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This study introduces efficient quantum computing methods to measure stabilizer entropies (SEs), quantifying quantum "magic." These new protocols enable practical exploration of nonstabilizerness and its effects on quantum systems.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Many-Body Physics

Background:

  • Stabilizer entropies (SEs) quantify nonstabilizerness, a key resource in quantum computation.
  • Existing measurement protocols for SEs exhibit exponential scaling, limiting practical applications.
  • SEs are linked to important phenomena like quantum scrambling and localization.

Purpose of the Study:

  • To develop efficient measurement protocols for SEs for N-qubit states.
  • To explore the practical measurement of nonstabilizerness monotones using quantum hardware.
  • To investigate the relationship between nonstabilizerness and quantum scrambling dynamics.

Main Methods:

  • Developed efficient measurement protocols for SEs using Bell measurements for integer Rényi index n>1.
  • Implemented algorithms for measuring SEs with O(n) state copies and O(nN) classical time.
  • Utilized the IonQ quantum computer to measure SEs of doped Clifford circuits and analyze scrambling dynamics.

Main Results:

  • Demonstrated efficient measurement of SEs and related nonstabilizerness monotones.
  • Provided bounds for stabilizer fidelity, extent, and robustness of magic.
  • Introduced efficient algorithms for out-of-time-order correlators and multifractal flatness.
  • Observed counterintuitive results of decreased scrambling in random Hamiltonian evolution at long times.

Conclusions:

  • The developed methods enable efficient, practical measurement of quantum nonstabilizerness.
  • This work facilitates the study of scrambling dynamics and other phenomena related to nonstabilizerness.
  • Opens new avenues for exploring quantum magic with current and future quantum computers.