Dual-unitary shadow tomography

Ahmed A. Akhtar; Namit Anand; Jeffrey Marshall; Yi-Zhuang You

doi:10.22331/q-2025-07-29-1816

Dual-unitary shadow tomography

Ahmed A. Akhtar^1,2,3, Namit Anand^2,3, Jeffrey Marshall^2,4, and Yi-Zhuang You¹

¹Department of Physics, University of California San Diego, La Jolla, California 92093, USA
²Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, California 94035, USA
³KBR, Inc., 601 Jefferson St., Houston, Texas 77002, USA
⁴USRA Research Institute for Advanced Computer Science, Mountain View, California 94043, USA

Published:	2025-07-29, volume 9, page 1816
Editor:	Ángela Capel
Eprint:	arXiv:2404.01068v4
Doi:	https://doi.org/10.22331/q-2025-07-29-1816
Citation:	Quantum 9, 1816 (2025).

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Abstract

We introduce “dual-unitary shadow tomography'' (DUST), a classical shadow tomography protocol based on dual-unitary brick-wall circuits. To quantify the performance of DUST, we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of $\rho(x,t)$, which represents the probability of having nontrivial support at site $x$ and depth $t$ starting from a fixed weight distribution. We develop an equation of state for $\rho(x,t)$ and simulate it numerically using Monte Carlo simulations. For the task of predicting operators with (nearly) full support, we show that DUST outperforms brick-wall Clifford shadows of equal depth. This advantage is further pronounced for small system sizes and our results are generally robust to finite-size effects.

Featured image: Ballistic versus diffusive propagation of the Pauli weight of initially localized operators in dual-unitary and Clifford circuits, respectively.

Popular summary

Exactly solvable models are rare yet fundamental to our understanding of the quantum many-body problem. In recent years, dual-unitary circuits have emerged as a cornerstone of this search, by enabling the exact calculation of spectral form factors, out-of-time-ordered correlators, entanglement and other features central to strongly interacting quantum systems. Dual-unitary circuits also possess a unique level of tunability: by varying a single parameter representing two-body interactions, they can be tuned from a noninteracting 'solitonic' model to a maximally chaotic one. It is thus natural to wonder if these tunable circuits can be utilized for the task of classical shadow tomography, and if they can do better than random Cliffords?

In this work, we answer this in the affirmative by introducing transfer matrix methods supplanted by Monte Carlo simulations. We use this to show that, for the task of predicting observables with (nearly) full-support, random dual-unitary circuits outperform random Cliffords at any depth. Our results highlight the competition between operator spreading and information scrambling, and how it can be utilized to develop novel classical shadow tomography schemes.

► BibTeX data

@article{Akhtar2025dualunitaryshadow,
  doi = {10.22331/q-2025-07-29-1816},
  url = {https://doi.org/10.22331/q-2025-07-29-1816},
  title = {Dual-unitary shadow tomography},
  author = {Akhtar, Ahmed A. and Anand, Namit and Marshall, Jeffrey and You, Yi-Zhuang},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1816},
  month = jul,
  year = {2025}
}

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