Learning And Certification Of Local Time-dependent Quantum Dynamics And Noise

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 $ϵ$ on an interval with success probability $1-\delta$, requiring only $O({ϵ}^{\{}-2\}poly(m)log(n{\delta }^{\{}-1\}))$ samples and $poly(n,m)$ pre/postprocessing. Importantly, the scaling in $m$ is polynomial, whereas naive extensi