Learning Quantum Hamiltonians from Single-qubit Measurements

Abstract

It is natural to measure the observables from the Hamiltonian-based quantum dynamics, and its inverse process that Hamiltonians are estimated from the measured data also is a vital topic. In this work, we propose a recurrent neural network to learn the parameters of the target Hamiltonians from the temporal records of single-qubit measurements. The method does not require the assumption of ground states and only measures single-qubit observables. It is applicable on both time-independent and time-dependent Hamiltonians and can simultaneously capture the magnitude and sign of Hamiltonian parameters. Taking quantum Ising Hamiltonians with the nearest-neighbor interactions as examples, we trained our recurrent neural networks to learn the Hamiltonian parameters with high accuracy, including the magnetic fields and coupling values. The numerical study also shows that our method has good robustness against the measurement noise and decoherence effect. Therefore, it has widespread applications in estimating the parameters of quantum devices and characterizing the Hamiltonian-based quantum dynamics.

arXiv comment9 pages and 6 figures. All comments are welcome

References in corpus (48)

• Quantum Simulation
• Trapped-Ion Quantum Computing: Progress and Challenges
• Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition
• Kitaev quantum spin liquid - concept and materialization
• Many-body quantum state tomography with neural networks
• Learning phase transitions by confusion
• Quantum control theory and applications: A survey
• Quantum Process Tomography: Resource Analysis of Different Strategies
• Fast quantum logic gates with trapped-ion qubits
• Identifying topological order through unsupervised machine learning
• Does a single eigenstate encode the full Hamiltonian?
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Learning a local Hamiltonian from local measurements
• Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement
• Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators
• Determining a local Hamiltonian from a single eigenstate
• Quantum Hamiltonian identification from measurement time traces
• Machine learning for discriminating quantum measurement trajectories and improving readout
• A general framework for randomized benchmarking
• Identifying Quantum Phase Transitions with Adversarial Neural Networks
• A Separability-Entanglement Classifier via Machine Learning
• Hamiltonian tomography in an access-limited setting without state initialization
• Robust All-Optical Single-Shot Readout of NV Centers in Diamond
• Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations
• Identifying an Experimental Two-State Hamiltonian to Arbitrary Accuracy
• Self-Learning Monte Carlo Method in Fermion Systems
• Hamiltonian Tomography via Quantum Quench
• Self-learning Monte Carlo with Deep Neural Networks
• Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks
• Quantum state tomography via reduced density matrices
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• Hamiltonian identifiability assisted by single-probe measurement
• Local-measurement-based quantum state tomography via neural networks
• Entanglement Classification via Neural Network Quantum States
• Self-Learning Monte Carlo Method: Continuous-Time Algorithm
• Identification of open quantum systems from observable time traces
• Experimental Detection of the Quantum Phases of a Three-Dimensional Topological Insulator on a Spin Quantum Simulator
• Scheme for direct measurement of a general two-qubit Hamiltonian
• Neural networks for detecting multimode Wigner-negativity
• Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
• Quantum and classical behavior of spin-$S$ Kitaev models in an anisotropic limit
• From eigenstate to Hamiltonian: Prospects for ergodicity and localization
• Machine learning effective models for quantum systems
• Quantum State Tomography with Conditional Generative Adversarial Networks
• Time-dependent atomic magnetometry with a recurrent neural network
• Improved Quantum State Tomography for the Systems with XX+YY Couplings and Z Readouts

Cited by in corpus (30)

• Learning Quantum Systems
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• Artificial Intelligence for Quantum Computing
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain
• Gradient-descent quantum process tomography by learning Kraus operators
• Learning shallow quantum circuits
• From observations to complexity of quantum states via unsupervised learning
• Scalably learning quantum many-body Hamiltonians from dynamical data
• Tomography of time-dependent quantum spin networks with machine learning
• Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
• Machine Learning for Estimation and Control of Quantum Systems
• Hamiltonian learning with real-space impurity tomography in topological moire superconductors
• Hamiltonian tomography by the quantum quench protocol with random noise
• Machine learning the Kondo entanglement cloud from local measurements
• Multiparameter estimation of continuous-time Quantum Walk Hamiltonians through Machine Learning
• Quantum Process Tomography of Unitary Maps from Time-Delayed Measurements
• Dual-Capability Machine Learning Models for Quantum Hamiltonian Parameter Estimation and Dynamics Prediction
• Learning quantum dissipation by the neural ordinary differential equation
• Hamiltonian-learning quantum magnets with non-local impurity tomography
• Learning interactions between Rydberg atoms
• Hamiltonian Learning of Triplon Excitations in an Artificial Nanoscale Molecular Quantum Magnet
• Unsupervised Learning of Effective Quantum Impurity Models
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
• Parent Hamiltonian Reconstruction via Inverse Quantum Annealing
• Machine-learning-enabled characterization of individual ring resonators in integrated photonic lattices
• Optimal Quantum Likelihood Estimation
• Artificial intelligence for representing and characterizing quantum systems
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Optimal Hamiltonian recognition of unknown quantum dynamics