Scalable Multi-Objective Genetic Algorithm for Quantum Circuit Optimization

The design of quantum circuits that are compact, efficient, and compatible with Noisy Intermediate-Scale Quantum (NISQ) hardware remains a key challenge in quantum computing. Most current approaches rely on a fidelity-based fitness function that requires computing the full unitary matrix. This becomes infeasible beyond 10–12 qubits due to exponential memory and time complexity. In this work we present a scalable multi-objective genetic algorithm for quantum circuit optimization targeting NISQ devices. To overcome the limitations of full-unitary fidelity evaluation, we introduce two efficient strategies: a projection-based approximation and a structure-aware local metric. Integrated into NSGA-II, our approach reduces computational cost while preserving fidelity, depth, and hardware compatibility. ponentially, making traditional algorithms—despite heuristics—difficult to scale efficiently. Quantum computing introduces a new paradigm by leveraging principles such as superposition and entanglement (1). Hybrid algorithms like the Quantum Approximate Optimization Algorithm (QAOA) (2) and the Varia-tional Quantum Eigensolver (VQE) (3) combine quantum circuits with classical optimizers to solve such problems, making them well-suited for today’s Noisy Intermediate-Scale Quantum (NISQ) hardware (4). However, running quantum algorithms on real hardware is challenging. NISQ devices are limited by gate fidelity, qubit connectivity, and decoher-ence, making deep or gate-heavy circuits impractical. Multi-qubit gates in particular, like CNOT, significantly reduce overall fidelity (5; 6; 7; 8), requiring careful trade-offs in circuit design. To address these challenges, evolutionary algorithms—especially genetic algorithms—have gained interest for automatically generating quantum circuits that balance fidelity, gate count, and depth (9; 10; 11). Yet most rely on evaluating full unitary matrices, which becomes computationally infeasible beyond 10–12 qubits due to exponential scaling (12). In this work, we make the following contributions: ; We introduce a scalable quantum circuit optimization framework built on a multi-objective genetic algorithm. ; We propose two scalable fidelity evaluation methods that avoid the need to compute full unitary matrices, which significantly reduces the computational overhead while preserving fidelity relevance. ; We integrate these fidelity strategies into a Pareto-based NSGA-II optimization loop that jointly minimizes fidelity error, circuit depth, and gate cost. ; We validate the framework on a diverse set of circuits, including random circuits and problem-oriented instances such as QAOA and VQE, demonstrating improved scalability and enhanced hardware-aware circuit design quality.