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Computers, materials & continua/Computers, materials & continua (Print)

Quantum-Inspired Optimization with Hamming-Distance Reinforcement for Hypercube-Encoded Reversible Circuit Synthesis

Yu-Chi Jiang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Quantum logic reversible synthesis is a fundamental operation in quantum computing. One of the most challenging issues in this field resides in navigating the immense search space to synthesize the most compact circuit configurations, which are critical for realizing reliable, noise-free, and error-free quantum computing systems. To address this challenge, this study proposes a novel hypercube-encoded quantum-inspired optimization framework to formulate the synthesis task as a trajectory-finding process. This structure-informed domain knowledge transformation delivers exceptional search direction guidance, moving away from blind, black-box exploration. Specifically, by mapping the reversible functions onto the hypercube architecture, the framework embeds explicit dual Hamming-distance (HMD) guidance metrics into a global-best guided quantum-inspired tabu search (GQTS) engine. To minimize computational cost and enhance search efficiency, the framework incorporates a domain-informed initialization and couples a streamlined two-particle configuration with a global-best mechanism, thereby amplifying the efficiency of the underlying quantum-inspired updating mechanism to escape local optima and rapidly converge once a successfully synthesized superior path is locked. Under an online step relaxation mechanism, the framework preserves exceptional structural optimization flexibility without altering the underlying hypercube representation. The framework’s significance is rigorously evaluated against both rigid hypercube rule-based methods and generic randomized search-based heuristics, using gate count and exact-optimality as primary evaluation metrics. Extensive ablation studies first validate the individual and synergistic contributions of each core algorithmic component. Experimental results demonstrate that for the complete set of 3-bit reversible functions, the proposed HMD-guided GQTS (HMD-GQTS) framework achieves over 98% exact-optimal circuits in a single fine-tuned sweep, with selective retries attaining 100% exhaustive optimal coverage. Furthermore, for typical 4-bit benchmark instances, the method consistently delivers competitive gate counts, matching or improving upon previous hypercube-based outcomes. Through the seamless integration of structure-informed guidance and coordinated optimization mechanisms, the framework preserves exceptional structural flexibility and algorithmic robustness, offering an effective, low-cost, and highly scalable avenue for reversible circuit synthesis.

