26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

On the connection between quantum chaos and randomness in closed- and open-system quantum dynamics

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Invited talk AIP | Quantum Science and Technology (QST)

Description

Quantum chaos is often understood as the dynamics found in quantum systems that exhibit classical chaos in the large-system limit. Classically chaotic systems exhibit randomness resulting from divergent sensitivity to system parameters, making accurate simulation difficult. In quantum computing, algorithms like digital quantum simulations will only be useful when systems cannot be simulated classically: exhibiting the same divergent sensitivity found in their classical counterparts, quantum chaotic systems are therefore ideal candidates for classically hard quantum simulations [Arute et al., Nature 574, 505 (2019)]. But ultimately, the promise of quantum computing relies on being able to build large-scale processors, fundamentally quantum in nature and with no meaningful classical limit: So can quantum chaos be defined in such a context?

Here, we illustrate how quantum chaos can be defined for purely finite-dimensional quantum dynamics, without any classical reference. We first describe a new objective and quantitatively rigorous technique for comparing the statistical properties of both closed- and open-system quantum dynamics, at the full distribution level, with the predictions of random matrix theory (RMT), using chi-squared tests [Kargi, et al., Quantum 9, 1924 (2025)]. We then show that a system can be identified as quantum chaotic if, by varying some system parameter, its dynamics effectively sample from a universal RMT ensemble. For closed systems, for example, we show how quantum chaos can be objectively identified even for very low-dimensional Hamiltonians which exhibit apparently quasiperiodic dynamics. For open systems, we describe two archetypal approaches, examining direct Liouvillian quantum chaos and underlying (residual) Hamiltonian quantum chaos [Manatuly, et al., in preparation (2026)], and illustrate direct support for the intuition that open-system quantum chaos arises when dissipation levels are balanced against the underlying Hamiltonian quantum chaos. This work provides new insight into the nature of intrinsically quantum chaos, which may find relevance for quantum technologies.