The Signal
Superconducting Qubit Experiment Shows Postselection Breaks Linearity
A superconducting transmon experiment finds nonlinear evolution in a subset of quantum measurement histories selected for having no quantum jumps. The full three-level system, counted without that filtering, retains linear evolution.
Quantum.world Team · Written with AI · fact-checked ·
Postselection changes the rule for a measured subset
Quantum dynamics preserve superposition: evolve two states separately, and their weighted sum should evolve into the same weighted sum of the results. Yet a superconducting transmon experiment published October 23 in Physical Review Research finds a qualified exception. Keep only measurement histories in which no quantum jump occurs, and the normalized states in the selected subset can evolve nonlinearly.
The result does not show that ordinary quantum mechanics has stopped being linear. The nonlinearity appears in an effective description of a postselected subset; when the researchers retain the full three-level system, its evolution remains linear. That distinction sets the terms of the finding: selection and renormalization change how the subset evolves, not the underlying dynamics of the complete system.
A transmon’s three levels set up the test
Orion Lee, Qian Cao, Yogesh N. Joglekar and Kater Murch use the three lowest energy states of a superconducting transmon, labeled |g⟩, |e⟩ and |f⟩. The |e⟩ state decays quickly to |g⟩, while the |f⟩ state decays to |e⟩ much more slowly. Coherent driving couples |e⟩ and |f⟩; retaining only trials without a jump to |g⟩ isolates an effective two-state system with non-Hermitian dynamics.
That filter is consequential because it changes the relative weights of different initial states. The unfiltered evolution remains linear, but the researchers renormalize the surviving trials to make their probabilities add to one. Initial states with different histories of population loss receive different normalization factors, so a superposition prepared at the start need not match a superposition assembled from the separately evolved components.
“The postselection process implies renormalization of the experimental trajectories into the postselected subset, resulting in a breakdown of linearity.”
Orion Lee, Qian Cao, Yogesh N. Joglekar and Kater Murch, the paper’s authors, write
Tomography tracks the mismatch
The team tests that difference by preparing basis states and superpositions, then using quantum state tomography to reconstruct their evolution. The experiment runs on a three-transmon section of a chip: one transmon supplies the dissipative three-level system, a second helps read it out, and a tunable coupler mediates the transfer. Because the excited state decays faster than the measurement can cleanly resolve it, the researchers transfer its population to the second transmon before reading both out.
They compare the measured evolution of a superposition with the superposition reconstructed from the separately evolved basis states. The two trajectories diverge, with the size of the discrepancy changing as the drive strength passes the system’s exceptional point—the parameter setting where the effective Hamiltonian’s eigenvectors coalesce. Above that point, the measured linearity score approaches one; below it, the departure is clearer, especially for an initial state orthogonal to the exceptional point’s surviving eigenstate.
The full qutrit keeps linear evolution
The authors also test mixtures of states, extending the comparison from state vectors to density matrices. In the postselected two-level subspace, the mixture’s evolution departs from the weighted combination of its components. When they include the |g⟩ state and keep all outcomes, the comparison agrees with linear evolution. The contrast shows why describing the result simply as “quantum evolution is nonlinear” would miss the experiment’s central condition: the departure arises after filtering and renormalizing.
Postselection comes with a probability cost
The paper presents the setup as a way to create and study anti-Hermitian nonlinear dynamics in a controlled quantum system, not as a demonstrated computing advantage. The authors note that possible information-processing uses would have to contend with reduced success rates and the probabilistic nature of postselection. Their concrete result is a measured mismatch between superposed trajectories in the selected two-level ensemble, alongside linear evolution when the complete three-level system is counted.