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arXiv:2512.20064

FastMPS: Revisit Data Parallel in Large-scale Matrix Product State Sampling

Yaojian Chen, Si-Qiu Gong, Lin Gan, Yanfei Liu, An Yang, Yinuo Wang, Chao-yang Lu, Guangwen Yang

Published Dec 23, 2025• 0 citations
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Abstract

Matrix Product State (MPS) is a versatile tensor network representation widely applied in quantum physics, quantum chemistry, and machine learning, etc. MPS sampling serves as a critical fundamental operation in these fields. As the problems become more complex, the scale of MPS is rapidly increasing. Traditional data parallelism is limited by memory and heavy I/O in large-scale MPS. Model parallelism that can handle large-scale MPS imposes rigid process bindings and lacks scalability. This work proposes Fast-MPS, a multi-level parallel framework for scalable MPS sampling. Our design combines data parallelism across samples with tensor parallelism along bond dimensions. We eliminate memory and I/O pressure through compression and overlapping, and revive data parallel in large-scale MPS sampling. We evaluate our approach on Gaussian Boson Sampling, a representative and demanding application. Fast-MPS achieves over 10x speedup compared to existing simulators, scales to thousands of processes, and enables simulations with 8,176 sites and bond dimension chi = 10^4, significantly outperforming the state of the art. Fast-MPS has demonstrated great potential in high-performance tensor network applications.

DOI
10.48550/arxiv.2512.20064

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Matrix Product State (MPS) is a versatile tensor network representation widely applied in quantum physics, quantum chemistry, and machine learning, etc. MPS sampling serves as a critical fundamental operation in these fields. As the problems become more complex, the scale of MPS is rapidly increasing. Traditional data parallelism is limited by memory and heavy I/O in large-scale MPS. Model parallelism that can handle large-scale MPS imposes rigid process bindings and lacks scalability. This work proposes Fast-MPS, a multi-level parallel framework for scalable MPS sampling. Our design combines data parallelism across samples with tensor parallelism along bond dimensions. We eliminate memory and I/O pressure through compression and overlapping, and revive data parallel in large-scale MPS sampling. We evaluate our approach on Gaussian Boson Sampling, a representative and demanding application. Fast-MPS achieves over 10x speedup compared to existing simulators, scales to thousands of processes, and enables simulations with 8,176 sites and bond dimension chi = 10^4, significantly outperforming the state of the art. Fast-MPS has demonstrated great potential in high-performance tensor network applications.
Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step, however, is hindered by a significant bottleneck due to the hafnian. We present an efficient algorithm that converts pure bosonic Gaussian states into matrix product states (MPSs), thereby establishing a versatile tool for probing bosonic Gaussian systems in settings where direct Gaussian-formalism-based calculations become inefficient. Our method combines a Gaussian singular value decomposition with a projected-creation-operator mapping that constructs local MPS tensors without computing hafnians. Benchmarking on covariance matrices from the Jiuzhang 2.0 and Jiuzhang 4.0 Gaussian boson sampling experiments demonstrates substantial speedups over previous tensor-network approaches in the low-entanglement regime relevant to lossy devices. The method provides a scalable classical simulation framework for bosonic Gaussian states with limited entanglement. In this regime, a target accuracy can be achieved with a bond dimension that remains computationally tractable, thereby extending the applicability of MPS-based methods to a broad range of bosonic systems.
Abstract Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These networks are used to approximate high-order tensors by contracting tensors with lower ranks. Originally developed for simulating quantum systems, tensor networks have become integral to quantum computing and, by extension, to QML. Their ability to efficiently represent and manipulate complex, high-dimensional data makes them suitable for various machine learning tasks within the quantum realm. Here, we present a matrix product state (MPS) model, where the MPS functions as both a classifier and a generator. The dual functionality of this novel MPS model permits a strategy that enhances the traditional training of supervised MPS models. This framework is inspired by generative adversarial networks and is geared towards generating more realistic samples by reducing outliers. Additionally, our contributions offer insights into the mechanics of tensor network methods for generation tasks. Specifically, we discuss alternative embedding functions and a new sampling method from non-normalized MPSs.
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These networks are used to approximate high-order tensors by contracting tensors with lower ranks. Initially developed for simulating quantum systems, tensor networks have become integral to quantum computing and, by extension, to QML. Drawing inspiration from these quantum methods, specifically the Matrix Product States (MPS), we apply them in a classical machine learning setting. Their ability to efficiently represent and manipulate complex, high-dimensional data makes them effective in a supervised learning framework. Here, we present an MPS model, in which the MPS functions as both a classifier and a generator. The dual functionality of this novel MPS model permits a strategy that enhances the traditional training of supervised MPS models. This framework is inspired by generative adversarial networks and is geared towards generating more realistic samples by reducing outliers. In addition, our contributions offer insights into the mechanics of tensor network methods for generation tasks. Specifically, we discuss alternative embedding functions and a new sampling method from non-normalized MPSs.
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Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for probabilistic modeling of sequence data. We first show that u-MPS enable sequence-level parallelism, with length-n sequences able to be evaluated in depth O(log n). We then introduce a novel generative algorithm giving trained u-MPS the ability to efficiently sample from a wide variety of conditional distributions, each one defined by a regular expression. Special cases of this algorithm correspond to autoregressive and fill-in-the-blank sampling, but more complex regular expressions permit the generation of richly structured data in a manner that has no direct analogue in neural generative models. Experiments on sequence modeling with synthetic and real text data show u-MPS outperforming a variety of baselines and effectively generalizing their predictions in the presence of limited data.