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arXiv:2604.08467

Accelerating Quantum Tensor Network Simulations with Unified Path Variations and Non-Degenerate Batched Sampling

Taylor Lee Patti, Paavai Pari, Yang Gao, Azzam Haidar, Thien Nguyen, Tom Lubowe, Daniel Lowell, Brucek Khailany

quant-phSubmitted Apr 9, 2026• Announced Apr 10, 2026• 0 citations
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Abstract

Quantum trajectory methods reduce the computational overhead of simulating noisy quantum systems, approximating them with $m$ stochastically sampled $2^n$-entry quantum statevectors rather than exact $2^{2n}$-entry density matrices. Recently, Pre-Trajectory Sampling with Batched Execution (PTSBE) has dramatically increased the data collection rate of these methods. While statevector PTSBE has demonstrated data collection speedups of over $10^6 \times$, tensor network implementations only achieved $\sim 15 \times$ speedup. This comparatively modest tensor network advantage stemmed from 1) contraction path recalculations, 2) sequential tensor network sampling, and 3) inflexible/unoptimized contraction hyperparameters. In this manuscript, we increase PTSBE's tensor network data collection rate to more than $10^8\times$ that of traditional trajectories methods by developing 1) error-independent unified path variation, 2) non-degenerate tensor network sampling, and 3) a flexible/optimized contraction framework. While our methods are particularly powerful for accelerating non-proportional sampling, we also demonstrate a more than $1000\times$ speedup for more general quantum simulations.

