arXiv subjects

Nozomu Togawa

Publications and source records attributed to Nozomu Togawa.

14 recordsLinked to original sources

arXiv2026

Mitigating Precision Errors in Quantum Annealing via Coefficient Reduction of Embedded Hamiltonians

Quantum annealing is a quantum algorithm to solve combinatorial optimization problems. In the current quantum annealing devices, the dynamic range of the input Ising Hamiltonian, defined as the ratio of the largest to the smallest coefficient, significantly affects the quality of the output solution due to limited hardware precision. Several methods have been proposed to reduce the dynamic range by reducing large coefficients in the Ising Hamiltonian. However, existing studies do not take into account minor-embedding, which is an essential process in current quantum annealers. In this study, we revisit three existing coefficient-reduction methods under the constraints of minor-embedding. We evaluate to what extent these methods reduce the dynamic range of the minor-embedded Hamiltonian and improve the sample quality obtained from the D-Wave Advantage quantum annealer. The results show that, on the set of problems tested in this study, the interaction-extension method effectively improves the sample quality by reducing the dynamic range, while the bounded-coefficient integer encoding and the augmented Lagrangian method have only limited effects. Furthermore, we empirically show that reducing external field coefficients at the logical Hamiltonian level is not required in practice, since minor-embedding automatically has the role of reducing them. These findings suggest future directions for enhancing the sample quality of quantum annealers by suppressing hardware errors through preprocessing of the input problem.

quant-ph↗

arXiv2025

Compressed space quantum approximate optimization algorithm for constrained combinatorial optimization

Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of combinatorial optimization problems (COPs). However, effectively dealing with constraints of COPs remains a significant challenge. Existing methods, such as tailoring mixing operators, are typically limited to specific constraint types, like one-hot constraints. To address these limitations, we introduce a method for engineering a compressed space that represents the feasible solution space with fewer qubits than the original. Our approach includes a scalable technique for determining the unitary transformation between the compressed and original spaces on gate-based quantum computers. We then propose compressed space QAOA, which seeks near-optimal solutions within this reduced space, while utilizing the Ising model formulated in the original Hilbert space. Experimental results on a quantum simulator demonstrate the effectiveness of our method in solving various constrained COPs.

quant-ph↗

arXiv2025

Effectiveness of Hybrid Optimization Method for Quantum Annealing Machines

To enhance the performance of quantum annealing machines, several methods have been proposed to reduce the number of spins by fixing spin values through preprocessing. We proposed a hybrid optimization method that combines a simulated annealing (SA)-based non-quantum-type Ising machine with a quantum annealing machine. However, its applicability remains unclear. Therefore, we evaluated the performance of the hybrid method on large-size Ising models and analyzed its characteristics. The results indicate that the hybrid method improves upon solutions obtained by the preprocessing SA, even if the Ising models cannot be embedded in the quantum annealing machine. We analyzed the method from three perspectives: preprocessing, spin-fixed sub-Ising model generation method, and the accuracy of the quantum annealing machine. From the viewpoint of the minimum energy gap, we found that solving the sub-Ising model with a quantum annealing machine results in a higher solution accuracy than solving the original Ising model. Additionally, we demonstrated that the number of fixed spins and the accuracy of the quantum annealing machine affect the dependency of the solution accuracy on the sub-Ising model size.

cond-mat.stat-mech↗

arXiv2024

Toward Practical Benchmarks of Ising Machines: A Case Study on the Quadratic Knapsack Problem

Combinatorial optimization has wide applications from industry to natural science. Ising machines bring an emerging computing paradigm for efficiently solving a combinatorial optimization problem by searching a ground state of a given Ising model. Current cutting-edge Ising machines achieve fast sampling of near-optimal solutions of the max-cut problem. However, for problems with additional constraint conditions, their advantages have been hardly shown due to difficulties in handling the constraints. In this work, we focus on benchmarks of Ising machines on the quadratic knapsack problem (QKP). To bring out their practical performance, we propose fast two-stage post-processing for Ising machines, which makes handling the constraint easier. Simulation based on simulated annealing shows that the proposed method substantially improves the solving performance of Ising machines and the improvement is robust to a choice of encoding of the constraint condition. Through evaluation using an Ising machine called Amplify Annealing Engine, the proposed method is shown to dramatically improve its solving performance on the QKP. These results are a crucial step toward showing advantages of Ising machines on practical problems involving various constraint conditions.

cond-mat.stat-mech↗

arXiv2024

Linearizing Binary Optimization Problems Using Variable Posets for Ising Machines

