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Strong Zero Modes in Integrable Quantum Circuits.

Eric Vernier1, Hsiu-Chung Yeh2, Lorenzo Piroli3

  • 1Laboratoire de Probabilités, <a href="https://ror.org/02feahw73">Statistique et Modélisation CNRS</a>-<a href="https://ror.org/05f82e368">Université Paris Cité</a>-<a href="https://ror.org/02en5vm52">Sorbonne Université.</a> Paris, France.

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This summary is machine-generated.

Researchers have identified strong zero modes (SZMs) in integrable quantum circuits, extending previous findings in spin chains. This work offers a new method for constructing SZM operators in Floquet systems, with potential applications in quantum computing.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Many-Body Systems

Background:

  • Integrable spin chains are known to host robust edge modes called strong zero modes (SZMs).
  • Extending these concepts to the discrete-time dynamics of local quantum circuits, particularly in the Floquet setting, remains an active area of research.

Purpose of the Study:

  • To investigate the existence and construction of strong zero modes (SZMs) in integrable quantum circuits.
  • To adapt the concept of SZMs from continuous-time spin chains to discrete-time Floquet quantum circuits.
  • To explore the potential for implementing these phenomena on current quantum platforms.

Main Methods:

  • Focus on a prototypical integrable Trotterization of the XXZ Heisenberg spin chain.
  • Exploitation of algebraic structures inherent to integrability, specifically commuting transfer matrices.
  • Construction of an exact SZM operator within specific parameter regimes of the quantum circuit.

Main Results:

  • Demonstrated the existence of an exact strong zero mode (SZM) operator in integrable Floquet quantum circuits.
  • The construction method recovers known results in the continuous-time limit.
  • Properties such as normalizability of the SZM are readily proven using the developed framework.
  • Numerical simulations of infinite-temperature autocorrelation functions corroborate the theoretical predictions.

Conclusions:

  • The study successfully extends the concept of strong zero modes (SZMs) to the realm of integrable quantum circuits.
  • The developed algebraic approach offers a novel perspective for constructing and analyzing SZMs, distinct from prior methods.
  • The findings hold promise for practical implementations of XXZ quantum circuits on existing quantum computing hardware.