Practical Black Box Hamiltonian Learning

Abstract

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality $k$). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol is practical for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.

arXiv comment32 pages, 10 figures

References in corpus (28)

• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Time-evolution methods for matrix-product states
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Procedure for systematically tuning up crosstalk in the cross resonance gate
• Practical characterization of quantum devices without tomography
• Experimental Quantum Hamiltonian Learning
• Hamiltonian Learning and Certification Using Quantum Resources
• Robust Online Hamiltonian Learning
• Suppressing qubit dephasing using real-time Hamiltonian estimation
• Machine Learning for Precise Quantum Measurement
• Learning a local Hamiltonian from local measurements
• Determining a local Hamiltonian from a single eigenstate
• Reducing unitary and spectator errors in cross resonance with optimized rotary echoes
• Sample-efficient learning of quantum many-body systems
• Coupling strength estimation for spin chains despite restricted access
• An Efficient Algorithm for Optimizing Adaptive Quantum Metrology Processes
• A Robust Method for Estimating the Lindblad Operators of a Dissipative Quantum Process from Measurements of the Density Operator at Multiple Time Points
• Finite-range interacting Ising quantum magnets with Rydberg atoms in optical lattices - From Rydberg superatoms to crystallization
• Theoretical and Experimental Perspectives of Quantum Verification
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• Evolution-free Hamiltonian parameter estimation through Zeeman markers
• Supervised learning of time-independent Hamiltonians for gate design
• Direct reconstruction of the quantum master equation dynamics of a trapped ion qubit
• Scalably learning quantum many-body Hamiltonians from dynamical data

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• Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix
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• The advantage of quantum control in many-body Hamiltonian learning
• Estimation of Hamiltonian parameters from thermal states
• Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems
• Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
• Hamiltonian Learning via Shadow Tomography of Pseudo-Choi States
• Learning interactions between Rydberg atoms
• Nearly query-optimal classical shadow estimation of unitary channels
• Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling
• Hamiltonian Learning via Inverse Physics-Informed Neural Networks
• Quantum natural gradient with thermal-state initialization
• Learning the structure of any Hamiltonian from minimal assumptions
• Spatial Leggett-Garg inequalities
• Optimal Hamiltonian recognition of unknown quantum dynamics