quantum circuit simulation

This paper presents a systematic survey of quantum circuit optimization, addressing the dual challenges of accelerating execution and mitigating noise-induced errors on Noisy Intermediate-Scale Quantum (NISQ) hardware—while preserving functional correctness. Methodologically, it unifies hardware-agnostic techniques (e.g., graph rewriting, algorithmic optimization) with hardware-aware approaches (e.g., instruction scheduling, NISQ-adaptive compilation), integrating heuristic search, reinforcement learning, supervised learning, and hybrid quantum-classical frameworks into a multidimensional evaluation framework. Key contributions include: (i) rigorous characterization of performance limits and robustness deficiencies across optimization paradigms; (ii) identification of three critical bottlenecks—deep compression, noise-aware optimization, and automated compiler design; and (iii) proposal of novel research directions in scalability, cross-platform generalization, and compilation robustness. The work provides both theoretical foundations and practical guidelines for advancing the quantum software stack.

To address the high manual design overhead and low execution fidelity/efficiency in mapping quantum algorithms to hardware, this paper proposes a cross-layer (algorithm–compiler–hardware) co-optimization framework. Methodologically, it pioneers the integration of deep reinforcement learning with graph neural networks to jointly automate quantum architecture search, logic synthesis, gate-level optimization, qubit mapping, and SWAP-based routing; it further introduces a superconducting-qubit hardware-adaptive modeling mechanism. Key contributions include: (1) establishing an AI-driven, end-to-end compilation optimization paradigm; (2) significantly reducing human intervention while improving circuit depth compression and quantum gate fidelity; and (3) empirically validating the feasibility and superior performance of the AI-enhanced compiler on medium-scale real superconducting quantum processors.

Global optimization of quantum circuits—being QMA-hard—faces a fundamental trade-off between computational efficiency and solution quality. Method: This paper introduces a novel optimization paradigm grounded in “local optimality”: formally defined as the requirement that every contiguous subcircuit must be globally optimal. We implement this principle via a cut-and-meld strategy—partitioning the circuit into segments, invoking an oracle to optimize each segment independently, and lazily merging adjacent segments across cut points. Crucially, our approach requires only a polynomial (specifically, linear) number of oracle calls. Contribution/Results: The method provides theoretically provable guarantees while remaining practically efficient. Experiments on standard benchmarks demonstrate that it outperforms state-of-the-art optimizers by over 10× in runtime, while further reducing CNOT count—validating local optimality as a robust and viable core criterion for quantum circuit optimization.

Existing variational quantum algorithms for solving nonlinear differential equations are constrained by NISQ hardware limitations due to the high sampling overhead of evaluating differential quantum circuits. Method: We propose a “measurement-first,” hardware-aware protocol featuring an engineering-friendly cost operator, differentiable quantum circuits (DQCs), classical-shadow-inspired randomized measurements, and a hardware-adapted variational optimization framework. This approach circumvents the sampling bottleneck inherent in conventional differential circuit evaluation. Contribution/Results: It achieves exponential reduction in quantum circuit evaluations—up to ~100× fewer evaluations on 1D/2D differential equation benchmarks—significantly accelerating hybrid quantum-classical training. Crucially, by prioritizing measurement strategy design and deeply co-designing it with hardware characteristics, our method delivers the first simultaneous breakthrough in both evaluation efficiency and hardware practicality for quantum solutions of nonlinear differential equations.

Variational quantum algorithms suffer from the “barren plateau” phenomenon—exponential gradient vanishing with system size—rendering optimization infeasible. Method: We propose and rigorously analyze a “warm-start” strategy within an iterative shallow-circuit learning framework, leveraging initial parameters near the solution—obtained via quantum real-time evolution—to enhance trainability. Contribution/Results: We prove that, within a neighborhood of the optimal solution, gradients decay at most polynomially, and local convexity is guaranteed. We further identify a novel mechanism—“optimal solution drift”—that can undermine warm-start efficacy. Our analysis shows warm-start maintains trainability over polynomially many time steps. Moreover, we establish the existence of “fertile valleys” in parameter space—regions where gradients remain non-negligible—providing both theoretical justification and a new direction for overcoming gradient starvation in variational quantum optimization.

To address the prevalent barren plateau (gradient vanishing) and saddle-point stagnation issues in training variational quantum circuits (VQCs) on noisy intermediate-scale quantum (NISQ) devices, this paper proposes a parameter regularization method that jointly leverages data-driven priors and Gaussian noise diffusion. It is the first to synergistically integrate Bayesian prior modeling with controllable noise injection into VQC optimization, regularizing parameter update trajectories to significantly enhance gradient signal strength and improve parameter-space trainability. Experiments across four benchmark quantum machine learning datasets demonstrate that the proposed strategy accelerates convergence by an average factor of 2.1×, boosts final classification accuracy by up to +8.7%, and robustly mitigates barren plateaus. The core contribution is the development of the first data-noise joint regularization framework explicitly designed to enhance the training robustness of VQCs.

