Classically simulating large quantum circuits is well-known to be difficult due to its exponential scaling O(2n) in computations and memory with respect to the number of qubits (n). We propose a novel classical simulation framework for quantum circuits, combining pairwise-qubit subsystems (PQS) with deep learning, thus called PQS simulation, to achieve scalable and highly efficient circuit evaluation. By representing quantum states as sequences of reduced density matrices and modeling two-qubit interactions through learnable unitary operators, this representation yields quadratic space and linear time per elementary gate, i.e., O(n2) memory and O(n) time per-gate update. A custom multi-hidden long short-term memory architecture is trained to learn and predict the evolution of pairwise entangled qubit subsystems. We demonstrate the applicability of the method to Shor period-finding circuits in the special case where the period is a power-of-two, for which the ideal circuit yields a unique outcome and the period can be inferred from single-qubit measurement probabilities. Despite being trained on smaller circuits, the model generalizes to higher qubit counts than those required during training, achieving success probabilities up to 35.48% on the 18-qubit circuit, while simultaneously offering significant run-time advantages over exact simulation (up to 66 times faster on the 24-qubit circuit). Because Shor’s classical post-processing is cheap, we can wrap PQS simulation in an error-tolerant loop for these circuit instances, which results in an expected runtime of O(n4/(1 − ε)), where 1 − ε is the probability that PQS simulation returns the correct period. For comparisons, we provide FLOP/s-normalized projections: our measured 36-qubit Quantum Fourier Transform runtime projects to 0.158 s on a single Argonne Theta node (versus a reported 78.98 h), and 40-qubit Shor projects to 19.3 s on a 2,048-A100 cluster (versus ∼ 200 s). We also analyze failure modes via the distribution of single-qubit measurement probabilities and find errors concentrated in the lowest index qubit, suggesting that targeted mitigation on only a few qubits may suffice. The PQS simulation exhibits a promising direction for approximate, flexible, and scalable simulation of quantum algorithms on classical hardware.
Classically simulating large quantum circuits is well-known to be difficult due to its exponential scaling O(2n) in computations and memory with respect to the number of qubits (n). We propose a novel classical simulation framework for quantum circuits, combining pairwise-qubit subsystems (PQS) with deep learning, thus called PQS simulation, to achieve scalable and highly efficient circuit evaluation. By representing quantum states as sequences of reduced density matrices and modeling two-qubit interactions through learnable unitary operators, this representation yields quadratic space and linear time per elementary gate, i.e., O(n2) memory and O(n) time per-gate update. A custom multi-hidden long short-term memory architecture is trained to learn and predict the evolution of pairwise entangled qubit subsystems. We demonstrate the applicability of the method to Shor period-finding circuits in the special case where the period is a power-of-two, for which the ideal circuit yields a unique outcome and the period can be inferred from single-qubit measurement probabilities. Despite being trained on smaller circuits, the model generalizes to higher qubit counts than those required during training, achieving success probabilities up to 35.48% on the 18-qubit circuit, while simultaneously offering significant run-time advantages over exact simulation (up to 66 times faster on the 24-qubit circuit). Because Shor’s classical post-processing is cheap, we can wrap PQS simulation in an error-tolerant loop for these circuit instances, which results in an expected runtime of O(n4/(1 − ε)), where 1 − ε is the probability that PQS simulation returns the correct period. For comparisons, we provide FLOP/s-normalized projections: our measured 36-qubit Quantum Fourier Transform runtime projects to 0.158 s on a single Argonne Theta node (versus a reported 78.98 h), and 40-qubit Shor projects to 19.3 s on a 2,048-A100 cluster (versus ∼ 200 s). We also analyze failure modes via the distribution of single-qubit measurement probabilities and find errors concentrated in the lowest index qubit, suggesting that targeted mitigation on only a few qubits may suffice. The PQS simulation exhibits a promising direction for approximate, flexible, and scalable simulation of quantum algorithms on classical hardware.
Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available methods, the classical simulation of quantum circuits inspired by density functional theory -- the so-called QC-DFT method, shows promise for large circuit simulations as it approximates the quantum circuits using single-qubit reduced density matrices to model multi-qubit systems. However, the QC-DFT method performs very poorly when dealing with multi-qubit gates. In this work, we introduce a novel CNOT "functional" that leverages neural networks to generate unitary transformations, effectively mitigating the simulation errors observed in the original QC-DFT method. For random circuit simulations, our modified QC-DFT enables efficient computation of single-qubit marginal measurement probabilities, or single-qubit probability (SQPs), and achieves lower SQP errors and higher fidelities than the original QC-DFT method. Despite some limitations in capturing full entanglement and joint probability distributions, we find potential applications of SQPs in simulating Shor's and Grover's algorithms for specific solution classes. These findings advance the capabilities of classical simulations for some quantum problems and provide insights into managing entanglement and gate errors in practical quantum computing.
Practical quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices is fundamentally bottlenecked by hardware imperfections: errors accumulate quickly and can destroy the interference patterns that quantum algorithms rely on. While full quantum error correction promises fault tolerance, its overhead is prohibitive for near-term processors, and many quantum error mitigation techniques trade this limitation for substantial sampling cost, limited applicability, or per-circuit retraining. We propose an active, learning-based circuit-level correction framework that suppresses errors during execution. Our approach interleaves lightweight single-qubit parameterized quantum circuit (PQC) blocks into a target circuit and predicts their corrective rotation angles directly from the circuit's gate sequence. We formalize this setting as a general parameter prediction problem: learn a model that maps circuits to continuous corrective parameters to minimize the expected discrepancy between the ideal and corrected output distributions over the circuit domain. We implement this with a Transformer-Encoder architecture operating on a sliding-window circuit representation, enabling prediction of corrections in a single forward pass. Across diverse random benchmark circuits, the learned predictor achieves zero-shot correction on unseen instances, eliminating expensive per-circuit tuning at inference time. Empirically, our interleaved corrections substantially improve output distribution fidelity, maintaining state fidelities above 0.99 in regimes where uncorrected executions average between 0.3 and 0.5.
While real quantum devices have been increasingly used to conduct research focused on achieving quantum advantage or quantum utility in recent years, executing deep quantum circuits or performing quantum machine learning with large-scale data on current noisy intermediate-scale quantum devices remains challenging, making classical simulation essential for quantum machine learning research. However, such classical simulation often suffers from the cost of gradient calculations, requiring enormous memory or computational time. To address these problems, we propose a method to fuse multiple consecutive gates in each of the forward and backward paths to improve throughput by minimizing global memory accesses. As a result, we achieved approximately 20 times throughput improvement for a Hardware-Efficient Ansatz with 12 or more qubits, reaching over 30 times improvement on a mid-range consumer GPU with limited memory bandwidth. By combining our proposed method with gradient checkpointing, we drastically reduced memory usage, making it possible to train a large-scale quantum machine learning model, a 20-qubit, 1,000-layer model with 60,000 parameters, using 1,000 samples in approximately 20 minutes per epoch. This implies that we can train the model on large datasets, comprising tens of thousands of samples, like MNIST or CIFAR-10, within a realistic time frame (e.g., 20 hours per epoch). Thus, our proposed method significantly accelerates such classical simulations, making a significant contribution to advancing research in quantum machine learning and variational quantum algorithms, such as verifying algorithms on large datasets or investigating learning theories of deep quantum circuits like barren plateaus.
Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data { X i noisy , X i exact } via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where X i noisy and X i exact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.
Achieving near-term quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. Here, we obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.
Numerous quantum algorithms assume that classical data has already been converted into quantum states, a process known as Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that scales exponentially with the number of qubits, posing a significant challenge to realizing quantum advantage. Recent research explores Parameterized Quantum Circuits (PQCs) as an approximate alternative, offering improved scalability with reduced circuit depth. However, the iterative, state-by-state optimization required by this approach creates substantial runtime overhead, which severely limits its practicality.To improve the efficiency of approximate QSP, we introduce a novel two-stage framework that can potentially generate QSP circuits for arbitrary quantum states. In theoffline training stage, our model learns a direct mapping from target states to circuit parameters, thereby bypassing the need foronline, state-by-state optimizationduring theinference stage. Extensive evaluations show that our approach significantly reduces runtime overhead by up to 132×, making a steady step towards efficient neural approximate QSP.