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arXiv:2603.02804

Fast and memory-efficient classical simulation of quantum machine learning via forward and backward gate fusion

Yoshiaki Kawase

quant-phcs.DCcs.ETSubmitted Mar 3, 2026• Announced Mar 4, 2026• 0 citations• Revised Apr 3, 2026 (v2)
v1 · Mar 3, 2026v2 · Apr 3, 2026
arXivHTMLPDF

Abstract

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.

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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 202020 times throughput improvement for a Hardware-Efficient Ansatz with 121212 or more qubits, reaching over 303030 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 202020-qubit, 1,0001{,}0001,000-layer model with 60,00060{,}00060,000 parameters, using 1,0001{,}0001,000 samples in approximately 202020 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., 202020 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.
We propose an approach to generative quantum machine learning that overcomes the fundamental scaling issues of variational quantum circuits. The core idea is to use a class of generative models based on instantaneous quantum polynomial circuits, which we show can be trained efficiently on classical hardware. Although training is classically efficient, sampling from these circuits is widely believed to be classically hard, and so computational advantages are possible when sampling from the trained model on quantum hardware. By combining our approach with a data-dependent parameter initialisation strategy, we do not encounter issues of barren plateaus and successfully circumvent the poor scaling of gradient estimation that plagues traditional approaches to quantum circuit optimisation. We investigate and evaluate our approach on a number of real and synthetic datasets, training models with up to one thousand qubits and hundreds of thousands of parameters. We find that the quantum models can successfully learn from high dimensional data, and perform surprisingly well compared to simple energy-based classical generative models trained with a similar amount of hyperparameter optimisation. Overall, our work demonstrates that a path to scalable quantum generative machine learning exists and can be investigated today at large scales.
Abstract Quantum machine learning, focusing on quantum neural networks (QNNs), remains a vastly uncharted field of study. Current QNN models primarily employ variational circuits on an ansatz or a quantum feature map, often requiring multiple entanglement layers. This methodology not only increases the computational cost of the circuit beyond what is practical on near-term quantum devices but also misleadingly labels these models as neural networks, given their divergence from the structure of a typical feed-forward neural network (FFNN). Moreover, the circuit depth and qubit needs of these models scale poorly with the number of data features, resulting in an efficiency challenge for real-world machine learning tasks. We introduce a bona fide QNN model, which seamlessly aligns with the versatility of a traditional FFNN in terms of its adaptable intermediate layers and nodes, absent from intermediate measurements such that our entire model is coherent. This model stands out with its reduced circuit depth and number of requisite CNOT gates, achieving a more than 50% reduction in both compared to prevailing QNN models. Furthermore, the qubit count in our model remains unaffected by the data’s feature quantity. We test our proposed model on various benchmarking datasets such as the breast cancer diagnostic (Wisconsin) and credit card fraud detection datasets. Our model achieved an accuracy of 91% on the breast cancer dataset and 85% on the credit card fraud detection dataset, outperforming existing QNN methods by 5–10% while requiring approximately 50% fewer quantum resources. These results showcase the advantageous efficacy of our approach, paving the way for the application of quantum neural networks to relevant real-world machine learning problems.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns have become increasingly pressing as conventional computers are soon expected to approach the physical limitations that will slow their performance improvements in the near future. For these reasons, scientists have begun to explore alternative computing platforms, like quantum computers, for training neural networks. In recent years, variational quantum circuits have emerged as one of the most successful approaches to quantum deep learning on noisy intermediate scale quantum devices. We propose a hybrid quantum-classical neural network architecture where each neuron is a variational quantum circuit. We empirically analyze the performance of this hybrid neural network on a series of binary classification data sets using a simulated IBM universal quantum computer and a state-of-the-art IBM universal quantum computer. On the simulated hardware, we observe that the hybrid neural network achieves around 10% higher classification accuracy and 20% better minimization of the cost function than an individual variational quantum circuit. On the quantum hardware, we observe that each model only performs well when the qubit and gate count is sufficiently small.
With the evolution of technology, the need to solve complex computational problems like machine learning and deep learning has shot up. However, even the most powerful classical supercomputers find it difficult to execute these tasks. Advancements in quantum computing are leading researchers and tech-giants who strive for better quantum circuits to do machine learning tasks. Current works on Quantum Machine Learning (QML) ensure less memory consumption and reduced model parameters. However, it is strenuous to simulate the classical deep learning approach on existing quantum computing devices due to the inflexibility of Deep quantum circuits. Consequently, designing viable quantum algorithms for QML for noisy intermediate-scale quantum (NISQ) devices is essential. The proposed work aims to explore Variational Quantum Circuits (VQC) for Deep Q network-based Reinforcement Learning by remodeling the target network and experience replay into a representation of VQC. In addition, to the reduction in model parameters, quantum information encoding schemes are used to achieve better results than classical neural networks. VQCs are employed for policyselection and decision-making reinforcement learning by approximating the deep Q-value function with target network and experience replay.
Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns have become increasingly pressing as conventional computers quickly approach physical limitations that will slow performance improvements in years to come. For these reasons, scientists have begun to explore alternative computing platforms, like quantum computers, for training neural networks. In recent years, variational quantum circuits have emerged as one of the most successful approaches to quantum deep learning on noisy intermediate scale quantum devices. We propose a hybrid quantum-classical neural network architecture where each neuron is a variational quantum circuit. We empirically analyze the performance of this hybrid neural network on a series of binary classification data sets using a simulated universal quantum computer and a state of the art universal quantum computer. On simulated hardware, we observe that the hybrid neural network achieves roughly 10% higher classification accuracy and 20% better minimization of cost than an individual variational quantum circuit. On quantum hardware, we observe that each model only performs well when the qubit and gate count is sufficiently small.