Quantum

Probing Krylov Dynamics in Driven Many-Body Systems

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Briefings

This article presents exact solutions for the time-dependent many-body Krylov problem in scale- and rotation-invariant quantum systems. The research establishes that driven dynamics can be mapped onto mutually orthogonal Krylov subspaces, allowing for a closed-form calculation of spread complexity based on initial Hamiltonian spectral properties and driving schedules. This approach enables experimental access to Krylov dynamics in thermal states via Liouville space and provides a method to probe collective spin precession in trapped-ion, cavity-QED, and circuit-QED platforms.

Key points

• The article solves the time-dependent many-body Krylov problem exactly and in closed form for scale- and rotation-invariant systems.
• Exact relations map driven dynamics onto mutually orthogonal Krylov subspaces, determining spread complexity from initial Hamiltonian spectral properties and driving schedule.

Context

Krylov complexity serves as a central probe for operator growth, scrambling, and quantum chaos. This work addresses the experimental challenge of driving laboratory quantum systems in time, which breaks the standard Krylov construction. The findings are relevant for quantum simulation and control platforms where initial thermal states and collective spin precession must be studied.

Limitations

The results apply strictly to scale- and rotation-invariant systems. The closed-form spread complexity depends solely on initial Hamiltonian spectral properties and driving schedule, not on specific system parameters beyond these constraints. Experimental verification in trapped-ion, cavity-QED, and circuit-QED platforms is supported, but direct time-of-flight imaging for atomic clouds is limited to scale-invariant quantum gases.

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