An ansatz-free Lindbladian learning algorithm via Bell sampling with a SPAM-robust extension for gauge-independent parts of sparse Lindbladians under constant noise.
Structure learning of Hamiltonians from real-time evolution
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$. This problem is already well-understood under the assumption that the interaction terms, $E_a$, are given, and only the interaction strengths, $\lambda_a$, are unknown. But how efficiently can we learn a local Hamiltonian without prior knowledge of its interaction structure? We present a new, general approach to Hamiltonian learning that not only solves the challenging structure learning variant, but also resolves other open questions in the area, all while achieving the gold standard of Heisenberg-limited scaling. In particular, our algorithm recovers the Hamiltonian to $\varepsilon$ error with total evolution time $O(\log (n)/\varepsilon)$, and has the following appealing properties: (1) it does not need to know the Hamiltonian terms; (2) it works beyond the short-range setting, extending to any Hamiltonian $H$ where the sum of terms interacting with a qubit has bounded norm; (3) it evolves according to $H$ in constant time $t$ increments, thus achieving constant time resolution. As an application, we can also learn Hamiltonians exhibiting power-law decay up to accuracy $\varepsilon$ with total evolution time beating the standard limit of $1/\varepsilon^2$.
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UNVERDICTED 4representative citing papers
PICK adds a parent-finding subroutine for leaf nodes to speed up pruning in score-matching causal discovery, extending it from i.i.d. data to static and temporal network data.
Rigorous worst- and average-case error bounds show comparable worst-case scaling for digital and analog quantum simulators under perturbative noise, with distinct average-case error cancellation and concentration bounds for Gaussian and Brownian noise.
A complete workflow for pairwise extraction of Liouvillian coefficients from randomized measurements is described for two-body long-range interactions with single-body noise, including parameter guidelines to minimize reconstruction error.
citing papers explorer
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Efficient and SPAM-Robust Ansatz-Free Lindbladian Learning
An ansatz-free Lindbladian learning algorithm via Bell sampling with a SPAM-robust extension for gauge-independent parts of sparse Lindbladians under constant noise.
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Score-matching-based Structure Learning for Temporal Data on Networks
PICK adds a parent-finding subroutine for leaf nodes to speed up pruning in score-matching causal discovery, extending it from i.i.d. data to static and temporal network data.
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Stability of digital and analog quantum simulations under noise
Rigorous worst- and average-case error bounds show comparable worst-case scaling for digital and analog quantum simulators under perturbative noise, with distinct average-case error cancellation and concentration bounds for Gaussian and Brownian noise.
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Pairwise Liouvillian learning from randomized measurements: practical aspects and guidelines for operating the protocol in large-scale experiments
A complete workflow for pairwise extraction of Liouvillian coefficients from randomized measurements is described for two-body long-range interactions with single-body noise, including parameter guidelines to minimize reconstruction error.