Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

Shirai, Tatsuhiko; Tanaka, Shu; Togawa, Nozomu

doi:10.1109/access.2020.3040017

Cited by 13 publications

(3 citation statements)

References 49 publications

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“…Many underlying algorithms for Ising machines have been proposed [26]- [28]. Recently, proposals have also been made for efficient input formats to Ising machines based on the operation principle of Ising machines [29]. Examples include simulated annealing (SA)-based machines [13]- [17], quantum annealing ma-chines [18]- [20], and photonics-based machines [21]- [24].…”

Section: A Motivationmentioning

confidence: 99%

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

et al. 2021

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The differences in performance among binary-integer encodings in an Ising machine, which can solve combinatorial optimization problems, are investigated. Many combinatorial optimization problems can be mapped to find the lowest-energy (ground) state of an Ising model or its equivalent model, the Quadratic Unconstrained Binary Optimization (QUBO). Since the Ising model and QUBO consist of binary variables, they often express integers as binary when using Ising machines. A typical example is the combinatorial optimization problem under inequality constraints. Here, the quadratic knapsack problem is adopted as a prototypical problem with an inequality constraint. It is solved using typical binaryinteger encodings: one-hot encoding, binary encoding, and unary encoding. Unary encoding shows the best performance for large-sized problems.

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Section: A Motivationmentioning

confidence: 99%

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

et al. 2021

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“…Andriyash et al [1] address the disparate tunneling dynamics of chains with different lengths in a problem by utilizing a technique called annealing offsets, where the anneal of qubits belonging to longer chains is delayed, thereby increasing the relative tunneling energy of such chains. For simulated-annealing-based Ising machines, Shirai et al [19] propose a formula based on statistical mechanics for the coupling strength of each chain and experimentally show that their proposed methods outperforms two existing methods on a set of benchmarking problems.…”

Section: Previous Workmentioning

confidence: 99%

Logical qubit implementation for quantum annealing: augmented Lagrangian approach

Djidjev

2023

Quantum Sci. Technol.

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Solving optimization problems on quantum annealers usually requires each variable of the problem to be represented by a connected set of qubits called a logical qubit or a chain. Chain weights, in the form of ferromagnetic coupling between the chain qubits, are applied so that the physical qubits in a chain favor taking the same value in low energy samples. Assigning a good chain-strength value is crucial for the ability of quantum annealing to solve hard problems, but there are no general methods for computing such a value and, even if an optimal value is found, it may still not be suitable by being too large for accurate annealing results. In this paper, we propose an optimization-based approach for producing suitable logical qubits representations that results in smaller chain weights and show that the resulting optimization problem can be successfully solved using the augmented Lagrangian method. Experiments on the D-Wave Advantage system and the maximum clique problem on random graphs show that our approach outperforms both the default D-Wave method for chain-strength assignment as well as the quadratic penalty method.

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“…The specifications of the various Ising machines are summarized in [32], [33]. Although various approaches have been proposed in previous research to overcome the limitations due to the number of spins [34]- [40] and the topology [41]- [47], few studies have been devoted to overcoming the bit-width limitation.…”

Section: B Ising Machinementioning

confidence: 99%

Dynamical Process of a Bit-Width Reduced Ising Model With Simulated Annealing

Kikuchi,

Togawa,

Tanaka

2023

IEEE Access

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Ising machines have attracted attention as fast and high-precision solvers for combinatorial optimization problems, which are often formulated as ground-state (lowest-energy) search problems of the Ising model. Since the bit-width of coefficients on Ising machines is limited, the Ising model must be transformed into a bit-width reduced (BWR) Ising model which reduces the coefficients. In a bit-width reduction method, which adds auxiliary spins, the ground state of the BWR Ising model is theoretically the same as the Ising model before bit-width reduction (original Ising model). However, the dynamical process of the BWR Ising model towards the ground state remains to be elucidated. Therefore, using simulated annealing (SA), we compared the dynamical processes of these models. The result shows that the dynamical process differs significantly by model. Analysis from the viewpoint of statistical mechanics found that the BWR Ising model has two characteristic properties: an effective temperature and a slow relaxation. It is suggested that these properties alter the effective temperature and spin flip probability in the BWR Ising model, contributing to the dynamical differences. Therefore, to obtain the same dynamical process as the original Ising model, we proposed SA parameters for the BWR Ising model. We demonstrated the proposed SA parameter using a square lattice Ising model, in which the interaction and magnetic field were set uniformly to the same positive values or randomly. As experimental evaluations, the dynamical process of the BWR Ising model became closer to that of the original Ising model.

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Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

Cited by 13 publications

References 49 publications

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

Logical qubit implementation for quantum annealing: augmented Lagrangian approach

Dynamical Process of a Bit-Width Reduced Ising Model With Simulated Annealing

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