Locality and Digital Quantum Simulation of Power-Law Interactions

Area of Science:

• Quantum Information Theory
• Condensed Matter Physics
• Computational Physics

Background:

• Information propagation in quantum systems is limited by Lieb-Robinson bounds.
• Previous bounds did not fully capture systems with power-law decaying interactions.

Purpose of the Study:

• Derive a novel Lieb-Robinson bound for quantum systems with power-law decaying interactions (1/r^α).
• Analyze the implications for effective light cone size and digital quantum simulation.

Main Methods:

• Developed a new Lieb-Robinson bound using an approximation technique for time evolution.
• Applied a known, weaker Lieb-Robinson bound to establish the error of the approximation.
• Analyzed the Haah et al. quantum simulation algorithm for power-law interactions.

Main Results:

• Established a new, tighter Lieb-Robinson bound for power-law decaying interactions.
• Demonstrated an improved gate count scaling for the Haah et al. algorithm when α > 3D.
• Revealed a significant connection between Lieb-Robinson bounds and digital quantum simulation.

Conclusions:

• The new Lieb-Robinson bound offers a more precise description of information propagation limits.
• The findings enhance the efficiency of quantum simulations for specific interaction types.
• This work deepens the theoretical understanding of quantum dynamics and simulation.