Ising machines are next-generation computers expected to efficiently sample near-optimal solutions of combinatorial optimization problems. Combinatorial optimization problems are modeled as quadratic unconstrained binary optimization (QUBO) problems to apply an Ising machine. However, current state-of-the-art Ising machines still often fail to output near-optimal solutions due to the complicated energy landscape of QUBO problems. Furthermore, the physical implementation of Ising machines severely restricts the size of QUBO problems to be input as a result of limited hardware graph structures. In this study, we take a new approach to these challenges by injecting auxiliary penalties preserving the optimum, which reduces quadratic terms in QUBO objective functions. The process simultaneously simplifies the energy landscape of QUBO problems, allowing the search for near-optimal solutions, and makes QUBO problems sparser, facilitating encoding into Ising machines with restriction on the hardware graph structure. We propose linearization of QUBO problems using variable posets as an outcome of the approach. By applying the proposed method to synthetic QUBO instances and to multi-dimensional knapsack problems, we empirically validate the effects on enhancing minor-embedding of QUBO problems and the performance of Ising machines.

math.OC↗

arXiv2024

Post-processing variationally scheduled quantum algorithm for constrained combinatorial optimization problems

We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a quantum annealer or gate-type quantum device. Variational methods are used to find an optimal schedule function that leads to high-quality solutions in a short amount of time. Post-processing techniques convert the output solutions of the quantum devices to satisfy the constraints of the COPs. pVSQA combines the variational methods and the post-processing technique. We obtain a sufficient condition for constrained COPs to apply pVSQA based on a greedy post-processing algorithm. We apply the proposed method to two constrained NP-hard COPs: the graph partitioning problem and the quadratic knapsack problem. pVSQA on a simulator shows that a small number of variational parameters is sufficient to achieve a (near-)optimal performance within a predetermined operation time. Then building upon the simulator results, we implement pVSQA on a quantum annealer and a gate-type quantum device. The experimental results demonstrate the effectiveness of our proposed method.

quant-ph↗

arXiv2023

Hybrid Optimization Method Using Simulated-Annealing-Based Ising Machine and Quantum Annealer

Ising machines have the potential to realize fast and highly accurate solvers for combinatorial optimization problems. They are classified based on their internal algorithms. Examples include simulated-annealing-based Ising machines (non-quantum-type Ising machines) and quantum-annealing-based Ising machines (quantum annealers). Herein we propose a hybrid optimization method, which utilizes the advantages of both types. In this hybrid optimization method, the preprocessing step is performed by solving the non-quantum-annealing Ising machine multiple times. Then sub-Ising models with a reduced size by spin fixing are solved using a quantum annealer. The performance of the hybrid optimization method is evaluated via simulations using Simulated Annealing (SA) as a non-quantum-type Ising machine and D-Wave Advantage as a quantum annealer. Additionally, we investigate the parameter dependence of the proposed hybrid optimization method. The hybrid optimization method outperforms the preprocessing SA and the quantum annealing machine alone in fully connected random Ising models.

cond-mat.stat-mech↗

arXiv2023

QuDASH: Quantum-inspired rate adaptation approach for DASH video streaming

Internet traffic is dramatically increasing with the development of network technologies and video streaming traffic accounts for large amount within the total traffic, which reveals the importance to guarantee the quality of content delivery service. Based on the network conditions, adaptive bitrate (ABR) control is utilized as a common technique which can choose the proper bitrate to ensure the video streaming quality. In this paper, new bitrate control method, QuDASH is proposed by taking advantage of the emerging quantum technology. In QuDASH, the adaptive control model is developed using the quadratic unconstrained binary optimization (QUBO), which aims at increasing the average bitrate and decreasing the video rebuffering events to maximize the user quality of experience (QoE). In order to formulate the video control model, first the QUBO terms of different factors are defined regarding video quality, bitrate change, and buffer condition. Then, all the individual QUBO terms are merged to generate an objective function. By minimizing the QUBO objective function, the bitrate choice is determined from the solution. The control model is solved by Digital Annealer, which is a quantum-inspired computing technology. The evaluation of the proposed method is carried out by simulation with the throughput traces obtained in real world under different scenarios and the comparison with other methods is conducted. Experiment results demonstrated that the proposed QuDASH method has better performance in terms of QoE compared with other advanced ABR methods. In 68.2% of the examined cases, QuDASH achieves the highest QoE results, which shows the superiority of the QuDASH over conventional methods.

cs.NI↗

arXiv2023

Dynamical process of a bit-width reduced Ising model with simulated annealing

Ising machines have attracted attention as efficient solvers for combinatorial optimization problems, which are formulated as ground-state (lowest-energy) search problems of the Ising model. Due to the limited bit-width of coefficients on Ising machines, the Ising model must be transformed into a bit-width reduced (BWR) Ising model. According to previous research, the bit-width reduction method, which adds auxiliary spins, ensures that the ground state of the BWR Ising model is theoretically the same as the Ising model before bit-width reduction (original Ising model). However, while the dynamical process is closely related to solution accuracy, how the BWR Ising model progresses towards the ground state remains to be elucidated. Therefore, we compared the dynamical processes of these models using simulated annealing (SA). Our findings reveal significant differences in the dynamical process across models. Analysis from the viewpoint of statistical mechanics found that the BWR Ising model has two characteristic properties: an effective temperature and a slow relaxation. These properties alter the temperature schedule and spin flip probability in the BWR Ising model, leading to differences in the dynamical process. 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 parameters using a square lattice Ising model, in which all coefficients were set uniformly to the same positive values or randomly. Our experimental evaluations demonstrated that the dynamical process of the BWR and original Ising model became closer.

