Nonlinear quantum evolution of a dissipative superconducting qubit

TL;DR

This paper investigates the breakdown of linearity in effective non-Hermitian quantum dynamics within a superconducting qubit, providing experimental evidence of nonlinearity arising from postselected quantum evolution.

Contribution

It offers the first experimental demonstration of nonlinearity in non-Hermitian quantum evolution using a superconducting transmon circuit, highlighting the breakdown of superposition principle.

Findings

Violations of linearity observed in superposition-state evolution

Nonlinearity confirmed in the two-level subspace

Linearity preserved in the full three-level system

Abstract

Unitary and dissipative models of quantum dynamics are linear maps on the space of states or density matrices. This linearity encodes the superposition principle, a key feature of quantum theory. However, this principle can break down in effective non-Hermitian dynamics arising from postselected quantum evolution. We theoretically characterize and experimentally investigate this breakdown in a dissipative superconducting transmon circuit. Within the circuit's three-level manifold, no-jump postselection generates an effective non-Hermitian Hamiltonian governing the excited two-level subspace and an anti-Hermitian nonlinearity. We prepare different initial states and use quantum state tomography to track their evolution under this effective, nonlinear Hamiltonian. By comparing the evolution of a superposition-state to a superposition of individually-evolved basis states, we test linearity and observe clear violations which we quantify across the exceptional-point (EP) degeneracy of the non-Hermitian Hamiltonian. We extend the analysis to density matrices, revealing a breakdown in linearity for the two-level subspace while demonstrating that linearity is preserved in the full three-level system. These results provide direct evidence of nonlinearity in non-Hermitian quantum evolution, highlighting unique features that are absent in classical non-Hermitian systems.