Deep Circuit Compression for Quantum Dynamics via Tensor Networks

Joe Gibbs; Lukasz Cincio

doi:10.22331/q-2025-07-09-1789

Deep Circuit Compression for Quantum Dynamics via Tensor Networks

Joe Gibbs^1,2 and Lukasz Cincio³

¹School of Mathematics and Physics, University of Surrey, Guildford, GU2 7XH, UK
²AWE, Aldermaston, Reading, RG7 4PR, UK
³Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Published:	2025-07-09, volume 9, page 1789
Editor:	Daniel Malz
Eprint:	arXiv:2409.16361v2
Doi:	https://doi.org/10.22331/q-2025-07-09-1789
Citation:	Quantum 9, 1789 (2025).

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Abstract

Dynamic quantum simulation is a leading application for achieving quantum advantage. However, high circuit depths remain a limiting factor on near-term quantum hardware. We present a compilation algorithm based on Matrix Product Operators for generating compressed circuits enabling real-time simulation on digital quantum computers, that for a given depth are more accurate than all Trotterizations of the same depth. By the efficient use of environment tensors, the algorithm is scalable in depth far beyond prior work, and we present circuit compilations of up to 64 layers of $SU(4)$ gates. Surpassing only 1D circuits, our approach can flexibly target a particular quasi-2D gate topology. We demonstrate this by compiling a 52-qubit 2D Transverse-Field Ising propagator onto the IBM Heavy-Hex topology. For all circuit depths and widths tested, we produce circuits with smaller errors than all equivalent depth Trotter unitaries, corresponding to reductions in error by up to 4 orders of magnitude and circuit depth compressions with a factor of over 6.

Popular summary

$\textbf{Overview of Algorithm. }$
1) The input is a Hamiltonian $H$ and time step $t$. The algorithm finds a shallow circuit that approximates the propagator $e^{-iHt}$.
2) The propagator is represented as an MPO by Trotterization with a fine time step for a negligible Trotter error, for the longest time that results in an MPO with a tractable bond dimension.
3) For the gate topology of a target quantum computer, an optimization is performed to maximize the overlap between the target unitary and the variational quantum circuit.
4) The compressed circuit for the propagator can enable real-time simulation on a quantum computer with a shorter circuit depth than possible using standard Trotterization methods.

► BibTeX data

@article{Gibbs2025deepcircuit,
  doi = {10.22331/q-2025-07-09-1789},
  url = {https://doi.org/10.22331/q-2025-07-09-1789},
  title = {Deep {C}ircuit {C}ompression for {Q}uantum {D}ynamics via {T}ensor {N}etworks},
  author = {Gibbs, Joe and Cincio, Lukasz},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1789},
  month = jul,
  year = {2025}
}

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[1] Isabel Nha Minh Le, Shuo Sun, and Christian B. Mendl, "Riemannian quantum circuit optimization based on matrix product operators", Quantum 9, 1833 (2025).

[2] Yuxuan Zhang, Roeland Wiersema, Juan Carrasquilla, Lukasz Cincio, and Yong Baek Kim, "Scalable quantum dynamics compilation via quantum machine learning", Physical Review Research 8 2, 023128 (2026).

[3] N. L. Diaz, Paolo Braccia, Martin Larocca, J. M. Matera, R. Rossignoli, and M. Cerezo, "Parallel-in-time quantum simulation via Page and Wootters quantum time", Physical Review Research 7 3, 033294 (2025).

[4] GUO Yuchen and YANG Shuo, "Frontiers of tensor networks and their applications in quantum many-body physics", SCIENTIA SINICA Physica, Mechanica & Astronomica 56 8, 280011 (2026).

[5] Pilsung Kang, "Emergent Bifurcations in Quantum Circuit Stability From Hidden Parameter Statistics", IEEE Transactions on Quantum Engineering 7, 2500608 (2026).

[6] Yahui Chai, Joe Gibbs, Vincent R. Pascuzzi, Zoë Holmes, Stefan Kühn, Francesco Tacchino, and Ivano Tavernelli, "Resource-efficient simulations of particle scattering on a digital quantum computer", npj Quantum Information 12 1, 100 (2026).

[7] Shu Kanno, Kenji Sugisaki, Rei Sakuma, Jumpei Kato, Hajime Nakamura, and Naoki Yamamoto, "Tensor-based phase difference estimation on time-series analysis", Physical Review A 113 5, 052433 (2026).

[8] Nikita A. Zemlevskiy, "Scalable quantum simulations of scattering in scalar field theory on 120 qubits", Physical Review D 112 3, 034502 (2025).

[9] Matteo D'Anna, Yuxuan Zhang, Roeland Wiersema, Manuel S. Rudolph, and Juan Carrasquilla, "Circuit compression for 2D quantum dynamics", arXiv:2507.01883, (2025).

[10] Joe Gibbs and Lukasz Cincio, "Learning Circuits with Infinite Tensor Networks", arXiv:2506.02105, (2025).

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