cond-mat.stat-mech↗

arXiv2022

Fast Hyperparameter Tuning for Ising Machines

In this paper, we propose a novel technique to accelerate Ising machines hyperparameter tuning. Firstly, we define Ising machine performance and explain the goal of hyperparameter tuning in regard to this performance definition. Secondly, we compare well-known hyperparameter tuning techniques, namely random sampling and Tree-structured Parzen Estimator (TPE) on different combinatorial optimization problems. Thirdly, we propose a new convergence acceleration method for TPE which we call "FastConvergence".It aims at limiting the number of required TPE trials to reach best performing hyperparameter values combination. We compare FastConvergence to previously mentioned well-known hyperparameter tuning techniques to show its effectiveness. For experiments, well-known Travel Salesman Problem (TSP) and Quadratic Assignment Problem (QAP) instances are used as input. The Ising machine used is Fujitsu's third generation Digital Annealer (DA). Results show, in most cases, FastConvergence can reach similar results to TPE alone within less than half the number of trials.

cs.LG↗

arXiv2022

Towards optimization of photonic-crystal surface-emitting lasers via quantum annealing

Photonic-crystal surface-emitting lasers (PCSELs), which utilize a two-dimensional (2D) optical resonance inside a photonic crystal for lasing, feature various outstanding functionalities such as single-mode high-power operation and arbitrary control of beam polarizations. Although most of the previous designs of PCSELs employ spatially uniform photonic crystals, it is expected that lasing performance can be further improved if it becomes possible to optimize the spatial distribution of photonic crystals. In this paper, we investigate the structural optimization of PCSELs via quantum annealing towards high-power, narrow-beam-divergence operation with linear polarization. The optimization of PCSELs is performed by the iteration of the following three steps: (1) time-dependent 3D coupled-wave analysis of lasing performance, (2) formulation of the lasing performance via a factorization machine, and (3) selection of optimal solution(s) via quantum annealing. By using this approach, we successfully discover an advanced PCSEL with a non-uniform spatial distribution of the band-edge frequency and injection current, which simultaneously enables higher output power, a narrower divergence angle, and a higher linear polarization ratio than conventional uniform PCSELs. Our results potentially indicate the universal applicability of quantum annealing, which has been mainly applied to specific types of discrete optimization problems so far, for various physics and engineering problems in the field of smart manufacturing.

physics.app-ph↗

arXiv2022

R-HTDetector: Robust Hardware-Trojan Detection Based on Adversarial Training

Hardware Trojans (HTs) have become a serious problem, and extermination of them is strongly required for enhancing the security and safety of integrated circuits. An effective solution is to identify HTs at the gate level via machine learning techniques. However, machine learning has specific vulnerabilities, such as adversarial examples. In reality, it has been reported that adversarial modified HTs greatly degrade the performance of a machine learning-based HT detection method. Therefore, we propose a robust HT detection method using adversarial training (R-HTDetector). We formally describe the robustness of R-HTDetector in modifying HTs. Our work gives the world-first adversarial training for HT detection with theoretical backgrounds. We show through experiments with Trust-HUB benchmarks that R-HTDetector overcomes adversarial examples while maintaining its original accuracy.

cs.CR↗

arXiv2022

Node-wise Hardware Trojan Detection Based on Graph Learning

In the fourth industrial revolution, securing the protection of the supply chain has become an ever-growing concern. One such cyber threat is a hardware Trojan (HT), a malicious modification to an IC. HTs are often identified in the hardware manufacturing process, but should be removed earlier, when the design is being specified. Machine learning-based HT detection in gate-level netlists is an efficient approach to identify HTs at the early stage. However, feature-based modeling has limitations in discovering an appropriate set of HT features. We thus propose NHTD-GL in this paper, a novel node-wise HT detection method based on graph learning (GL). Given the formal analysis of HT features obtained from domain knowledge, NHTD-GL bridges the gap between graph representation learning and feature-based HT detection. The experimental results demonstrate that NHTD-GL achieves 0.998 detection accuracy and outperforms state-of-the-art node-wise HT detection methods. NHTD-GL extracts HT features without heuristic feature engineering.

cs.CR↗

arXiv2020

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

We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground (lowest-energy) state of the logical Ising model. When connectivity is restricted on Ising machines, ME is required for mapping from the logical Ising model to a physical Ising model, which corresponds to a specific Ising machine. Herein we discuss the guiding principle of ME design to achieve a high performance in Ising machines. We derive the proposed ME based on a theoretical argument of statistical mechanics. The performance of the proposed ME is compared with two existing types of MEs for different benchmarking problems. Simulated annealing shows that the proposed ME outperforms existing MEs for all benchmarking problems, especially when the distribution of the degree in a logical Ising model has a large standard deviation. This study validates the guiding principle of using statistical mechanics for ME to realize fast and high-precision solvers for combinatorial optimization problems.

cond-mat.stat-mech↗