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Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions.

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Digital quantum simulation (DQS) errors are typically uncontrolled. However, for integrable systems, errors remain bounded, revealing a novel Trotter transition linked to conserved quantities and staggered magnetization.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Digital quantum simulation (DQS) approximates continuous dynamics using discrete Trotter steps.
  • Previous studies indicated a sharp Trotter transition where errors become uncontrolled due to quantum chaos.
  • Integrable systems, possessing exact conservation laws, offer a different perspective on DQS fidelity.

Purpose of the Study:

  • To investigate the behavior of Trotterized evolution in an integrable system, specifically the XXZ Heisenberg spin chain.
  • To contrast the typical Trotter transition with phenomena observed in integrable DQS.
  • To identify novel signatures of Trotter transitions in digital quantum simulations of integrable models.

Main Methods:

  • Focusing on a quench from a spin-wave state in the XXZ Heisenberg spin chain.
  • Analyzing the integrable Trotterized evolution as a function of Trotter step duration (τ).
  • Employing exact calculations to determine the properties of the late-time dynamics, described by a discrete generalized Gibbs ensemble (dGGE).

Main Results:

  • For small τ, the dGGE depends analytically on the Trotter step, keeping discretization errors bounded.
  • A novel Trotter transition occurs at a threshold τ_{th}, where the dGGE changes abruptly.
  • This transition is detectable locally via the emergence of nonzero staggered magnetization, dependent on τ.

Conclusions:

  • Integrable DQS does not necessarily lead to uncontrolled errors, challenging previous assumptions about Trotter transitions.
  • A new type of Trotter transition exists in integrable systems, characterized by abrupt changes in the dGGE.
  • Discrete GGEs represent unique nonequilibrium states specific to digital quantum platforms.