhile, quantum annealers like those developed by D-Wave Systems have shown advantages in tackling specific problem configurations involving deep energy barriers, suggesting a potential domain where quantum mechanics offers computational benefit.

The authors acknowledge the technological challenges faced by both classical and quantum Ising machines, especially regarding connectivity and decoherence in quantum systems, underscoring issues that must be addressed for practical wide-scale deployment.

In conclusion, while current digital and simulated annealing methods exhibit commendable performance, the paper suggests that ongoing advancements in quantum and hybrid systems could pivotally alter the current landscape. Future research directions include enhancing connectivity in hardware architectures and exploring non-stoquastic Hamiltonians for quantum approaches, which may unlock further computational potential. Hybrid quantum-classical and digital-analog methodologies remain promising frontiers, potentially bestowing the computational community with systems capable of efficiently tackling a broader array of optimization problems.