Efficient and robust estimation of many-qubit Hamiltonians

2022/05/19 by Daniel Stilck França, L. A. Markovich, França, Daniel Stilck +7 · 12 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2205.09567

openalex publication_date 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in the development of quantum technologies. We propose an efficient protocol based on the estimation of the time derivatives of few qubit observables using polynomial interpolation for characterizing the underlying Hamiltonian dynamics and Markovian noise of a multi-qubit device. For finite range dynamics, our protocol exponentially relaxes the necessary time resolution of the measurements and quadratically reduces the overall sample complexity compared to previous approaches. Furthermore, we show that our protocol can characterize the dynamics of systems with algebraically decaying interactions. The implementation of the protocol requires only the preparation of product states and single-qubit measurements. Furthermore, we develop a shadow tomography method for quantum channels that is of independent interest. This protocol can be used to parallelize to learn the Hamiltonian, rendering it applicable for the characterization of both current and future quantum devices.

Cited by

• Characterizing Arbitrary Lindbladian Dynamics with a Few Pauli Measurements
• Optimal certification of constant-local Hamiltonians
• Shadow Tomography Against Adversaries
• Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning
• Robust Iterative Learning Hidden Quantum Markov Models
• Quantum Probe Tomography
• Lower Bounds for Learning Hamiltonians from Time Evolution
• Hamiltonian learning via quantum Zeno effect
• Certifying and learning quantum Ising Hamiltonians
• Improved Hamiltonian learning and sparsity testing through Bell sampling
• Adversarially robust quantum state learning and testing
• Heisenberg-Limited Quantum Hamiltonian Learning via Randomly Spread Product-States

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