Abstract
Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to coupling to an external environment. This raises the question whether the steady states of such open quantum systems contain sufficient information allowing for full and efficient reconstruction of the system’s dynamics. We find that such a reconstruction is possible for generic local Markovian dynamics. We propose a recovery method that uses only local measurements; for systems with finite-range interactions, the method recovers the Lindbladian acting on each spatial domain using only observables within that domain. We numerically study the accuracy of the reconstruction as a function of the number of measurements, type of open-system dynamics and system size. Interestingly, we show that couplings to external environments can in fact facilitate the reconstruction of Hamiltonians composed of commuting terms.
Highlights
The development of quantum simulators and computation devices has rapidly progressed over the last few years1
We focus on open quantum systems evolving under Markovian and local dynamics, for which the evolution can be described by the Lindblad master equation formalism[52,53]: ρ = L (ρ) =
The steady state of any Lindbladian whose jump operators Lj are all Hermitian is the fully mixed state ρ ∝ 1, from which there is no hope to recover the Lindbladian. Does this impose a fundamental difficulty to Lindbladian reconstruction? Or do the steady states of local many-body dissipative dynamics generically bear clear signatures of the preceding dynamics? Can these dynamics be extracted efficiently and accurately?. We study this question by providing an efficient algorithm for learning the dynamics of local Lindbladians from their steady states
Summary
The development of quantum simulators and computation devices has rapidly progressed over the last few years. An isolated quantum system can be characterized by learning its underlying Hamiltonian This can be achieved by monitoring the dynamics that the Hamiltonian generates[18,19,20,21,22,23,24,25,26,27,28,29,30,31], or by measuring local observables in one of its eigenstates or thermal states[32,33,34,35,36,37,38,39,40]. We (i) explore which types of Lindbladians can be accurately reconstructed from their steady states, (ii) study numerically and analytically the system-size scaling of the reconstruction accuracy, and (iii) show that coupling to a bath can facilitate the reconstruction of certain classes of Hamiltonians, which pose a challenge for methods based on their eigenstates or Gibbs states
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