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

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.