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  3. Realizing Unitary K-designs With A Single Quench.
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  3. Realizing Unitary K-designs With A Single Quench.

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Realizing Unitary k-Designs with a Single Quench.

Yi-Neng Zhou1, Robin Löwenberg1, Julian Sonner1

  • 1University of Geneva, Department of Theoretical Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland.

Physical Review Letters
|June 22, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

We introduce a simple single-quench protocol to create unitary k-designs, essential for quantum computing. This method uses minimal control, simplifying complex quantum dynamics and enabling efficient generation of quantum randomness.

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Area of Science:

  • Quantum Information Science
  • Quantum Chaos
  • Condensed Matter Physics

Background:

  • Unitary k-designs are crucial for quantum information processing, enabling tasks like quantum computation and error correction.
  • Generating k-designs often requires complex protocols with continuous randomization or frequent quenches.
  • Understanding quantum chaos and spectral correlations is key to controlling quantum system dynamics.

Purpose of the Study:

  • To present a novel, simplified single-quench protocol for generating unitary k-designs.
  • To demonstrate that a single quantum quench can break spectral correlations hindering chaotic dynamics.
  • To establish a practical method for achieving high-fidelity quantum randomness.

Main Methods:

  • The protocol involves evolving a system under a random Hamiltonian H1, followed by a single quench to a second random Hamiltonian H2 at the Thouless time (t_s >= t_Th).
  • Analytical derivations were performed for Gaussian unitary random matrices.
  • Numerical simulations were conducted using the Sachdev-Ye-Kitaev (SYK) model.

    • Main Results:

    • The single-quench protocol efficiently generates ensembles approximating unitary k-designs.
    • This method requires significantly less control compared to existing Brownian or multi-quench schemes.
    • The protocol provides a measurement-friendly definition of the Thouless time and a quantitative measure of chaoticity.

    Conclusions:

    • The presented single-quench protocol offers a practical and efficient route to generating unitary k-designs and Haar-like randomness.
    • This approach simplifies the experimental realization of quantum chaotic dynamics and related applications.
    • The protocol has potential extensions to symmetry-resolved studies, open quantum systems, and applications in quantum metrology and tomography.