Protocol learns k-local Lindbladians to ε accuracy with Õ(n^{2k}/ε²) samples and projects to valid generators; improves to log n under sparsity assumptions.
Optimal short-time measurements for Hamiltonian learning
8 Pith papers cite this work, alongside 14 external citations. Polarity classification is still indexing.
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Pith papers citing it
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external citations · Pith
abstract
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires exponential computational complexity. Here, we propose efficient measurement schemes based on short-time dynamics which circumvent this exponential difficulty. We provide estimates for the optimal measurement schedule and reconstruction error, and verify these estimates numerically. We demonstrate that the reconstruction requires a system-size independent number of experimental shots, and identify a minimal set of state preparations and measurements which yields optimal accuracy for learning short-ranged Hamiltonians. Finally, we show how grouping of commuting observables and use of Hamiltonian symmetries improve the accuracy of the Hamiltonian reconstruction.
fields
quant-ph 8representative citing papers
An ansatz-free Lindbladian learning algorithm via Bell sampling with a SPAM-robust extension for gauge-independent parts of sparse Lindbladians under constant noise.
Heisenberg-limited Hamiltonian learning is achievable with any constant minimum evolution time T per query, attaining optimal 1/ε total-time scaling for logarithmically sparse Hamiltonians.
Establishes n^{Ω(k)} lower bounds for learning k-local Hamiltonians from time evolution, including single-coefficient and effective Hamiltonian learning, via a new connection to Boolean function analysis.
Local Lindbladians can be learned with Õ(Λ²/ε²) channel uses and Õ(Λ/ε²) total time; matching lower bounds prove this optimal even for adaptive, entangling strategies.
A provable exponential quantum-classical learning separation is established for predicting expectation values of time-evolved quantum states under unknown low-intersection Hamiltonians, assuming BQP ⊄ P/poly.
An iterative Fourier-based algorithm learns constant-local Lindbladian coefficients from non-adaptive Pauli measurements with near-optimal sample complexity and without prior knowledge of the interaction graph.
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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Robust Structure Learning of $k$-local Lindbladians
Protocol learns k-local Lindbladians to ε accuracy with Õ(n^{2k}/ε²) samples and projects to valid generators; improves to log n under sparsity assumptions.
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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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Heisenberg-limited Hamiltonian learning without short-time control
Heisenberg-limited Hamiltonian learning is achievable with any constant minimum evolution time T per query, attaining optimal 1/ε total-time scaling for logarithmically sparse Hamiltonians.
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Lower Bounds for Learning Hamiltonians from Time Evolution
Establishes n^{Ω(k)} lower bounds for learning k-local Hamiltonians from time evolution, including single-coefficient and effective Hamiltonian learning, via a new connection to Boolean function analysis.
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Near-Optimal Learning of Local Lindbladians
Local Lindbladians can be learned with Õ(Λ²/ε²) channel uses and Õ(Λ/ε²) total time; matching lower bounds prove this optimal even for adaptive, entangling strategies.
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Provable learning separation for predicting time-evolution of quantum many-body systems
A provable exponential quantum-classical learning separation is established for predicting expectation values of time-evolved quantum states under unknown low-intersection Hamiltonians, assuming BQP ⊄ P/poly.
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Learning the structure of open quantum systems
An iterative Fourier-based algorithm learns constant-local Lindbladian coefficients from non-adaptive Pauli measurements with near-optimal sample complexity and without prior knowledge of the interaction graph.
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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.