DOI
10.32604/cmc.2026.083187

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Quantum logic reversible synthesis is a fundamental operation in quantum computing. One of the most challenging issues in this field resides in navigating the immense search space to synthesize the most compact circuit configurations, which are critical for realizing reliable, noise-free, and error-free quantum computing systems. To address this challenge, this study proposes a novel hypercube-encoded quantum-inspired optimization framework to formulate the synthesis task as a trajectory-finding process. This structure-informed domain knowledge transformation delivers exceptional search direction guidance, moving away from blind, black-box exploration. Specifically, by mapping the reversible functions onto the hypercube architecture, the framework embeds explicit dual Hamming-distance (HMD) guidance metrics into a global-best guided quantum-inspired tabu search (GQTS) engine. To minimize computational cost and enhance search efficiency, the framework incorporates a domain-informed initialization and couples a streamlined two-particle configuration with a global-best mechanism, thereby amplifying the efficiency of the underlying quantum-inspired updating mechanism to escape local optima and rapidly converge once a successfully synthesized superior path is locked. Under an online step relaxation mechanism, the framework preserves exceptional structural optimization flexibility without altering the underlying hypercube representation. The framework’s significance is rigorously evaluated against both rigid hypercube rule-based methods and generic randomized search-based heuristics, using gate count and exact-optimality as primary evaluation metrics. Extensive ablation studies first validate the individual and synergistic contributions of each core algorithmic component. Experimental results demonstrate that for the complete set of 3-bit reversible functions, the proposed HMD-guided GQTS (HMD-GQTS) framework achieves over 98% exact-optimal circuits in a single fine-tuned sweep, with selective retries attaining 100% exhaustive optimal coverage. Furthermore, for typical 4-bit benchmark instances, the method consistently delivers competitive gate counts, matching or improving upon previous hypercube-based outcomes. Through the seamless integration of structure-informed guidance and coordinated optimization mechanisms, the framework preserves exceptional structural flexibility and algorithmic robustness, offering an effective, low-cost, and highly scalable avenue for reversible circuit synthesis.
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.
Quantum computation has extraordinary capabilities for solving complicated problems. As quantum computations are reversible by nature, reversible circuits are important for the development of quantum computation techniques. Designing an effective and efficient method for synthesizing reversible circuits to reduce costs and stabilize circuit efficiency is crucial. The traditional synthesis methods of solving reversible circuits focus on the conversion efficiency rather than discussing the properties of the reversible function. Thus, this paper aims to propose a novel synthesis method that directly and efficiently optimizes reversible circuit synthesis with the properties of the reversible circuit. The proposed method converts the reversible function into a hypercube, allowing visual observations of the overall circuit. Two new indicators, the adjacent Hamming distance (AHD) and total cycle distance (TCD), aid in effective decision-making, generating shorter circuits. Furthermore, we use the generalized Toffoli gate set, which without requiring any additional ancilla bits and has applications in error correction and fault tolerance. The experimental results show that our method can find better solutions than traditional methods, significantly reducing the gate count, while the hypercube assists in synthesizing the reversible circuit.
Quantum and reversible circuit optimization stand as pivotal areas in quantum computing, crucial for error mitigation, size reduction, and cost minimization. In this scenario, computational intelligence (CI) is an efficient approach for improving circuit optimization issues and constructing equivalent small-scale quantum algorithms. In this paper, we propose a novel quantum-inspired computational intelligence method to automatically synthesize quantum circuits, benefiting reliable quantum computing realization. The proposed algorithm uses the feature of quantum mechanics to enhance the exploration ability of computational intelligence. It then detects situations when encountering local optima and reacts appropriately, drawing inspiration from the controlled-swap gate to navigate candidate solutions effectively and escape local optima with preference. Given the uncertain landscape of future quantum technologies and the diverse preferable gate sets with different platforms, our approach is a flexible algorithm that can simply adapt to different gate sets. The experimental results demonstrate that our method achieves superior performance compared to previous synthesis methods, with fewer circuit costs and more stable efficiency. Furthermore, we provide all circuits synthesized by our novel method to facilitate future studies to conduct in-depth research, simplify circuits, and map to different logic gate sets. This study advances reliable quantum computing through a quantum-inspired CI to mutually benefit both realms, promoting insight into interdisciplinary collaboration.
A reinforcement learning (RL) framework is introduced for the efficient synthesis of quantum circuits that generate specified target quantum states from a fixed initial state, addressing a central challenge in both the Noisy Intermediate-Scale Quantum (NISQ) era and future fault-tolerant quantum computing. The approach utilizes tabular Q-learning, based on action sequences, within a discretized quantum state space, to effectively manage the exponential growth of the space dimension. The framework introduces a hybrid reward mechanism, combining a static, domain-informed reward that guides the agent toward the target state with customizable dynamic penalties that discourage inefficient circuit structures such as gate congestion and redundant state revisits. This is a circuit-aware reward, in contrast to the current trend of works on this topic, which are primarily fidelity-based. By leveraging sparse matrix representations and state-space discretization, the method enables practical navigation of high-dimensional environments while minimizing computational overhead. Benchmarking on graph-state preparation tasks for up to seven qubits, we demonstrate that the algorithm consistently discovers minimal-depth circuits with optimized gate counts. Moreover, extending the framework to a universal gate set still yields low depth circuits, highlighting the algorithm’s robustness and adaptability. The results confirm that this RL-driven approach, with our completely circuit-aware method, efficiently explores the complex quantum state space and synthesizes near-optimal quantum circuits, providing a resource-efficient foundation for quantum circuit optimization.
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.