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Low-Depth Unitary Quantum Circuits for Dualities in One-Dimensional Quantum Lattice Models.

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We present a method to implement quantum dualities using unitary quantum circuits. These circuits efficiently prepare entangled states and map topological model boundaries.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Computing

Background:

  • Duality transformations in quantum systems are crucial for understanding symmetries and phases.
  • Previous work established a framework for dualities in (1+1)d quantum lattice models using module categories.
  • These dualities were previously implemented using unitary matrix product operators.

Purpose of the Study:

  • To develop efficient quantum circuits for implementing dualities in quantum lattice models.
  • To explore the realization of dualities in constant-depth quantum circuits.
  • To demonstrate applications in preparing entangled states and analyzing topological models.

Main Methods:

  • Introduction of ancillary degrees of freedom to track charge sectors.
  • Construction of unitary linear depth quantum circuits from duality operators.
  • Utilizing measurements to achieve constant-depth circuits for specific symmetries.

Main Results:

  • Successfully transformed duality operators into unitary linear depth quantum circuits.
  • Demonstrated that these circuits are consistent with phase changes in quantum states.
  • Showcased the ability to realize dualities in constant depth with measurements.

Conclusions:

  • The developed quantum circuits provide an efficient method for implementing dualities.
  • These circuits have practical applications in quantum state preparation and topological phase analysis.
  • The approach offers a pathway for simulating complex quantum phenomena on quantum computers.