Robustly learning the Hamiltonian dynamics of a superconducting quantum processor

Abstract

The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. The key to solving these issues are precise means of characterizing analog quantum simulators. Here, we robustly estimate the free Hamiltonian parameters of bosonic excitations in a superconducting-qubit analog quantum simulator from measured time-series of single-mode canonical coordinates. We achieve high levels of precision in estimating the Hamiltonian parameters by exploiting a priori knowledge, making it robust against noise and state-preparation and measurement (SPAM) errors. Importantly, we are also able to obtain tomographic information about those SPAM errors from the same data, crucial for the experimental applicability of Hamiltonian learning in dynamical quantum-quench experiments. Our learning algorithm is scalable both in terms of the required amounts of data and post-processing. To achieve this, we develop a new super-resolution technique coined tensorESPRIT for frequency extraction from matrix time-series. The algorithm then combines tensorESPRIT with constrained manifold optimization for the eigenspace reconstruction with pre- and post-processing stages. For up to 14 coupled superconducting qubits on two Sycamore processors, we identify the Hamiltonian parameters -- verifying the implementation on one of them up to sub-MHz precision -- and 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 characterized using a new diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.

13+18 pages, 7+7 figures. v2: Substantial method development (tensorESPRIT), additional large-scale data and numerical benchmarking added + 18 pages of SM; JF added as author. v3: presentation improved

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• Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
• Learning interacting fermionic Hamiltonians at the Heisenberg limit
• Hamiltonian-learning quantum magnets with non-local impurity tomography
• Benchmarking Digital-Analog Quantum Computation
• Short-time simulation of quantum dynamics by Pauli measurements
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Probing the nonclassical dynamics of a quantum particle in a gravitational field
• Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation
• Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning