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Quantum state complexity metrics like anticoncentration and nonstabilizerness reveal differences in Floquet versus Hamiltonian systems. Floquet systems rapidly reach saturation, while Hamiltonian systems show slower, constrained growth, highlighting the role of conservation laws.

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Area of Science:

  • Quantum physics
  • Many-body systems
  • Quantum information

Background:

  • Quantum state complexity metrics, including anticoncentration and nonstabilizerness, are crucial for understanding many-body physics, information scrambling, and quantum computing.
  • Random quantum circuits exhibit logarithmic scaling for anticoncentration and magic resource equilibration with system size.

Purpose of the Study:

  • To investigate quantum state complexity dynamics in one-dimensional ergodic Floquet models and thermalizing Hamiltonian systems.
  • To compare the behavior of anticoncentration and magic resources in these two distinct physical settings.

Main Methods:

  • Utilized participation entropy and stabilizer entropy as probes for anticoncentration and magic resources.
  • Analyzed dynamics in one-dimensional ergodic Floquet models and thermalizing Hamiltonian systems.

Main Results:

  • Floquet systems demonstrate anticoncentration and magic saturation at timescales logarithmic to system size, consistent with random circuit predictions.
  • Hamiltonian systems exhibit deviations from random circuit predictions, requiring approximately linear system size scaling for saturation.
  • In Hamiltonian systems, participation and stabilizer entropies saturate at values lower than those of typical quantum states, even at long times.

Conclusions:

  • Established the phenomenology of participation and stabilizer entropy growth in generic many-body systems.
  • Emphasized the significant impact of conservation laws in constraining anticoncentration and magic resource dynamics in Hamiltonian systems.