Efficient Local Classical Shadow Tomography with Number Conservation

Abstract

Shadow tomography aims to build a classical description of a quantum state from a sequence of simple random measurements. Physical observables are then reconstructed from the resulting classical shadow. Shadow protocols which use single-body random measurements are simple to implement and capture few-body observables efficiently, but do not apply to systems with fundamental number conservation laws, such as ultracold atoms. We address this shortcoming by proposing and analyzing a new local shadow protocol adapted to such systems. The "All-Pairs" protocol requires one layer of two-body gates and only $\text{poly}(V)$ samples to reconstruct arbitrary few body observables. Moreover, by exploiting the permutation symmetry of the protocol, we derive a linear time post-processing algorithm. We provide a proof-of-principle reference implementation and demonstrate the reconstruction of 2- and 4-point functions in a paired Luttinger liquid of hardcore bosons.

6 pages 3 figures

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Cold atoms in cavity-generated dynamical optical potentials
• The randomized measurement toolbox
• Fermionic partial tomography via classical shadows
• Robust shadow estimation
• Classical Shadows With Noise
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• Restrictions on realizable unitary operations imposed by symmetry and locality
• Scalable and Flexible Classical Shadow Tomography with Tensor Networks
• Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Quantum scrambling with classical shadows
• Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers
• Probing post-measurement entanglement without post-selection
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation
• Operator relaxation and the optimal depth of classical shadows
• Benchmarking Quantum Simulators using Ergodic Quantum Dynamics
• Classical shadows based on locally-entangled measurements
• Randomized measurement protocols for lattice gauge theories
• On Classical and Hybrid Shadows of Quantum States

Cited by in corpus (6)

• Designs via Free Probability
• Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
• Deep thermalization under charge-conserving quantum dynamics
• Unitary Designs of Symmetric Local Random Circuits
• Selective and efficient quantum state tomography for multi-qubit systems
• Classical Shadows with Improved Median-of-Means Estimation