Designing quantum circuits is a major challenge due to their sensitivity to noise and the complexity of quantum logic. This paper presents an evolutionary algorithm that balances multiple design criteria, namely fidelity and circuit depth, by combining them into a single scalarised fitness function. This approach enables efficient optimisation while avoiding the computational cost of fully multi-objective methods. A novel circuit representation and set of noise-aware genetic operators are introduced, and the technique is applied to evolve implementations of the Quantum Fourier Transform (QFT) for two- and three-qubit systems. Experimental results show that evolved circuits match or exceed ideal fidelity and outperform textbook QFT implementations under simulated noise. These findings highlight the potential of hardware-aware evolutionary design for producing circuits that are both accurate and resilient on near-term quantum hardware.
Designing quantum circuits is a major challenge due to their sensitivity to noise and the complexity of quantum logic. This paper presents an evolutionary algorithm that balances multiple design criteria, namely fidelity and circuit depth, by combining them into a single scalarised fitness function. This approach enables efficient optimisation while avoiding the computational cost of fully multi-objective methods. A novel circuit representation and set of noise-aware genetic operators are introduced, and the technique is applied to evolve implementations of the Quantum Fourier Transform (QFT) for two- and three-qubit systems. Experimental results show that evolved circuits match or exceed ideal fidelity and outperform textbook QFT implementations under simulated noise. These findings highlight the potential of hardware-aware evolutionary design for producing circuits that are both accurate and resilient on near-term quantum hardware.
Abstract Designing compact and efficient quantum circuits that are compatible with Noisy Intermediate-Scale Quantum (NISQ) hardware remains a central challenge in quantum computing. Most existing optimization approaches rely on fidelity-based fitness functions that require computing the full unitary matrix of the circuit. However, this quickly becomes computationally intractable beyond 10–12 qubits due to the exponential memory and time complexity O(22n) . In this work, we propose a scalable multi-objective genetic algorithm for quantum circuit optimization tailored to NISQ devices. Although evolutionary algorithms have demonstrated strong potential for circuit synthesis, current methods generally depend on full-unitary fidelity evaluation, which severely limits scalability. To address this bottleneck, we introduce two complementary strategies: (1) an independent block-based evaluation using graph partitioning, and (2) an overlapping sliding-window decomposition approach. Both strategies reduce computational complexity from O(22n) to O(22k) , where k≪n , making it possible to optimize circuits with more than 20 qubits in practice. Our methods are integrated into the NSGA-II multi-objective framework, enabling simultaneous optimization of fidelity, circuit depth, and gate cost, while maintaining structural compatibility with NISQ hardware–without requiring full-unitary simulation. Experimental results on benchmark circuits demonstrate high fidelity (above 0.94 for small circuits up to 8 qubits, above 0.85 for medium-scale circuits of 10–16 qubits, and above 0.80 for large-scale circuits up to 32 qubits), up to 45% reduction in circuit depth, and a 10× speedup compared to exact evaluation at 14 qubits.
Multi‐objective optimization in quantum systems poses formidable challenges stemming from the high dimensionality, complex constraints, and conflicting performance metrics inherent to quantum control tasks and circuit synthesis. This study presents a comprehensive exploration of genetic AI algorithms—evolutionary strategies inspired by natural selection—tailored specifically for multi‐objective optimization in quantum computing contexts. We propose a hybrid framework that synergistically combines the elitist, Pareto‐based selection mechanics of NSGA-II with quantum‐inspired crossover and mutation operators designed to preserve entanglement structures and exploit hardware‐specific gate sets. In this framework, candidate solutions encoding circuit topologies or control‐pulse parameters undergo iterative evolution, guided by fitness vectors that balance gate fidelity, circuit depth, and resource overhead. To benchmark performance, we apply the algorithm to canonical quantum computing problems: Fourier transform circuits, QAOA ansätze for MaxCut instances, and random Clifford+T circuits. Through extensive simulation on noise-modelled quantum devices, we evaluate Pareto front coverage, convergence speed, diversity maintenance, and robustness under decoherence. Our results demonstrate that the proposed genetic AI algorithm outperforms classical single‐objective genetic methods and established multi‐objective evolutionary algorithms (e.g., SPEA2) by achieving broader Pareto fronts and faster convergence rates, while maintaining solution diversity. Furthermore, noise-resilience experiments show graceful degradation, indicating practical applicability on near-term quantum hardware. These findings substantiate the potential of evolutionary computation paradigms—augmented with quantum‐inspired operators—to address the intricate trade-off surfaces that define NISQ-era optimization problems, paving the way toward automated quantum circuit design and control parameter tuning for real-world quantum computing applications.
