Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
Nature Communications volume 15, Article number: 9595 (2024 ) Cite this article
Precise means of characterizing analog quantum simulators are key to developing quantum simulators capable of beyond-classical computations. Here, we precisely estimate the free Hamiltonian parameters of a superconducting-qubit analog quantum simulator from measured time-series data on up to 14 qubits. To achieve this, we develop a scalable Hamiltonian learning algorithm that is robust against state-preparation and measurement (SPAM) errors and yields tomographic information about those SPAM errors. The key subroutines are a novel super-resolution technique for frequency extraction from matrix time-series, tensorESPRIT, and constrained manifold optimization. Our learning results verify the Hamiltonian dynamics on a Sycamore processor up to sub-MHz accuracy, and allow us to construct a spatial implementation error map for a grid of 27 qubits. Our results constitute an accurate implementation of a dynamical quantum simulation that is precisely characterized using a new diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.
Analog quantum simulators promise to shed light on fundamental questions of physics that have remained elusive to the standard methods of inference1,2. Recently, enormous progress in controlling individual quantum degrees of freedom has been made towards making this vision a reality3,4,5,6. While in digital quantum computers small errors can be corrected7, it is intrinsically difficult to error-correct analog devices. Yet, the usefulness of analog quantum simulators as computational tools depends on the error of the implemented dynamics. Meeting this requirement hinges on devising characterization methods that not only yield a benchmark of the overall functioning of the device [e.g.,8,9,10], but more importantly provide diagnostic information about the sources of errors.
