Short remarks on shallow unitary circuits

Jeongwan Haah

doi:10.22331/q-2025-12-11-1940

Short remarks on shallow unitary circuits

Leinweber Institute for Theoretical Physics, Stanford University
Google Quantum AI

Published:	2025-12-11, volume 9, page 1940
Editor:	Daniel Malz
Eprint:	arXiv:2504.14005v5
Doi:	https://doi.org/10.22331/q-2025-12-11-1940
Citation:	Quantum 9, 1940 (2025).

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Abstract

(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the case with a continuous onsite symmetry or with a local energy conservation law. (ii) We explain a simple algorithm for a formulation of the shallow unitary circuit learning problem and relate it to an open question on strictly locality-preserving unitaries (quantum cellular automata). (iii) We show that any translation-invariant quantum cellular automaton in $D$-dimensional lattice of volume $V$ can be implemented using only $O(V)$ local gates in a staircase fashion using invertible subalgebra pumping.

► BibTeX data

@article{Haah2025shortremarksshallow,
  doi = {10.22331/q-2025-12-11-1940},
  url = {https://doi.org/10.22331/q-2025-12-11-1940},
  title = {Short remarks on shallow unitary circuits},
  author = {Haah, Jeongwan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1940},
  month = dec,
  year = {2025}
}

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Cited by

[1] Emanuele Tirrito, Xhek Turkeshi, and Piotr Sierant, "Anticoncentration and Nonstabilizerness Spreading under Ergodic Quantum Dynamics", Physical Review Letters 135 22, 220401 (2025).

[2] Piotr Sierant, Paolo Stornati, and Xhek Turkeshi, "Fermionic Magic Resources of Quantum Many-Body Systems", PRX Quantum 7 1, 010302 (2026).

[3] Hsin-Yuan Huang, Michael Broughton, Norhan Eassa, Hartmut Neven, Ryan Babbush, and Jarrod R. McClean, "Generative quantum advantage for classical and quantum problems", arXiv:2509.09033, (2025).

[4] Laura Cui, Thomas Schuster, Liang Mao, Hsin-Yuan Huang, and Fernando Brandao, "Random unitaries from Hamiltonian dynamics", arXiv:2510.08434, (2025).

[5] Maxwell West, Diego García-Martín, N. L. Diaz, M. Cerezo, and Martin Larocca, "No-go theorems for sublinear-depth group designs", arXiv:2506.16005, (2025).

[6] Thomas Schuster, Dominik Kufel, Norman Y. Yao, and Hsin-Yuan Huang, "Hardness of recognizing phases of matter", arXiv:2510.08503, (2025).

[7] Sabee Grewal and Daniel Liang, "Efficient Learning of Structured Quantum Circuits via Pauli Dimensionality and Sparsity", arXiv:2510.00168, (2025).

The above citations are from SAO/NASA ADS (last updated successfully 2026-08-07 18:02:09). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2026-08-07 18:02:07).

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