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  • Open Access

Nonlinear quantum evolution of a dissipative superconducting qubit

Orion Lee1,*, Qian Cao1,*, Yogesh N. Joglekar2,3,4, and Kater Murch1,5,6,†

  • *These authors contributed equally to this work.
  • †Contact author: katermurch@berkeley.edu
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Phys. Rev. Research 8, 043089 – Published 23 October, 2026

DOI: https://doi.org/10.1103/7w9t-c5xf

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 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 an operational demonstration of postselection-induced nonlinearity in a controlled superconducting platform. The observed nonlinearity, organized by the exceptional-point degeneracy of the non-Hermitian Hamiltonian, is absent in classical non-Hermitian systems, where norm change reflects real exchange with an environment rather than renormalization.

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Outline

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Phys. Rev. Research 8, 043089– Published 23 October, 2026
  • Received 3 November 2025
  • Revised 26 February 2026
  • Accepted 2 October 2026
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