Five superconducting qubits on a chip: the stage for a performance of quantum chaos. Four qubits form the system, and the fifth acts as the environment, introducing dissipation. After a short evolution, the environment is discarded, leaving the system with an open quantum map, an operator that transforms the system's state. Previously, this scenario was purely theoretical: predictions about dissipative quantum chaos awaited experimental verification for over forty years.
The key tool is the distribution of complex ratios of eigenvalue spacings of the quantum map. For a chaotic circuit, it takes the form of a "bitten bagel": the density is suppressed near the center and along the positive real axis, indicating level repulsion. For an integrable circuit, there is a sharp peak at zero, with no correlations. This difference is the fingerprint of chaos in the spectrum of an open system.
As the depth of the integrable circuit increases from 5 to 50 layers, the distribution smoothly transitions from a peak to a "bagel." The mean values ⟨r⟩ and ⟨−cos θ⟩ shift from free-fermion statistics toward the random matrix class AI. Noise is not a hindrance but a conductor, guiding the system from order to chaos.
This work makes dissipative quantum chaos experimentally observable for the first time. The method can be applied to benchmarking quantum processors and studying the impact of noise on quantum algorithms. It opens the way to using quantum processors as testbeds for open many-body phenomena, from dissipative localization to phase transitions in open systems. Noise, which once drowned out quantum music, now sets the rhythm of chaos.
The processor's intrinsic noise, usually considered the enemy of precision, here acts as a source of chaos: the deeper the circuit, the more the noise disrupts integrability and leads to chaotic statistics.