Dual-Unitary Classical Shadow Tomography
- URL: http://arxiv.org/abs/2404.01068v2
- Date: Fri, 14 Jun 2024 07:38:08 GMT
- Title: Dual-Unitary Classical Shadow Tomography
- Authors: Ahmed A. Akhtar, Namit Anand, Jeffrey Marshall, Yi-Zhuang You,
- Abstract summary: We study operator spreading and Pauli weight dynamics in one-dimensional qubit systems.
We develop an equation of state for $rho(x,t)$, and simulate it numerically using Monte Carlo simulations.
Our results are robust to finite-size effects due to the chirality of dual-unitary brick-wall circuits.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce a classical shadow tomography scheme based on dual-unitary brick-wall circuits termed "dual-unitary shadow tomography" (DUST). For this 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 final measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. We first show that dual-unitaries must have a minimal amount of entropy production. 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. Lastly, we demonstrate that the fast-thermalizing properties of dual-unitary circuits make them better at predicting large operators than shallow brick-wall Clifford circuits. Our results are robust to finite-size effects due to the chirality of dual-unitary brick-wall circuits.
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