Learning and certification of local time-dependent quantum dynamics and noise

• URL: http://arxiv.org/abs/2510.08500v1
• Date: Thu, 09 Oct 2025 17:39:40 GMT
• Title: Learning and certification of local time-dependent quantum dynamics and noise
• Abstract summary: Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators.<n>We learn the time-dependent evolution of a locally interacting $nqubit system on a graph of effective dimensionD$.<n>Our protocol outputs function approximating coefficients to accuracy $epsilon$ on an interval with success probability $1-delta$.
• Score: 5.1798081822960365
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the time-dependent evolution of a locally interacting $n$-qubit system on a graph of effective dimension $D$ using only preparation of product Pauli eigenstates, evolution under the time-dependent generator for given times, and measurements in product Pauli bases. We assume the time-dependent parameters are well approximated by functions in a known space of dimension $m$ admitting stable interpolation, e.g. by polynomials. Our protocol outputs functions approximating these coefficients to accuracy $\epsilon$ on an interval with success probability $1-\delta$, requiring only $O\big(\epsilon^{-2}poly(m)\log(n\delta^{-1})\big)$ samples and $poly(n,m)$ pre/postprocessing. Importantly, the scaling in $m$ is polynomial, whereas naive extensions of previous methods scale exponentially. The method estimates time derivatives of observable expectations via interpolation, yielding well-conditioned linear systems for the generator's coefficients. The main difficulty in the time-dependent setting is to evaluate these coefficients at finite times while preserving a controlled link between derivatives and dynamical parameters. Our innovation is to combine Lieb-Robinson bounds, process shadows, and semidefinite programs to recover the coefficients efficiently at constant times. Along the way, we extend state-of-the-art Lieb-Robinson bounds on general graphs to time-dependent, dissipative dynamics, a contribution of independent interest. These results provide a scalable tool to verify state-preparation procedures (e.g. adiabatic protocols) and characterize time-dependent noise in quantum devices.

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