Comments
11 pages, 7 figures

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Quantum trajectory methods reduce the computational overhead of simulating noisy quantum systems, approximating them with mmm stochastically sampled 2n2^n2n-entry quantum statevectors rather than exact 22n2^{2n}22n-entry density matrices. Recently, Pre-Trajectory Sampling with Batched Execution (PTSBE) has dramatically increased the data collection rate of these methods. While statevector PTSBE has demonstrated data collection speedups of over 106×10^6 \times106×, tensor network implementations only achieved ∼15×\sim 15 \times∼15× speedup. This comparatively modest tensor network advantage stemmed from 1) contraction path recalculations, 2) sequential tensor network sampling, and 3) inflexible/unoptimized contraction hyperparameters. In this manuscript, we increase PTSBE's tensor network data collection rate to more than 108×10^8\times108× that of traditional trajectories methods by developing 1) error-independent unified path variation, 2) non-degenerate tensor network sampling, and 3) a flexible/optimized contraction framework. While our methods are particularly powerful for accelerating non-proportional sampling, we also demonstrate a more than 1000×1000\times1000× speedup for more general quantum simulations.
Classically simulating quantum systems is challenging, as even noiseless n-qubit quantum states scale as 2n. The complexity of noisy quantum systems is even greater, requiring 2n × 2n-dimensional density matrices. Various approximations reduce density matrix overhead, including quantum trajectory-based methods, which instead use an ensemble of m ≪ 2n noisy states. While this method is dramatically more efficient, current implementations use unoptimized sampling, redundant state preparation, and single-shot data collection. In this manuscript, we present the Pre-Trajectory Sampling technique, increasing the efficiency and utility of trajectory simulations by tailoring error types, batching sampling without redundant computation, and collecting error information. We demonstrate the effectiveness of our method with both a mature statevector simulation of a 35-qubit quantum error-correction code and a preliminary tensor network simulation of 85 qubits, yielding speedups of up to 106x and 16x, as well as generating massive datasets of one trillion and one million shots, respectively.
A crucial aspect of validating quantum protocols is understanding the noise produced by quantum computing devices. Using simulations that can replicate this noise allows for a lower-cost alternative to hardware experiments. Stochastic, so-called "trajectory" methods are often used as a quadratically reduced approximation to density matrix simulations, but traditional implementations have limited sampling capacity and provide no error-based metadata. The Pre-Trajectory Sampling with Batched Execution (PTSBE) [Patti et al., 2025] algorithm provides a solution by combining fine-tuned, well-documented noise sampling with computational intermediate caching. While the original work is effective on quantum error correction circuits, its performance on general circuits has yet to be explored. This project gauges PTSBE on random quantum circuits to understand convergence behavior and accuracy compared to traditional methods. To accomplish this, an automated simulation pipeline was developed by using Apache Airflow and CUDA-Q to generate a collection of noisy circuits, run both exact and approximate simulations, and analyze error criteria across various qubit counts and circuit depths. Early tests have confirmed the system's ability to scale to 20-qubit circuits and produce accurate comparison data. Our work aims to provide guidance for researchers using PTSBE in noisy simulation environments, expanding its use beyond specific cases.
Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector-based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determining the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. First, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Second, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96× reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5× compared to the state-of-the-art CPU-based results and 4.48–6.78× compared to the state-of-the-art GPU-based results reported in the literature. Furthermore, the strategies presented in this article hold general applicability for accelerating problems that can be tackled by contracting tensor networks such as graphical models and combinatorial optimizations.
Classical simulation of noisy quantum circuits is essential for validating algorithms, benchmarking hardware, and assessing error-mitigation strategies, but remains limited by the exponential cost of density-matrix methods and the high variance of standard trajectory sampling. We introduce a variance-aware tensor network framework that combines the tensor jump method with local TDVP gate evolution on matrix product states and sparse Pauli-Lindblad hardware noise models. Gates are applied as short variational evolutions on the MPS manifold, while noise is sampled per circuit window from Pauli-Lindblad jump sets with state-independent hazards and dissipative contractions that reduce to irrelevant global factors after renormalization. The method supports correlated multi-qubit Lindblad noise consistent with hardware connectivity, including long-range operators on non-adjacent qubits, enabling direct simulation of crosstalk and other connectivity-induced errors beyond local noise models. We develop two unbiased variance-aware unravelings. An analog unitary-mixture unraveling matches the Lindblad generator exactly under symmetric Gaussian or two-point angle laws, while a projector-jump unraveling yields state-independent hazards and closed-form variance laws. Both retain the standard 1/sqrt(N) Monte Carlo convergence but with reduced prefactors. Empirically, projector sampling strongly reduces trajectory variance and bond-dimension growth across many circuit architectures, whereas analog sampling is most effective at weak noise. We demonstrate accurate, scalable noisy-circuit simulation on a 25-qubit noisy XY quench and IBM's 127-qubit kicked-Ising benchmark with long-range depolarizing noise, achieving reduced Monte Carlo variance and favorable MPS bond-dimension growth compared with standard Kraus-insertion baselines.
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on computation time and memory footprint. In this work, we implement new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks. We test our methods on a variety of benchmarks, including the random quantum circuit instances recently implemented on Google quantum chips. We find that the paths obtained can be very close to optimal, and often many orders or magnitude better than the most established approaches. As different underlying geometries suit different methods, we also introduce a hyper-optimization approach, where both the method applied and its algorithmic parameters are tuned during the path finding. The increase in quality of contraction schemes found has significant practical implications for the simulation of quantum many-body systems and particularly for the benchmarking of new quantum chips. Concretely, we estimate a speed-up of over 10,000 × compared to the original expectation for the classical simulation of the Sycamore `supremacy' circuits.
The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical simulations, it has been suggested that the addition of non-linear elements to the experiment will help retain the quantum advantage. We propose a classical simulation tool for general continuous variable sampling problems, including Gaussian Boson Sampling and beyond. We reformulate the sampling problem as that of finding the ground state of a simple few-body Hamiltonian. This allows us to employ powerful variational methods based on tensor networks and to read off the simulation error directly from the expectation value of the Hamiltonian. We validate our method by simulating Gaussian Boson Sampling, where we achieve results comparable to the state of the art. We also consider a non-Gaussian sampling problem, for which we develop novel local basis optimization techniques based on a non-linear parameterization of the implicit basis, resulting in high effective cutoffs with diminished computational overhead.