Quantum computing is a new way of data processing based on the concept of quantum mechanics. Quantum circuit design is a process of converting a quantum gate to a series of basic gates and is divided into two general categories based on the decomposition and composition. In the second group, using evolutionary algorithms and especially genetic algorithms, multiplication of matrix gates was used to achieve the final characteristic of quantum circuit. Genetic programming is a subfield of evolutionary computing in which computer programs evolve to solve studied problems. In past research that has been done in the field of quantum circuits design, only one cost metrics (usually quantum cost) has been investigated. In this paper for the first time, a multi-objective approach has been provided to design quantum circuits using genetic programming that considers the depth and the cost of nearest neighbor metrics in addition to quantum cost metric. Another innovation of this article is the use of two-step fitness function and taking into account the equivalence of global phase in quantum gates. The results show that the proposed method is able to find a good answer in a short time.
Quantum hardware continues to advance, yet finding new quantum algorithms - quantum software - remains a challenge, with classically trained computer programmers having little intuition of how computational tasks may be performed in the quantum realm. As such, the idea of developing automated tools for algorithm development is even more appealing for quantum computing than for classical. Here we develop a robust, multi-objective evolutionary search strategy to design quantum circuits 'from scratch', by combining and parameterizing a task-generic library of quantum circuit elements. When applied to 'ab initio' design of quantum circuits for the input/output mapping requirements of the quantum Fourier transform and Grover's search algorithm, it finds textbook circuit designs, along with alternative structures that achieve the same functionality. Exploiting its multi-objective nature, the discovery algorithm can trade off performance measures such as accuracy, circuit width or depth, gate count, or implementability - a crucial requirement for first-generation quantum processors and applications.
Abstract Designing expressive yet hardware-efficient quantum circuits remains a central challenge in quantum machine learning (QML). Existing approaches to quantum circuit synthesis primarily optimize for classical performance metrics, often overlooking intrinsic quantum characteristics that govern circuit quality and generalization. This work introduces a quantumness-aware genetic optimization (QAGO) framework for circuit synthesis that integrates quantum properties such as entanglement and non-Clifford gate utilization into the evolutionary design process. We formulate circuit synthesis as both a single-objective optimization (SOO) and a multi-objective optimization (MOO) problem within a genetic framework. The SOO formulation explores quantumness-aware objectives balancing predictive performance and circuit-level quantum structure, while the MOO formulation approximates Pareto-efficient trade-offs between these goals. This dual perspective enables systematic analysis of how increasing quantum expressivity influences predictive behavior and resource cost. Experimental evaluations across three quantum kernel-based algorithms include quantum support vector machines, quantum kernel trainers, and projected quantum kernels demonstrate that circuits evolved under quantumness-aware objectives consistently outperform baseline kernel circuits such as ZZFeatureMap. Comprehensive benchmarking against classical baselines shows that QAGO achieves up to 2.5% area under the ROC curve improvement on the Higgs Boson dataset and 1.5%–9.2% gains across six of nine targets in the LIT-PCBA drug discovery benchmark. Compared to prior work (Wu et al 2021 J. Phys. G: Nucl. Part. Phys. 48 125003, Mensa et al 2023 Mach. Learn.: Sci. Technol. 4 015023) QAGO yields up to 4% improvement on Higgs and 5%–20% gains across eight of nine targets. These results provide quantitative evidence that optimizing for quantumness enhances both performance and quantum expressivity of QML models, establishing QAGO as a principled framework for quantumness-aware circuit evolution.
Noise in current quantum hardware (NISQ devices) poses a major obstacle by degrading gate operations and overall circuit fidelity toward FTQC. Traditional quantum error correction (QEC) is effective but resource-intensive, requiring several extra qubits and operations beyond the reach of near-term devices. Quantum error mitigation (QEM) offers a complementary path by reducing the impact of error prior to full correction. We present an adaptive pulse-level QEM using genetic algorithms to dynamically adjust control pulses in real-time, improving algorithm fidelity without modifying the logic structure of a quantum circuit. By targeting pulse parameters directly, this method reduces the impact of various noise sources, improving algorithm resilience in quantum circuits. To demonstrate the effectiveness of our methodology, we apply our protocol to five key quantum algorithms, including Bernstein-Vazirani, DeutschJozsa, Grover's search, Quantum Fourier Transform (QFT), and its inverse (IQFT). Experimental results show that our pulse-level optimization strategy provides a flexible and efficient solution for increasing fidelity during the noisy execution of quantum circuits. Our work contributes to advance error mitigation techniques, essential for robust quantum computing, which will increasingly require HPC infrastructure as quantum systems scale.