A new randomized-sampling algorithm for ansatz-free Hamiltonian learning achieves optimal control-free evolution time Θ(Λ/ε² log(Λ/ε)) with a proven matching lower bound.
Scalably learning quantum many-body Hamiltonians from dynamical data
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abstract
The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system. In this work, we introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data, by bringing together techniques from gradient-based optimization from machine learning with efficient quantum state representations in terms of tensor networks. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins. In particular, we demonstrate on synthetic data that the algorithm works even if one is restricted to one simple initial state, a small number of single-qubit observables, and time evolution up to relatively short times. For the concrete example of the one-dimensional Heisenberg model our algorithm exhibits an error constant in the system size and scaling as the inverse square root of the size of the data set.
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UNVERDICTED 3representative citing papers
Except for a few specific cases, digital-analog quantum computation is disadvantageous compared to digital quantum computation based on scaling analysis across three quantum algorithms.
The paper proves sample complexity bounds showing that any efficiently representable unitary can be learned incoherently with arbitrary measurements, but only low-entangling unitaries with shallow-depth measurements, and demonstrates this on a 16-qubit hardware device.
citing papers explorer
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Optimal Ansatz-free Hamiltonian Learning In Situ
A new randomized-sampling algorithm for ansatz-free Hamiltonian learning achieves optimal control-free evolution time Θ(Λ/ε² log(Λ/ε)) with a proven matching lower bound.
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Benchmarking Digital-Analog Quantum Computation
Except for a few specific cases, digital-analog quantum computation is disadvantageous compared to digital quantum computation based on scaling analysis across three quantum algorithms.
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The power and limitations of learning quantum dynamics incoherently
The paper proves sample complexity bounds showing that any efficiently representable unitary can be learned incoherently with arbitrary measurements, but only low-entangling unitaries with shallow-depth measurements, and demonstrates this on a 16-qubit hardware device.