How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

Oku, Daisuke; Tawada, Masashi; Tanaka, Shu; Togawa, Nozomu

doi:10.1109/tc.2020.3045112

Cited by 16 publications

(13 citation statements)

References 39 publications

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“…Examples include simulated annealing (SA)-based machines [13]- [17], quantum annealing ma-chines [18]- [20], and photonics-based machines [21]- [24]. The features of the various Ising machines are summarized in [30].…”

Section: A Motivationmentioning

confidence: 99%

“…The same trends are observed for all other values n and c for both types of encoding. Moreover, the values of A necessary to obtain a high FS rate are smaller for unary encoding than binary encoding, except for (n, c) = (20,30). For the problem with (n, c) = (800, 1200), the FS rate approaches 1 around A = 1.6 × 10 3 in binary encoding [Fig.…”

Section: A A-dependences Of Feasible Solution Rates and Average Energiesmentioning

confidence: 99%

“…This feature becomes more pronounced as the values of n and c increase. On the other hand, in one-hot encoding, few FSs are obtained even when the parameter A is large except for (n, c) = (20,30). That is, FSs can be obtained with a high frequency in binary encoding and unary encoding at a sufficiently large A, whereas one-hot encoding cannot provide FSs for problems with large n and c.…”

Section: A A-dependences Of Feasible Solution Rates and Average Energiesmentioning

confidence: 99%

“…Table 4 also shows the mode values of α 1 and α 2 . Note that, in one-hot encoding, optimal hyperparameters cannot be determined since a sufficient number of FSs were not obtained except for the case of (n, c) = (20,30).…”

Section: Appendix a Optimal Values Of The Hyperparametersmentioning

confidence: 99%

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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%

Section: A A-dependences Of Feasible Solution Rates and Average Energiesmentioning

confidence: 99%

Section: A A-dependences Of Feasible Solution Rates and Average Energiesmentioning

confidence: 99%

Section: Appendix a Optimal Values Of The Hyperparametersmentioning

confidence: 99%

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

et al. 2021

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“…When a logical Ising model is converted into a physical Ising model, the logical Ising model's topology is converted into the physical Ising model's topology (topology conversion) [20]- [22]. The bit-widths of interaction and external magnetic field coefficients of a logical Ising model need to be converted into the those of a physical Ising model (bitwidth conversion) [23]. To solve a combinatorial optimization problem with using annealing machines, both topology and bit-width conversions are necessary.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Combined Bit-Width Reducing Method for Ising Models

Yachi

Tawada

Togawa

2023

IEICE Trans. Inf. & Syst.

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Annealing machines such as quantum annealing machines and semiconductor-based annealing machines have been attracting attention as an efficient computing alternative for solving combinatorial optimization problems. They solve original combinatorial optimization problems by transforming them into a data structure called an Ising model. At that time, the bit-widths of the coefficients of the Ising model have to be kept within the range that an annealing machine can deal with. However, by reducing the Ising-model bit-widths, its minimum energy state, or ground state, may become different from that of the original one, and hence the targeted combinatorial optimization problem cannot be well solved. This paper proposes an effective method for reducing Ising model's bit-widths. The proposed method is composed of two processes: First, given an Ising model with large coefficient bit-widths, the shift method is applied to reduce its bit-widths roughly. Second, the spin-adding method is applied to further reduce its bit-widths to those that annealing machines can deal with. Without adding too many extra spins, we efficiently reduce the coefficient bit-widths of the original Ising model. Furthermore, the ground state before and after reducing the coefficient bit-widths is not much changed in most of the practical cases. Experimental evaluations demonstrate the effectiveness of the proposed method, compared to existing methods.

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Utilizing Graph Sparsification for Pre-processing in Max Cut QUBO Solver

Suppakitpaisarn,

Hao

2024

Lecture Notes in Computer Science

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How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

Cited by 16 publications

References 39 publications

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

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

An Efficient Combined Bit-Width Reducing Method for Ising Models

Utilizing Graph Sparsification for Pre-processing in Max Cut QUBO Solver

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