Robust and Efficient Hamiltonian Learning
arXiv:2201.00190 · doi:10.22331/q-2023-06-29-1045
Abstract
With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.
arXiv comment41 pages, 6 figures, Open source implementation available at https://github.com/zyHan2077/HamiltonianLearning
References in corpus (69)
- Quantum Computing in the NISQ era and beyond
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Quantum sensing
- Quantum algorithm for solving linear systems of equations
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Quantum Simulation
- A Quantum Engineer's Guide to Superconducting Qubits
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Superconducting Qubits: Current State of Play
- Scalable multi-particle entanglement of trapped ions
- Strong quantum computational advantage using a superconducting quantum processor
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Extending the computational reach of a noisy superconducting quantum processor
- Prescription for experimental determination of the dynamics of a quantum black box
- Hamiltonian Simulation by Qubitization
- Advances in Photonic Quantum Sensing
- Quantum Annealing and Analog Quantum Computation
- Complete Characterization of a Quantum Process: the Two-Bit Quantum Gate
- Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Quantum Simulators: Architectures and Opportunities
- Toward the first quantum simulation with quantum speedup
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- Ancilla-assisted quantum process tomography
- Molecular engineering of antiferromagnetic rings for quantum computation
- Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
- Quantum sensing with arbitrary frequency resolution
- Can One Trust Quantum Simulators?
- Self-Consistent Quantum Process Tomography
- Does a single eigenstate encode the full Hamiltonian?
- Characterizing large-scale quantum computers via cycle benchmarking
- Experimental Quantum Hamiltonian Learning
- Experimental demonstration of fault-tolerant state preparation with superconducting qubits
- Efficient measurement of quantum dynamics via compressive sensing
- Hamiltonian Learning and Certification Using Quantum Resources
- Robust Online Hamiltonian Learning
- Efficient learning of quantum noise
- Learning a local Hamiltonian from local measurements
- Determining a local Hamiltonian from a single eigenstate
- A general framework for randomized benchmarking
- Sample-efficient learning of quantum many-body systems
- Efficient estimation of Pauli channels
- Digital Quantum Rabi and Dicke Models in Superconducting Circuits
- Coherent coupled qubits for quantum annealing
- Choi's Proof and Quantum Process Tomography
- Molecular nanomagnets as quantum simulators
- Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
- Mitigating realistic noise in practical noisy intermediate-scale quantum devices
- Quantum process tomography of unitary and near-unitary maps
- Randomized benchmarking with gate-dependent noise
- Quantum Hamiltonian Learning Using Imperfect Quantum Resources
- Hamiltonian Tomography via Quantum Quench
- Quantum process tomography with coherent states
- Learning many-body Hamiltonians with Heisenberg-limited scaling
- Accurately computing electronic properties of a quantum ring
- Quantum advantages for Pauli channel estimation
- Multi-qubit Randomized Benchmarking Using Few Samples
- Independent, extensible control of same-frequency superconducting qubits by selective broadcasting
- Fast Estimation of Sparse Quantum Noise
- Stochastic Estimation of Dynamical Variables
- Simulating single photons with realistic photon sources
- Millisecond coherence in a superconducting qubit
- Scalably learning quantum many-body Hamiltonians from dynamical data
- Determining system Hamiltonian from eigenstate measurements without correlation functions
- Optimal short-time measurements for Hamiltonian learning
- Efficient and robust estimation of many-qubit Hamiltonians
Cited by in corpus (24)
- Local readout and control of current and kinetic energy operators in optical lattices
- Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix
- Machine Learning Microscopic Form of Nematic Order in twisted double-bilayer graphene
- The advantage of quantum control in many-body Hamiltonian learning
- Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
- Estimation of Hamiltonian parameters from thermal states
- Unified Quantum State Tomography and Hamiltonian Learning Using Transformer Models: A Language-Translation-Like Approach for Quantum Systems
- Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems
- Hamiltonian learning for 300 trapped ion qubits with long-range couplings
- Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
- A protocol to characterize errors in quantum simulation of many-body physics
- Learning interacting fermionic Hamiltonians at the Heisenberg limit
- Hamiltonian Learning via Shadow Tomography of Pseudo-Choi States
- Hamiltonian-learning quantum magnets with non-local impurity tomography
- Random Projection using Random Quantum Circuits
- Efficient and robust estimation of many-qubit Hamiltonians
- Nearly query-optimal classical shadow estimation of unitary channels
- Trans-dimensional Hamiltonian model selection and parameter estimation from sparse, noisy data
- Benchmarking Digital-Analog Quantum Computation
- Learning the structure of any Hamiltonian from minimal assumptions
- Hamiltonian Learning via Inverse Physics-Informed Neural Networks
- Optimal Hamiltonian recognition of unknown quantum dynamics
- Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation
- Spatial Leggett-Garg inequalities