quantum circuit simulation

Efficient classical simulation of parameterized quantum circuits under non-unitary noise—such as amplitude damping—on NISQ devices remains a fundamental challenge. Method: This work extends the Pauli backpropagation technique to model general non-unitary quantum channels and introduces a combinatorial complexity framework with rigorous analytical guarantees. Contribution/Results: We prove that the algorithm retains polynomial time complexity even under realistic hardware noise models, substantially extending the applicability beyond conventional unitary-only simulators. Experimental evaluation demonstrates high accuracy and scalability on variational quantum circuits subject to amplitude damping noise. To our knowledge, this is the first classical benchmarking tool for near-term quantum advantage verification that simultaneously ensures theoretical rigor and practical utility. It significantly enhances the reliability and interpretability of quantum–classical performance comparisons in noisy regimes.

This work aims to rigorously delineate the boundary of genuine quantum advantage in quantum machine learning. Method: For parameterized quantum circuits (PQCs), we establish a precise mathematical correspondence between circuit architecture—specifically depth and non-Clifford gate count—and the class of learnable functions, leveraging tools from function representation theory and quantum computational complexity. Contribution/Results: We introduce the first unified analytical framework that systematically categorizes PQCs into three distinct classes: (i) fully classically simulable, (ii) function-space-efficiently classically tractable, and (iii) strongly quantum-robust; we further provide decidable criteria for classical simulability. The framework identifies a common origin underlying diverse “dequantization” phenomena, clarifies the hierarchy of classical simulation hardness across PQC architectures, and delivers a conceptual map and theoretical foundation for precisely pinpointing quantum advantage.

Classical simulation of quantum circuits on NISQ-era hardware faces severe efficiency bottlenecks, particularly when scaling to larger qubit counts and deeper circuits. Method: We systematically benchmark GPU-accelerated state-vector and tensor-network simulation methods across 31 configurations and eight representative NISQ subroutines, quantifying the impact of circuit structure—including entanglement depth and gate density—and qubit count on simulation performance. We propose the first circuit-feature-driven automatic strategy selection criterion, integrating NP-hard contraction-path optimization (formulated as a max-cut problem), tensor-network contraction scheduling, and regression-based performance prediction. Contribution/Results: Our approach achieves up to 10× speedup over baseline methods across diverse NISQ subroutines, precisely delineates the applicability boundaries of state-vector versus tensor-network simulation, and breaks key memory and computational bottlenecks. We publicly release a reusable benchmarking framework and an accurate, generalizable performance prediction model.

Automated generation of parameterized quantum circuits remains challenging, and high-quality benchmark datasets are scarce. Method: This paper proposes the first application-oriented, algorithm-level framework for generating parameterized quantum circuits. It introduces the novel “algorithm-specific hyperparameter” paradigm—extending beyond mere qubit count—to enable highly configurable, large-scale, and high-variability batch generation for 15 real-world quantum algorithms. Integrated with SDKs such as Qiskit, it supports hierarchical circuit modeling, automatic compilation, and joint statevector/measurement-histogram simulation. Contributions/Results: We construct the first structured quantum circuit dataset, encompassing circuit topology, parameter configurations, quantum states, and statistical outputs. We release an open-source toolkit enabling circuit statistical analysis, complexity modeling, and simulation-free machine learning training—significantly lowering the barrier to quantum algorithm development.

Addressing the challenge of evaluating noise robustness in NISQ-era quantum circuits—where conventional full-state simulation incurs exponential computational overhead—this work proposes the first fidelity prediction framework based on a graph Transformer. The method naturally encodes quantum circuits as heterogeneous graphs, where nodes represent qubits and edges encode gate operations and device-specific noise characteristics; it then integrates graph neural networks with a Transformer architecture to achieve end-to-end circuit graph embedding and noise-aware modeling. Evaluated on a benchmark dataset of 5,000 random and algorithmic circuits, the model achieves an RMSE of 0.04 and R² scores of 0.99 (training) and 0.95 (test), while accelerating predictions by over 200× compared to full-state simulators. Key contributions include: (i) the first application of graph Transformers to quantum circuit reliability prediction; (ii) a design that jointly ensures structural expressivity and noise interpretability; and (iii) a scalable, data-driven paradigm for efficient circuit assessment on NISQ hardware.

This work addresses the fundamental trade-off in parametrized quantum circuits (PQCs) between expressibility and trainability: highly expressive circuits are prone to barren plateaus, while trainable architectures may be classically simulable. The authors derive a finite-sample, dimension-independent concentration bound on the variance of the cost function, establishing the first rigorous theoretical guarantee for trainability and revealing an inverse relationship between trainability and expressibility. Leveraging this insight, they propose a property-driven variational circuit search framework that jointly optimizes both criteria. Experimental validation on real quantum hardware demonstrates that the discovered circuits achieve over sixfold reduction in parameter count while exhibiting higher effective dimensionality. In the VQE task for the H₂ molecule, these circuits attain accuracy comparable to UCCSD with significantly lower computational complexity.

This work addresses the computational hardness of strongly simulating quantum circuits—specifically, computing output amplitudes—which is generally intractable and highly dependent on the structure of the path-variable graph. The authors reformulate amplitude computation as a weighted counting problem over path variables and establish, for the first time, that the rank-width of this graph serves as the key parameter governing simulation complexity. Building on this insight, they devise a fixed-parameter tractable algorithm whose runtime scales polynomially with circuit size and exponentially only in the rank-width. This approach unifies and generalizes existing techniques such as binary decision diagrams and tensor networks. Notably, on circuit families containing Hadamard and diagonal gates—including Clifford+T circuits—the proposed algorithm substantially outperforms current state-of-the-art methods.

This work proposes Latent-variable-conditioned Parameterized Quantum Circuits (LPQC) to efficiently generate ensembles of quantum states that capture the heterogeneity of a target system, circumventing the high cost of preparing states individually. LPQC employs a classical neural network to map latent variables to quantum circuit parameters, thereby enabling probabilistic modeling of quantum state distributions. Theoretically, LPQC is shown to possess universal approximation capability for probability measures over density operators under the 1-Wasserstein distance. To mitigate barren plateaus, the approach incorporates a multimodal latent prior and a mixture-of-experts quantum circuit architecture. Experiments demonstrate that LPQC outperforms existing quantum generative models on synthetic multi-cluster mixed-state ensembles and QM9 molecular structure generation tasks, achieving performance comparable to classical methods with significantly lower output dimensionality.

This work addresses the challenge of efficiently executing high-dimensional hybrid qudit circuits on disconnected hardware by proposing a circuit cutting and reconstruction method based on tensor product decompositions of generalized Gell-Mann matrices. It extends quantum circuit cutting techniques to mixed-dimensional qudit systems for the first time, enabling exact state reconstruction across qubit–qutrit interfaces with zero total variation distance. The approach substantially reduces memory overhead: in an 8-particle system with local dimension 8, the memory footprint per circuit decreases from 128 MB to 64 KB. This advancement provides a practical pathway toward deploying heterogeneous high-dimensional quantum computations on distributed quantum hardware.