2024/04/01 by Ahmed A. Akhtar, Namit Anand, Akhtar, Ahmed A. +5 · 1 citation
Engineering · Medicine · #Advanced X-ray and CT Imaging #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Medical Imaging Techniques and Applications #Quantum Physics (quant-ph) #Radiation Dose and Imaging #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2404.01068
openalex publication_date 2024/04/01 · openalex created_date 2024/04/03 · openalex updated_date 2026/08/01
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 ρ(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 ρ(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.