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The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For sparse Hamiltonian simulation, the gate complexity scales with the L 1 norm ∫ 0 t d τ ‖ H ( τ ) ‖ max , whereas the best previous results scale with t max τ ∈ [ 0 , t ] ‖ H ( τ ) ‖ max . We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrödinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. These algorithms could potentially be applied to semi-classical simulations of scattering processes in quantum chemistry.
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This content will become publicly available on December 14, 2026
Learning quantum Gibbs states locally and efficiently
Learning the Hamiltonian underlying a quantum many-body system in thermal equilibrium is a fundamental task in quantum learning theory and experimental sciences. To learn the Gibbs state of local Hamiltonians at any inverse temperature β, the state-of-the-art provable algorithms fall short of the optimal sample and computational complexity, in sharp contrast with the locality and simplicity in the classical cases. In this work, we present a learning algorithm that learns each local term of a n-qubit D-dimensional Hamiltonian to an additive error ϵ with sample complexity $$\tilde{O}\left(\frac{e^{\mathrm{poly}(\beta)}}{\beta^2\epsilon^2}\right)\log(n)$$. The protocol uses parallelizable local quantum measurements that act within bounded regions of the lattice and near-linear-time classical post-processing. Thus, our complexity is near optimal with respect to n, ϵ and is polynomially tight with respect to β. We also give a learning algorithm for Hamiltonians with bounded interaction degree with sample and time complexities of similar scaling on n but worse on β, ϵ. At the heart of our algorithm is the interplay between locality, the Kubo-Martin-Schwinger condition, and the operator Fourier transform at arbitrary temperatures.
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- Award ID(s):
- 2013303
- PAR ID:
- 10658492
- Publisher / Repository:
- IEEE
- Date Published:
- Subject(s) / Keyword(s):
- quantum many-body systems quantum learning theory Gibbs states
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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