Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems

Abstract

We discuss Hamiltonian and Liouvillian learning for analog quantum simulation from non-equilibrium quench dynamics in the limit of weakly dissipative many-body systems. We present and compare various methods and strategies to learn the operator content of the Hamiltonian and the Lindblad operators of the Liouvillian. We compare different ansätze based on an experimentally accessible "learning error" which we consider as a function of the number of runs of the experiment. Initially, the learning error decreases with the inverse square root of the number of runs, as the error in the reconstructed parameters is dominated by shot noise. Eventually the learning error remains constant, allowing us to recognize missing ansatz terms. A central aspect of our approaches is to (re-)parametrize ansätze by introducing and varying the dependencies between parameters. This allows us to identify the relevant parameters of the system, thereby reducing the complexity of the learning task. Importantly, this (re-)parametrization relies solely on classical post-processing, which is compelling given the finite amount of data available from experiments. We illustrate and compare our methods with two experimentally relevant spin models.

20 pages, 9 figures

References in corpus (33)

• Quantum computational chemistry
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• A high-bias, low-variance introduction to Machine Learning for physicists
• A Rydberg Quantum Simulator
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• The randomized measurement toolbox
• Quantum certification and benchmarking
• Quantum Simulation for High Energy Physics
• Hamiltonian Learning and Certification Using Quantum Resources
• Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
• Learning a local Hamiltonian from local measurements
• Realization of a fractional quantum Hall state with ultracold atoms
• Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Theoretical and Experimental Perspectives of Quantum Verification
• Exploring Large-Scale Entanglement in Quantum Simulation
• Hamiltonian Tomography via Quantum Quench
• Frenkel-Kontorova model with cold trapped ions
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• Direct certification of a class of quantum simulations
• Learning the dynamics of open quantum systems from their steady states
• Controlling two-dimensional Coulomb crystals of more than 100 ions in a monolithic radio-frequency trap
• Hamiltonian tomography for quantum many-body systems with arbitrary couplings
• Robust and Efficient Hamiltonian Learning
• Scalable reconstruction of unitary processes and Hamiltonians
• Functional building blocks for scalable multipartite entanglement in optical lattices
• Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning
• Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
• Practical Black Box Hamiltonian Learning
• Hamiltonian Learning in Quantum Field Theories
• Dynamics of quantum discommensurations in the Frenkel-Kontorova chain

Cited by in corpus (7)

• Probing the Kitaev honeycomb model on a neutral-atom quantum computer
• Scalably learning quantum many-body Hamiltonians from dynamical data
• Efficient Lindblad synthesis for noise model construction
• Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
• Learning interactions between Rydberg atoms
• Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning
• Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach