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arXiv:1910.12784 · Physical Review X

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

Lucas Sá, Pedro Ribeiro, Tomaž Prosen

Published Apr 27, 2020• 178 citations
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Abstract

Mathematical tools for distinguishing open quantum systems that are chaotic from those that are exactly solvable fill an important gap in understanding dissipation and decoherence in scenarios relevant to quantum-based technologies.
DOI
10.1103/physrevx.10.021019

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More than four decades of research on chaos in isolated quantum systems have led to the identification of universal signatures -- such as level repulsion and eigenstate thermalization -- that serve as cornerstones in our understanding of complex quantum dynamics. The emerging field of dissipative quantum chaos explores how these properties manifest in open quantum systems, where interactions with the environment play an essential role. We report the first experimental detection of dissipative quantum chaos and integrability by measuring the complex spacing ratios (CSRs) of open many-body quantum systems implemented on a high-fidelity superconducting quantum processor. Employing gradient-based tomography, we retrieve a ``donut-shaped'' CSR distribution for chaotic dissipative circuits, a hallmark of level repulsion in open quantum systems. For an integrable circuit, spectral correlations vanish, evidenced by a sharp peak at the origin in the CSR distribution. As we increase the depth of the integrable dissipative circuit, the CSR distribution undergoes an integrability-to-chaos crossover, demonstrating that intrinsic noise in the quantum processor is a dissipative chaotic process. Our results reveal the universal spectral features of dissipative many-body systems and establish present-day quantum computation platforms, which are predominantly used to run unitary simulations, as testbeds to explore dissipative many-body phenomena.