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.
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.
Circuit design with no energy dissipation is possible in the reversible logic. Also, using the quantum multiple‐valued logic in the design of circuits due to the reduction of circuit width leads to the smaller chip area and lower power consumption. Quaternary reversible logic potentially has several advantages in comparison to the equivalent ternary and binary quantum technologies. Hence, the quaternary quantum technology is a promising choice for the future digital system design. Here, the authors proposed an efficient design of 1‐qudit and n ‐qudit quantum comparators. The comparator module is widely used in search conditions, such as Grover's quantum search algorithm in quantum computing. The proposed circuits were better than their existing counterparts in terms of quantum cost, the number of constant inputs, the number of garbage outputs, and hardware complexity. To design these circuits, they have used 1‐qudit gates and 2‐qudit Muthukrishnan–Stroud gates. The efficiency of their proposed circuits was reported.
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.
Quantum computation relies on exploiting quantum mechanical phenomena, and has received significant attention in recent years. Higher-dimensional quantum systems increase the density of encoded information per computing element (e.g., qutrit for three-level system), resulting in less resource overhead. For instance, 63% reduction in the number of qutrits is possible for ternary quantum systems as compared to the corresponding binary systems. The proposed work exploits this fact to synthesize ternary reversible circuits employing a cycle-based technique. The method starts from the ternary reversible specification of a given function in the form of a permutation. The permutation cycles are factored into simpler three-cycles and two-cycles, which are then mapped to ternary reversible gates. Different gate libraries are used to synthesize three-cycles and two-cycles, respectively. A gate decomposition approach is also proposed to synthesize a quantum gate netlist in terms of elementary ternary quantum gates, viz. Muthukrishnan–Stroud gate and shift gate. Synthesis results on benchmark functions indicate that the proposed method results in 27% and 6% improvements in quantum cost and gate count, respectively, over existing works in the literature.
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.
With the continuous shrinkage of transistor sizes in very large scale integrated circuits, power consumption forms a serious concern to be tackled. With their ability to allow for zero energy dissipation, reversible circuits have been considered as promising solution to meetup with low power design requirements. Moreover, advances in their synthesis methodologies can be easily applied to quantum circuits due to the inherited reversibility of the latter. Although numerous algorithms have been proposed in the literature to synthesize reversible circuits and map them into their corresponding quantum circuits, the scalability and computational effort of such algorithms form a serious concern when synthesizing large size input functions. Binary Decision Diagram-based synthesis for reversible circuits has shown great evidence in realizing reversible circuits with low quantum cost through exploiting proper reduction rules for smaller graph size. However, the order of the variables in the decision diagram impacts its overall size, and thus, the cost of its corresponding reversible circuit. While several reordering algorithms have been proposed in this manner, their direct impact on the quantum cost has not been considered. In this article, a Binary Decision Diagram-based algorithm for reversible circuit synthesis is proposed to synthesize reversible circuits for a given Boolean function with low quantum cost through exploiting a linearized relationship between the decision diagram size and the corresponding quantum cost. Thereafter, different decision diagram reordering algorithms have been integrated with the proposed algorithm and compared in terms of their impact on the quantum cost. Experimental results show that Genetic Algorithm-based reordering for decision diagram, supported with, cycle crossover, inverse mutation, and tournament selection, results in the least quantum cost of the output circuit if compared with other algorithms due to its property in preserving the nodes of the decision diagram in their near-optimal locations during the optimiation recipe.
Abstract In recent years, quantum computing has emerged as a leading approach for accelerating complex computations, leveraging quantum parallelism and entanglement to surpass classical limits. Although numerous quantum circuits based on reversible gates have been proposed, optimizing circuit efficiency remains a critical challenge, particularly in the noisy intermediate-scale quantum era, where error rates and coherence times constrain performance. Ternary quantum computing, which operates on three-level quantum systems (qutrits), offers a promising alternative by reducing circuit complexity and resource overhead. In particular, balanced ternary logic presents advantages over conventional ternary logic by enhancing resource efficiency and potentially mitigating quantum gate error rates. This paper focuses on two key objectives: first, the synthesis of a reversible 1-qutrit comparator circuit using balanced ternary logic, and second, the extension to a generalized n-qutrit comparator. The proposed 1-qutrit comparator achieves notable improvements over existing unbalanced designs, demonstrating a 65% reduction in quantum cost, 50% fewer constant inputs, and a 33% decrease in garbage outputs. These results highlight the potential of balanced ternary logic to enhance the efficiency of quantum circuits, making it a valuable contribution to the development of scalable and error-resilient quantum hardware.