Shadow tomography from emergent state designs in analog quantum simulators

Abstract

We introduce a method that allows one to infer many properties of a quantum state -- including nonlinear functions such as Rényi entropies -- using only global control over the constituent degrees of freedom. In this protocol, the state of interest is first entangled with a set of ancillas under a fixed global unitary, before projective measurements are made. We show that when the unitary is sufficiently entangling, a universal relationship between the statistics of the measurement outcomes and properties of the state emerges, which can be connected to the recently discovered phenomenon of emergent quantum state designs in chaotic systems. Thanks to this relationship, arbitrary observables can be reconstructed using the same number of experimental repetitions that would be required in classical shadow tomography [Huang et al., Nat. Phys. 16, 1050 (2020)]. Unlike previous approaches to shadow tomography, our protocol can be implemented using only global operations, as opposed to qubit-selective logic gates, which makes it particularly well-suited to analog quantum simulators, including ultracold atoms in optical lattices and arrays of Rydberg atoms.

7+15 pages, 3 figures

References in corpus (12)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Strong and weak thermalization of infinite non-integrable quantum systems
• The randomized measurement toolbox
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Tight informationally complete quantum measurements
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Generalized Deep Thermalization for Free Fermions
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation

Cited by in corpus (22)

• Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Probing post-measurement entanglement without post-selection
• Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
• Postselection-free learning of measurement-induced quantum dynamics
• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Designs via Free Probability
• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• Classical shadows based on locally-entangled measurements
• Quantum criticality under imperfect teleportation
• Deep thermalization under charge-conserving quantum dynamics
• Unraveling the emergence of quantum state designs in systems with symmetry
• Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions
• Optimising quantum tomography via shadow inversion
• Deep thermalization in Gaussian continuous-variable quantum systems
• Optimal Conversion from Classical to Quantum Randomness via Quantum Chaos
• Boundary transitions from a single round of measurements on gapless quantum states
• Matchgate circuits deeply thermalize
• Estimating many properties of a quantum state via quantum reservoir processing
• Holographic Classical Shadow Tomography
• Fast computational deep thermalization
• Quantum Advantage via Efficient Post-processing on Qudit Classical Shadow tomography
• Simple Diagonal State Designs with Reconfigurable Real-Time Circuits