Flux noise in superconducting qubits: A second principles theory*

Impurity spins randomly distributed at the surfaces and interfaces of superconducting wires are known to cause flux noise in Superconducting Quantum Interference Devices (SQUIDs), providing a dominant mechanism for decoherence and Hamiltonian noise in all flux-tunable superconducting qubits [1]. While flux noise is well characterized experimentally, the microscopic model underlying spin dynamics remains a great puzzle. Available first-principles theories are too computationally expensive to capture spin diffusion over large length scales, hindering comparisons between microscopic models and experimental data. In contrast, third principles approaches lump spin dynamics into a single phenomenological spin-diffusion operator D∇², preventing connection to microscopic models and the impact of different disorder scenarios such as the presence of spin clusters. Here we propose an intermediate "second principles" method to describe spin diffusion and flux noise. It is based on a discrete version of the diffusion operator that connects directly to microscopic models, and becomes the usual Laplacian in the continuum limit. We apply the method to Heisenberg models in two dimensional square lattices with a random distribution of vacancies, with nearest-neighbor spins coupled by constant ferromagnetic exchange. At high frequencies ω our results reveal the regime of quantum 1/ω flux noise, with amplitude determined by inhomogeneity (spin cluster formation) and confining effects such as the presence of wire edges.  The method  establishes a connection between flux noise experiments and microscopic Hamiltonians with the goal of guiding strategies for reducing flux noise. 

[1] T. Zaborniak and R. de Sousa, Benchmarking Hamiltonian noise in the D-Wave quantum annealer, IEEE Trans. Quantum Eng. 2, 3100206 (2021).