Learning a local Hamiltonian from local measurements

Abstract

Recovering an unknown Hamiltonian from measurements is an increasingly important task for certification of noisy quantum devices and simulators. Recent works have succeeded in recovering the Hamiltonian of an isolated quantum system with local interactions from long-ranged correlators of a single eigenstate. Here, we show that such Hamiltonians can be recovered from local observables alone, using computational and measurement resources scaling linearly with the system size. In fact, to recover the Hamiltonian acting on each finite spatial domain, only observables within that domain are required. The observables can be measured in a Gibbs state as well as a single eigenstate; furthermore, they can be measured in a state evolved by the Hamiltonian for a long time, allowing to recover a large family of time-dependent Hamiltonians. We derive an estimate for the statistical recovery error due to approximation of expectation values using a finite number of samples, which agrees well with numerical simulations.

8 pages, 6 figures

References in corpus (23)

• Quantum Computing in the NISQ era and beyond
• A "missing" family of classical orthogonal polynomials
• Calculation of reduced density matrices from correlation functions
• Reduced density matrices and entanglement entropy in free lattice models
• Practical characterization of quantum devices without tomography
• Experimental Quantum Hamiltonian Learning
• Hamiltonian Learning and Certification Using Quantum Resources
• Robust Online Hamiltonian Learning
• Tomography and Generative Data Modeling via Quantum Boltzmann Training
• Quantum Hamiltonian identification from measurement time traces
• Coupling strength estimation for spin chains despite restricted access
• Hamiltonian tomography in an access-limited setting without state initialization
• Computational inverse method for constructing spaces of quantum models from wave functions
• A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Efficient estimation of nearly sparse many-body quantum Hamiltonians
• Hamiltonian identifiability assisted by single-probe measurement
• Hamiltonian tomography for quantum many-body systems with arbitrary couplings
• Method to identify parent Hamiltonians for trial states
• Quantum Bootstrapping via Compressed Quantum Hamiltonian Learning
• Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
• Compressed sensing for Hamiltonian reconstruction
• How local is the information in MPS/PEPS tensor networks?

Cited by in corpus (114)

• The randomized measurement toolbox
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Learning Quantum Systems
• Entanglement Hamiltonian Tomography in Quantum Simulation
• Sample-efficient learning of quantum many-body systems
• Quantum sensing with atomic, molecular, and optical platforms for fundamental physics
• Theoretical and Experimental Perspectives of Quantum Verification
• Hamiltonian Tomography via Quantum Quench
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• Learning models of quantum systems from experiments
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• Quantum Variational Learning of the Entanglement Hamiltonian
• Hamiltonian Learning for Quantum Error Correction
• Learning the dynamics of open quantum systems from their steady states
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Robust and Efficient Hamiltonian Learning
• Fast Estimation of Sparse Quantum Noise
• Learning Quantum Hamiltonians from Single-qubit Measurements
• Entanglement guided search for parent Hamiltonians
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• Quantum many-body systems in thermal equilibrium
• Quantum algorithms for estimating quantum entropies
• Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning
• Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain
• Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
• Supervised learning of time-independent Hamiltonians for gate design
• Practical Black Box Hamiltonian Learning
• Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data
• Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix
• Digital-Analog Quantum Simulations Using The Cross-Resonance Effect
• Direct reconstruction of the quantum master equation dynamics of a trapped ion qubit
• Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates
• Entanglement Hamiltonian of Many-body Dynamics in Strongly-correlated Systems
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• The advantage of quantum control in many-body Hamiltonian learning
• Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection
• Machine learning effective models for quantum systems
• Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments
• Scalably learning quantum many-body Hamiltonians from dynamical data
• Learned Optimizers for Analytic Continuation
• Determining system Hamiltonian from eigenstate measurements without correlation functions
• Estimation of Hamiltonian parameters from thermal states
• Tomography of time-dependent quantum spin networks with machine learning
• Optimal short-time measurements for Hamiltonian learning
• Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction
• Hamiltonian reconstruction via ringdown dynamics
• Experimental Bayesian estimation of quantum state preparation, measurement, and gate errors in multi-qubit devices
• Quantum Model Learning Agent: characterisation of quantum systems through machine learning
• Hamiltonian inference from dynamical excitations in confined quantum magnets
• Automatic design of Hamiltonians
• Probing infinite many-body quantum systems with finite-size quantum simulators
• Reconstructing effective Hamiltonians from nonequilibrium (pre-)thermal steady states
• Hamiltonian learning with real-space impurity tomography in topological moire superconductors
• Unified Quantum State Tomography and Hamiltonian Learning Using Transformer Models: A Language-Translation-Like Approach for Quantum Systems
• Deep reinforcement learning for preparation of thermal and prethermal quantum states
• Hamiltonian tomography by the quantum quench protocol with random noise
• High-accuracy Hamiltonian learning via delocalized quantum state evolutions
• Quantifying Quantum Computational Advantage on a Processor of Ultracold Atoms
• Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems
• Hamiltonian learning from time dynamics using variational algorithms
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
• Hamiltonian Learning in Quantum Field Theories
• Hamiltonian Assignment for Open Quantum Systems
• Inferring interpretable dynamical generators of local quantum observables from projective measurements through machine learning
• Optimal parent Hamiltonians for time-dependent states
• Hamiltonian learning for 300 trapped ion qubits with long-range couplings
• Learning a quantum channel from its steady-state
• Structure learning of Hamiltonians from real-time evolution
• Programmable quantum simulations on a trapped-ions quantum simulator with a global drive
• When can a local Hamiltonian be recovered from a steady state?
• Dimension reduction and redundancy removal through successive Schmidt decompositions
• Digital Quantum Simulation, Learning of the Floquet Hamiltonian, and Quantum Chaos of the Kicked Top
• Hamiltonian Learning using Machine Learning Models Trained with Continuous Measurements
• Learning quantum dissipation by the neural ordinary differential equation
• Supervised Training of Neural-Network Quantum States for the Next Nearest Neighbor Ising model
• Accreditation of Analogue Quantum Simulators
• The spectrum of local random Hamiltonians
• Relationship between the ground-state wave function of a magnet and its static structure factor
• Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient
• On the complexity of finding the maximum entropy compatible quantum state
• A protocol to characterize errors in quantum simulation of many-body physics
• Hamiltonian-learning quantum magnets with non-local impurity tomography
• Hamiltonian Learning of Triplon Excitations in an Artificial Nanoscale Molecular Quantum Magnet
• Learning interactions between Rydberg atoms
• Preparing Quantum States by Measurement-feedback Control with Bayesian Optimization
• Efficient and robust estimation of many-qubit Hamiltonians
• Quantum State Driving along Arbitrary Trajectories
• Motion from Measurement: The Role of Symmetry of Quantum Measurements
• Nearly query-optimal classical shadow estimation of unitary channels
• Error Mitigation Thresholds in Noisy Random Quantum Circuits
• Parent Hamiltonian Reconstruction via Inverse Quantum Annealing
• Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
• Machine-learning-enabled characterization of individual ring resonators in integrated photonic lattices
• Learning the structure of any Hamiltonian from minimal assumptions
• Predicting Quantum Potentials by Deep Neural Network and Metropolis Sampling
• Applicability of coupling strength estimation for linear chains of restricted access
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Short-time simulation of quantum dynamics by Pauli measurements
• Lieb-Robinson bounds imply locality of interactions
• Entanglement Clustering for ground-stateable quantum many-body states
• Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach
• Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation
• Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning
• Characterizing errors in parameter estimation by local measurements
• Optimal Hamiltonian recognition of unknown quantum dynamics
• Fitness landscape for quantum state tomography from neutron scattering
• Learning and simulating bosonic systems via finite-energy locality
• Hamiltonian-reconstruction distance as a success metric for the Variational Quantum Eigensolver
• Topology identification of autonomous quantum dynamical networks
• Hamiltonian Reconstruction: the Correlation Matrix and Incomplete Operator Bases