Digital quantum magnetism on a trapped-ion quantum computer

Area of Science:

• Quantum Computing
• Condensed Matter Physics
• Quantum Simulation

Background:

• Digital quantum matter, approximated by discrete quantum gates, is prone to heating into chaotic states.
• Suppressing digitization errors allows observation of approximate energy-conserving dynamics in gate-based quantum computers.
• Energy conservation facilitates the study of complex behaviors like thermalization and emergent properties in equilibrium systems.

Purpose of the Study:

• To simulate digitized dynamics of the quantum Ising model on a gate-based quantum computer.
• To explore thermalization and emergent phenomena in a regime challenging for classical simulation.
• To investigate emergent hydrodynamics and topological constraints in quantum simulations.

Main Methods:

• Utilized Quantinuum's H2 quantum computer for simulating digitized quantum Ising model dynamics.
• Suppressed digitization errors to achieve a long-lived transient regime of approximate energy conservation.
• Simulated dynamics on both a standard and a triangular lattice with periodic boundary conditions.

Main Results:

• Observed thermalization on timescales that challenge classical simulation methods.
• Revealed emergent hydrodynamics from approximate energy conservation and computed the diffusion constant.
• Observed thermalization consistent with emergent gauge and topological constraints on a triangular lattice.

Conclusions:

• Digital quantum computers, with sufficiently suppressed errors and high gate fidelity, are powerful tools for studying effectively continuous-time quantum dynamics.
• The study demonstrates the capability to observe complex quantum phenomena like emergent hydrodynamics and thermalization.
• Advances in two-qubit gate quality are crucial for enabling these sophisticated quantum simulations.