Incorporating multi-qubit exchange coupling effects between transmon qubits in Maxwell-Schr\"{o}dinger numerical methods

TL;DR

This paper extends Maxwell-Schrödinger numerical methods to include multi-qubit exchange coupling effects between transmon qubits, enabling more accurate modeling of multi-qubit dynamics and classical crosstalk in superconducting quantum circuits.

Contribution

It provides a rigorous derivation for embedding multi-qubit coupling effects into Maxwell-Schrödinger methods, improving the understanding of classical crosstalk in multi-qubit superconducting systems.

Findings

Multi-qubit effects can cause strong classical crosstalk.

Classical crosstalk significantly impacts multi-qubit dynamics.

Maxwell-Schrödinger methods can now model these effects accurately.

Abstract

Superconducting qubits have emerged as a leading platform for realizing quantum computers. Accurate modeling of these devices is essential for predicting performance, improving design, and optimizing control. Many modeling approaches currently rely on lumped circuit approximations or other simplified treatments that can be limited in resolving the interplay between the qubit dynamics and the electromagnetic circuitry, leading to significant experimental deviations from numerical predictions at times. To address many of these limitations, methods that self-consistently solve the Schr\"{o}dinger equation for qubit dynamics with the classical Maxwell's equations have been developed and shown to accurately predict a wide range of effects related to superconducting qubit control and readout. Despite these successes, these methods have not been able to consider multi-qubit effects that give rise to qubit-qubit entanglement. Here, we address this by rigorously deriving how multi-qubit coupling effects between transmon qubits can be embedded into Maxwell-Schr\"{o}dinger methods. To support this, we build on earlier first-principles derivations of Maxwell-Schr\"{o}dinger methods for the specific case of two transmon qubits coupled together through a common electromagnetic system in the dispersive regime. To aid in validating aspects of the Maxwell-Schr\"{o}dinger framework, we also provide a new interpretation of Maxwell-Schr\"{o}dinger methods as an efficient simulation strategy to capture the class of non-Markovian open quantum system dynamics. Our results demonstrate that these effects can give rise to strong classical crosstalk that can significantly alter multi-qubit dynamics, which we demonstrate for the cross-resonance gate. These classical crosstalk effects have been noted in cross-resonance experiments, but previous quantum theory and device analysis could not explain their origin.