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Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics

Amplitude-Ensemble Quantum-Inspired Tabu Search Algorithm for Quantum Boolean Circuit Synthesis

Kuo-Chun Tseng, Ziyi Sun, Pei-Lun Ho, Yu-Chieh Cho, Yu-Syuan Liu, Wei-Chieh Lai, Wei-Chun Huang, Jen‐Shin Hong

Published Oct 5, 2025• 0 citations
Publisher

Abstract

Quantum circuit synthesis is a key technique in quantum computing. Traditional methods often generate circuits with high cost, making it crucial to produce correct and low-cost circuits efficiently. This study proposes the Amplitude-Ensemble Quantum-inspired Tabu Search (AE-QTS) algorithm for quantum Boolean circuit synthesis. AE-QTS demonstrates strong search capability with fewer parameters. Experimental results show that it outperforms other algorithms on low-bit problems and retains a certain level of synthesis ability on high-bit ones. However, the results also reveal that if the encoding frequently produces infeasible solutions, all algorithms will eventually fail, regardless of design. Therefore, future work should focus on developing encoding methods that consistently generate feasible solutions, which is essential for effectively applying metaheuristics to quantum Boolean circuit synthesis.

DOI
10.1109/smc58881.2025.11343273

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Quantum circuit synthesis is a key technique in quantum computing. Traditional methods often generate circuits with high cost, making it crucial to produce correct and low-cost circuits efficiently. This study proposes the Amplitude-Ensemble Quantum-inspired Tabu Search (AE-QTS) algorithm for quantum Boolean circuit synthesis. AE-QTS demonstrates strong search capability with fewer parameters. Experimental results show that it outperforms other algorithms on low-bit problems and retains a certain level of synthesis ability on high-bit ones. However, the results also reveal that if the encoding frequently produces infeasible solutions, all algorithms will eventually fail, regardless of design. Therefore, future work should focus on developing encoding methods that consistently generate feasible solutions, which is essential for effectively applying metaheuristics to quantum Boolean circuit synthesis.
In this study, we learned more about quantum properties from quantum and metaheuristic algorithms after conducting many experiments. We then propose an improved version of Quantum-inspired Tabu Search (QTS), which en-hances the utilization of population information. The new version is called “Amplitude-Ensemble” QTS (AE-QTS). This makes AE-QTS more similar to the real quantum search algorithm, Grover Search Algorithm, in abstract concept, while keeping the simplicity of the algorithm. Later, we demonstrate the AE-QTS on the classical combinatorial optimization 0/1 knapsack problem. Experimental results show that the AE-QTS outperforms other algorithms, including the QTS, by at least an average increase of nearly 20% in all cases and even by 30% in some cases. Even as the problem complexity increases, the quality of the solutions found by our method remains superior to that of the QTS. These results confirm that our method has better search performance.
Reversible logic plays an important role in quantum computation, which is a promising research field. The reversible logic synthesis problem focuses on generating a reversible circuit automatically and finding the lowest cost when an output function is given. The synthesis of reversible logic circuits can be formulated as a combinatorial optimization problem. This paper proposes a new evolutionary algorithm for synthesizing reversible circuits based on Quantum-Inspired Tabu Search Algorithm (QTS). The proposed algorithm uses the QTS-based approach to find fewer gates and reduce the cost of reversible circuits. This method is simpler, has better performance in computational cost, and reduce the gate counts of reversible circuits. This paper also compares experimental results with other heuristic and evolutionary algorithms. The final outcome shows that the QTS-based approach performs much better than other algorithms.
Reversible circuits are the essential building blocks of quantum computers and have zero energy dissipation. However, there is no general rule on how to synthesize an effective circuit with minimal cost. Many researchers have placed a high value on the design of algorithms for reversible circuit synthesis as it is the fundamental component to implement in many paradigms, such as Shor’s algorithm. In this paper, the knowledge navigated quantum-inspired tabu search algorithm (KNQTS) is proposed to synthesize several benchmark functions. KNQTS is a quantum-inspired algorithm with the concept of getting closer to the best solution and keeping away from the worst solution, and it has a great search ability. Furthermore, the proposed algorithm uses self-adaptive, global-best guided and Quantum-Not gate mechanisms to make all procedures more efficient and avoid sticking to the local optimum. This paper also compares the KNQTS approach’s experimental results with those obtained via other metaheuristics and previous algorithms. Finally, the result shows that the proposed KNQTS method outperforms other state-of-the-art methods and achieves the same functionality at a lower cost. The solutions are optimal or near-optimal.