This work addresses combinatorial optimization problems—exemplified by Max-Cut—by proposing a class of *sub-universal classical probabilistic variational circuits* based on two-bit random matrices, serving as a strong classical benchmark for quantum variational algorithms such as QAOA. The method replaces quantum circuits with efficient classical probabilistic circuits, enabling scalable parameterization and gradient-based variational optimization; it establishes the first systematic sub-universal classical variational framework. Numerical experiments across diverse graph topologies demonstrate that this classical approach consistently achieves higher Max-Cut solution quality and greater robustness than same-depth QAOA. The study provides a computationally efficient, directly comparable classical reference for assessing quantum advantage, while clarifying the practical applicability limits of quantum variational algorithms in combinatorial optimization and identifying concrete avenues for their improvement.

This work addresses industrial-scale combinatorial optimization problems in the NISQ era, focusing on enhancing the practicality and constraint handling of the Quantum Approximate Optimization Algorithm (QAOA). Method: For NP-hard problems such as Max-Cut, we propose a Grover-mixer-based constraint-encoding scheme that rigorously embeds the feasible solution space into the QAOA variational circuit, eliminating sampling of infeasible solutions. We further generalize QAOA to a constrained Variational Quantum Eigensolver (c-VQE), supporting high-order Ising Hamiltonian modeling and analytical gradient computation via the parameter-shift rule. Contribution/Results: Implemented end-to-end on PennyLane, our approach demonstrates significant improvements in solution quality and convergence speed over unconstrained baselines. Systematic evaluation confirms c-VQE’s robustness under realistic noise models and its scalability to larger problem instances, establishing a foundation for near-term quantum optimization with hard constraints.

This work addresses the challenge of designing high-fidelity quantum circuits, which often suffer from limited generality and suboptimal performance. The authors propose modeling the design problem as differentiable logic programming, uniquely integrating continuous logic with quantum unitary evolution. They develop an optimization framework based on T-norm fuzzy logic and geodesic interpolation, augmented with bias-aware initialization to mitigate barren plateaus. The approach enables users to specify custom differentiable logical axioms—such as correctness, simplicity, and robustness—and automatically discovers a 4-qubit quantum Fourier transform (QFT) circuit from a space of 21 candidate gates. Validated on the IBM Torino processor for local routing tasks, the method achieves a 59.3-percentage-point fidelity improvement over baselines and demonstrates resilience to hardware faults.

This study addresses the industrial applicability of quantum computing to combinatorial optimization problems. It provides a systematic review of mainstream quantum optimization approaches—including quantum annealing, the Quantum Approximate Optimization Algorithm (QAOA), Quantum Reinforcement Learning (QRL), and Quantum Generative Modeling (QGM)—and, for the first time, aligns these methods precisely with real-world domains such as logistics, finance, and telecommunications. Leveraging authoritative benchmarking platforms like QOBLIB and QUARK, the work evaluates the engineering maturity and empirical evidence of quantum advantage across these algorithms. Findings indicate that quantum annealing currently offers the highest practical utility, QAOA demonstrates feasibility on NISQ devices, and QRL and QGM represent promising high-impact directions for future development. This research establishes a comprehensive evaluation framework and strategic roadmap for the industrial deployment of quantum optimization technologies.

Classical numerical methods for solving differential equations and optimizing function extrema incur high computational overhead, while fault-tolerant digital quantum hardware remains immature. Method: We propose a closed-loop framework integrating differentiable quantum circuits (DQCs) with quantum extremum learning (QEL), enabling direct search for extrema of implicitly defined functions—partially circumventing explicit differential equation solving. Contribution/Results: This framework is the first to be end-to-end experimentally validated on a commercially available neutral-atom analog quantum simulator, eliminating reliance on gate-based digital hardware. By synergistically combining variational optimization and machine-learning surrogate models, we successfully solve differential equations and locate extrema. Evaluations on synthetic benchmarks demonstrate robust convergence and stability, establishing a viable pathway for analog quantum simulation in scientific computing and highlighting its practical potential for real-world applications.

During the Qiskit 1.x→2.x migration, the default shot count for QAOA was drastically reduced, causing insufficient state-space coverage (only 23%) and leading to output distribution shifts and significant accuracy degradation—undermining reproducibility. Method: We developed a standardized QAOA implementation based on Qiskit 2.x v2 primitives, rigorously controlling circuit construction, optimizer selection, and Hamiltonian encoding, and systematically quantified performance decay across varying shot counts. Contribution/Results: We identified the shot reduction as the root cause and proposed a reproducibility-preserving shot count of 250,000, which fully restores original accuracy. This work is the first to expose the critical impact of implicit parameters in the quantum-classical interface layer on hybrid algorithm performance. It establishes a parameter calibration paradigm and empirical benchmark for quantum software version migration, enabling robust cross-version algorithm deployment.