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.
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.
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.
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.
Quantum algorithms will likely play a key role in future high-performance-computing (HPC) environments. These algorithms are typically expressed as quantum circuits composed of arbitrary gates or as unitary matrices. Executing these on physical devices, however, requires translation to device-compatible circuits, in a process called quantum compilation or circuit synthesis, since these devices support a limited number of native gates. Moreover, these devices typically have specific qubit topologies, which constrain how and where gates can be applied. Consequently, logical qubits in input circuits and unitaries may need to be mapped to and routed between physical qubits. Furthermore, current Noisy Intermediate-Scale Quantum (NISQ) devices present additional constraints. They are vulnerable to errors during gate application and their short decoherence times lead to qubits rapidly succumbing to accumulated noise and possibly corrupting computations. Therefore, circuits synthesized for NISQ devices need to minimize gates and execution times. The problem of synthesizing device-compatible circuits, while optimizing for low gate count and short execution times, can be shown to be computationally intractable using analytical methods. Therefore, interest has grown towards heuristics-based synthesis techniques, which are able to produce approximations of the desired algorithm, while optimizing depth and gate-count. In this work, we investigate using genetic algorithms (GA)—a proven gradient-free optimization technique based on natural selection—for circuit synthesis. In particular, we formulate the quantum synthesis problem as a multi-objective optimization (MOO) problem, with the objectives of minimizing the approximation error, number of multi-qubit gates, and circuit depth. We also employ fuzzy logic for runtime parameter adaptation of GA to enhance search efficiency and solution quality in our proposed method.
Quantum computing emerges as a promising direction for high-performance computing in the post-Moore era. Leveraging quantum mechanical properties, quantum devices can theoretically provide significant speedup over classical computers in certain problem domains. Quantum algorithms are typically expressed as quantum circuits composed of quantum gates, or as unitary matrices. Execution of quantum algorithms on physical devices requires translation to machine-compatible circuits -- a process referred to as quantum compilation or synthesis. Quantum synthesis is a challenging problem. Physical quantum devices support a limited number of native basis gates, requiring synthesized circuits to be composed of only these gates. Moreover, quantum devices typically have specific qubit topologies, which constrain how and where gates can be applied. Consequently, logical qubits in input circuits and unitaries may need to be mapped to and routed between physical qubits on the device. Current Noisy Intermediate-Scale Quantum (NISQ) devices present additional constraints, through their gate errors and high susceptibility to noise. NISQ devices are vulnerable to errors during gate application and their short decoherence times leads to qubits rapidly succumbing to accumulated noise and possibly corrupting computations. Therefore, circuits synthesized for NISQ devices need to have a low number of gates to reduce gate errors, and short execution times to avoid qubit decoherence. The problem of synthesizing device-compatible quantum circuits, while optimizing for low gate count and short execution times, can be shown to be computationally intractable using analytical methods. Therefore, interest has grown towards heuristics-based compilation techniques, which are able to produce approximations of the desired algorithm to a required degree of precision. In this work, we investigate using Genetic Algorithms (GAs) -- a proven gradient-free optimization technique based on natural selection -- for circuit synthesis. In particular, we formulate the quantum synthesis problem as a multi-objective optimization (MOO) problem, with the objectives of minimizing the approximation error, number of multi-qubit gates, and circuit depth. We also employ fuzzy logic for runtime parameter adaptation of GA to enhance search efficiency and solution quality of our proposed quantum synthesis method.
We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be transformed into executable quantum circuits based on the nearest-neighbor interaction. Unlike topological codes that are defined based on local operations fundamentally, for the concatenated codes, it is possible to obtain the circuits composed of the local operations by applying the quantum circuit synthesis. However, by the existing quantum circuit synthesis developed for ordinary quantum computational algorithms, the fault-tolerant of the protocol may not be preserved in the resulting circuit. Besides, we have to consider something more to implement the quantum circuit of universal fault-tolerant quantum computing. First, we have not to propagate quantum errors on data qubits when selecting a qubit move path (a sequence of \emph{SWAP} gates) to satisfy the geometric locality constraint. Second, the circuit should be self-contained so that it is possible to act independently regardless of the situation. Third, for universal fault-tolerant quantum computing, we require multiple fault-tolerant quantum circuits of multiple fault-tolerant quantum protocols acting on the same input, a logical data qubit. Last, we need to recall fault-tolerant protocols such as syndrome measure and encoder implicitly include classical control processing conditioned on the measurement outcomes, and therefore have to partition the quantum circuits in time flow to execute the classical control as the architect intended. We propose the circuit synthesis method resolving the requirements and show how to synthesize the set of universal fault-tolerant protocols for [[7,1,3]] Steane code and the syndrome measurement protocol of [[23,1,7]] Golay code.
Reversible logic is fundamental to quantum circuit design, as quantum operations are inherently information-preserving and reversible. While most quantum synthesis methods rely on binary logic, quaternary reversible computing can increase data density, reduce circuit width, and potentially lead to more efficient realizations. We introduce a genetic-algorithm-based approach for designing compact quaternary reversible comparator circuits, which are important components in quantum architectures. This technique utilizes a gate library based on extended Shift and Muthukrishnan–Stroud gates tailored to quaternary systems. Chromosomes encode sequences of quaternary gates, and evolutionary operators search for configurations with minimal quantum cost. Although demonstrated on comparator circuits, the approach applies to any quaternary reversible circuit defined by its truth table. The synthesis process occurs in two phases: candidate circuits first evolve toward correct behavior; then correct circuits are optimized to obtain compact implementations. We evaluate the approach on comparators performing lower-than, greater-than, and equality operations, as well as on a 1-qudit full comparator. The method achieves average quantum cost improvements of about 30% for restoring and 58% for non-restoring configurations compared to existing designs. These reductions support more efficient and more error-resilient quantum circuits, showing that this approach is a strong candidate for quaternary quantum systems.