Robust and Efficient Hamiltonian Learning

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.

41 pages, 6 figures, Open source implementation available at https://github.com/zyHan2077/HamiltonianLearning

References in corpus (26)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum algorithm for solving linear systems of equations
• Scalable multi-particle entanglement of trapped ions
• Strong quantum computational advantage using a superconducting quantum processor
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Quantum Process Tomography: Resource Analysis of Different Strategies
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
• Quantum sensing with arbitrary frequency resolution
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• Robust Online Hamiltonian Learning
• Sample-efficient learning of quantum many-body systems
• A general framework for randomized benchmarking
• Digital Quantum Rabi and Dicke Models in Superconducting Circuits
• Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
• Quantum process tomography of unitary and near-unitary maps
• 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
• Fast Estimation of Sparse Quantum Noise
• Simulating single photons with realistic photon sources
• Millisecond coherence in a superconducting qubit
• Scalably learning quantum many-body Hamiltonians from dynamical data
• Optimal short-time measurements for Hamiltonian learning
• Efficient and robust estimation of many-qubit Hamiltonians

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• 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