Learning fermionic correlations by evolving with random translationally invariant Hamiltonians

Abstract

Schemes of classical shadows have been developed to facilitate the read-out of digital quantum devices, but similar tools for analog quantum simulators are scarce and experimentally impractical. In this work, we provide a measurement scheme for fermionic quantum devices that estimates second and fourth order correlation functions by means of free fermionic, translationally invariant evolutions - or quenches - and measurements in the mode occupation number basis. We precisely characterize what correlation functions can be recovered and equip the estimates with rigorous bounds on sample complexities, a particularly important feature in light of the difficulty of getting good statistics in reasonable experimental platforms, with measurements being slow. Finally, we demonstrate how our procedure can be approximately implemented with just nearest-neighbour, translationally invariant hopping quenches, a very plausible procedure under current experimental requirements, and requiring only random time-evolution with respect to a single native Hamiltonian. On a conceptual level, this work brings the idea of classical shadows to the realm of large scale analog quantum simulators.

27 pages, 10 figures

References in corpus (15)

• Variational Quantum Algorithms
• Randomized Benchmarking of Quantum Gates
• Single-Spin Addressing in an Atomic Mott Insulator
• Quantum advantage in learning from experiments
• The randomized measurement toolbox
• Matchgates and classical simulation of quantum circuits
• Fermionic partial tomography via classical shadows
• Robust shadow estimation
• Theory of quantum system certification: a tutorial
• When are correlations quantum? -- Verification and quantification of entanglement by simple measurements
• Fermionic Gaussian states: an introduction to numerical approaches
• Matchgate Shadows for Fermionic Quantum Simulation
• Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation
• Fermionic correlation functions from randomized measurements in programmable atomic quantum devices

Cited by in corpus (7)

• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Fermionic Magic Resources of Quantum Many-Body Systems
• Learning topological states from randomized measurements using variational tensor network tomography
• Tomography of parametrized quantum states
• Analyzing the free states of one quantum resource theory as resource states of another
• PAC-learning of free-fermionic states is NP-hard
• Majorana edge modes in isolated wires