It is important to construct quantum algorithms within shallow-depth quantum circuits due to the current imperfections and decoherence in quantum devices. Efficient quantum circuit synthesis and optimization are critical tasks that generate relatively small quantum circuits tailored to specific requirements. However, an efficient circuit may vary depending on the physical realization platforms of quantum computers. For example, the Clifford+T gate library has recently gained prominence for its superior fault tolerance and error correction capabilities, but the T gate dominates circuit execution time. Therefore, the objectives of synthesis algorithms in this gate set include reducing T-depth and T-count, as well as overall circuit depth and gate count. Most traditional synthesis methods produce a single optimized circuit. In contrast, this study introduces a multi-objective quantum-inspired tabu search algorithm in quantum circuit synthesis to construct a diverse set of optimized circuits based on four distinct metrics. The values of these metrics in the optimized circuit display the entanglement relationship, and the proposed method simulates the formula to assist in building the entangled optimal circuit. Results show that the construction of the Pareto front can flexibly offer a variety of functionally equivalent circuits that adapt to advancements in quantum technology. Providing multiple optimized circuit structures facilitates circuit replacement and further simplification, thereby enhancing the development of quantum computing.
The quantum circuit is the prime factor to realize quantum computation. This paper proposes a novel quantum-inspired evolutionary computation method to synthesize quantum circuits effectively and efficiently. Recently, the Clifford+T gate library has become popular, as the T gate has a better fault-tolerant and error correction efficacy, which is essential to near-term quantum computation. The proposed quantum-inspired evolutionary computation is more flexible in constructing diverse solutions than the classical synthesis method. The entangled local search mechanism further enhances the ability to discover the optimal solutions on an efficient frontier. The encoding can be slightly changed to achieve various gate libraries circuit synthesis in the quantum or reversible Boolean circuits. The experiments demonstrate that our proposed method can be more effective in composing a compact quantum circuit than the state-of-the-art method. Meanwhile, the T-depth can attain an optimal value without ancilla bits. Furthermore, we provide an illustration to construct the function equivalent quantum circuit with the NOT, CNOT, Controlled-Square-Root-of-NOT quantum gate library (NCV). We also conduct exhaustion to prove that our synthesized circuit is an optimal solution, requiring far fewer resources in time and evaluation than exhaustion.
Many metaheuristic algorithms have been proposed to solve combinatorial and numerical optimization problems. Most optimization problems have high dependence, meaning that variables are strongly dependent on one another. If a method were to attempt to optimize each variable independently, its performance would suffer significantly. When traditional optimization techniques are applied to highdependence problems, they experience difficulty in finding the global optimum. To address this problem, this paper proposes a novel metaheuristic algorithm, the entanglement-enhanced quantum-inspired tabu search algorithm (Entanglement-QTS), which is based on the quantum-inspired tabu search (QTS) algorithm and the feature of quantum entanglement. Entanglement-QTS differs from other quantum-inspired evolutionary algorithms in that its Q-bits have entangled states, which can express a high degree of correlation, rendering the variables more intertwined. Entangled Q-bits represent a state-of-the-art idea that can significantly improve the treatment of multimodal and high-dependence problems. Entanglement-QTS can discover optimal solutions, balance diversification and intensification, escape numerous local optimal solutions by using the quantum not gate, reinforce the intensification effect by local search and entanglement local search, and manage strong-dependence problems and accelerate the optimization process by using entangled states. This paper uses nine benchmark functions to test the search ability of the entanglement-QTS algorithm. The results demonstrate that Entanglement-QTS outperforms QTS and other metaheuristic algorithms in both its effectiveness at finding the global optimum and its computational efficiency.