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.
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 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.
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.
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.
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.
Considering the relentless progress in the miniaturization of electronic devices and the need to reduce energy consumption, technical challenges in the synthesis of circuit design solutions have become evident. According to Moore's Law, the reduction of transistor sizes to the atomic scale faces physical limits, which complicate further development. Additionally, reducing transistor sizes causes current leakage, leading to increased thermal noise, which can disrupt the proper functioning of digital devices. A promising solution to these problems is the application of reversible logic in circuit design. Reversible logic allows for a reduction in energy and information losses because logical reversible operations are performed without loss. The research synthesized optimal reversible circuits based on reversible gates using evolutionary algorithms and compare them with existing analogues. The focus of this study is on logical circuits built using reversible gates, which can significantly reduce energy losses, which is critical for modern and future electronic devices. The synthesis of reversible circuits is closely related to quantum computing, where quantum gates also possess a reversible nature. This enables the use of synthesis methods to create quantum reversible logical computing devices, which in turn promotes the development of quantum technologies. The study focuses on the application of evolutionary artificial intelligence algorithms, specifically genetic algorithms and ant colony optimization algorithms, for the optimal synthesis of reversible circuits. As a result, a detailed description of the key concepts of the improved algorithms, simulation results, and comparison of the two methods is provided. The efficiency of the reversible device synthesis was evaluated using the proposed implementation of the genetic algorithm and the ant colony optimization algorithm. The obtained results were compared to existing analogs and verified using the Qiskit framework in the IBM quantum computing laboratory. The conclusions describe the developed algorithms, which demonstrate high efficiency in solving circuit topology optimization problems. A genetic algorithm was developed, featuring multi-component mutation and a matrix approach to chromosome encoding combined with Tabu search to avoid local optima. The ant colony optimization algorithms were improved, including several changes to the proposed data representation model, structure, and operational principles of the synthesis algorithm, enabling effective synthesis of devices on the NCT basis along with Fredkin gates. An improved structure for storing and using pheromones was developed to enable multi-criteria navigation in the solution space.
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.