Loops and Strings in a Superconducting Lattice Gauge Simulator.

Area of Science:

• Quantum Simulation
• Condensed Matter Physics
• Quantum Electromagnetism

Background:

• Analog quantum simulators offer a powerful platform for studying complex quantum systems.
• Lattice gauge theories, like compact U(1) gauge theory, are fundamental to understanding fundamental forces but are computationally challenging.
• Superconducting circuits provide a promising hardware basis for building controllable quantum simulators.

Purpose of the Study:

• To propose and detail an architecture for an analog quantum simulator of 2+1 dimensional electromagnetism.
• To demonstrate the feasibility of simulating compact U(1) lattice gauge theory using superconducting fluxonium devices.
• To provide methods for verifying the existence of the confining phase in the simulated system.

Main Methods:

• Utilizing an array of superconducting fluxonium devices for quantum simulation.
• Encoding the quantum link model in the integer (spin-1) representation.
• Engineering Gauss' law using ancilla-mediated gadget construction.
• Tuning between strongly and intermediately coupled regimes.
• Measuring nonlocal order parameters (Wilson loops) and disorder parameters ('t Hooft strings) nondestructively.

Main Results:

• Successfully engineered Gauss' law and controlled coupling regimes.
• Demonstrated the construction and nondestructive measurement of order and disorder parameters.
• Provided numerical evidence for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.

Conclusions:

• The proposed architecture is a viable approach for analog quantum simulation of 2+1 dimensional electromagnetism.
• The study confirms the existence of the confining phase, a key prediction of the quantum link model.
• This work paves the way for future investigations into non-perturbative quantum field theories using quantum simulators.