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Magic spreading in random quantum circuits.

Xhek Turkeshi1, Emanuele Tirrito2,3, Piotr Sierant4,5

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This study reveals how quantum magic resources spread in many-body systems. Magic equilibrates logarithmically with system size, offering insights into quantum computation and simulation costs.

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Area of Science:

  • Quantum Information Science
  • Many-Body Quantum Dynamics

Background:

  • Magic quantifies beyond-Clifford operations essential for universal quantum computing.
  • It bounds the classical simulation cost of quantum systems using stabilizer circuits.
  • Understanding magic resource generation and spreading is crucial for quantum error correction and computation.

Purpose of the Study:

  • Investigate the speed of generic many-body dynamics in generating magic resources.
  • Analyze magic spreading in brick-wall random unitary circuits under locality and unitarity constraints.
  • Develop scalable magic measures connected to the Clifford group's algebraic structure.

Main Methods:

  • Utilized scalable magic measures based on Clifford group algebra.
  • Simulated magic spreading in brick-wall random unitary circuits.
  • Analyzed systems up to 1024 qudits, significantly beyond prior limitations.

Main Results:

  • Demonstrated that magic resources equilibrate on timescales logarithmic in system size.
  • Observed phenomena akin to anti-concentration and Hilbert space delocalization.
  • Highlighted qualitative differences in magic spreading compared to entanglement entropy.

Conclusions:

  • Magic resource growth in chaotic many-body systems follows a logarithmic timescale.
  • Findings suggest a universal phenomenology for magic resource generation in chaotic dynamics.
  • The study provides a new framework for analyzing quantum computational costs.