Quantum Simulation with Sum-of-Squares Spectral Amplification.

Area of Science:

• Quantum Computing
• Quantum Simulation
• Low-Energy Physics

Background:

• Quantum simulations are crucial for understanding complex quantum systems.
• Existing methods face challenges with strongly correlated systems and achieving high precision.
• Efficient algorithms are needed to reduce computational costs in quantum simulations.

Purpose of the Study:

• Introduce the Sum-of-Squares Spectral Amplification (SOSSA) framework.
• Develop fast quantum algorithms for energy and phase estimation.
• Demonstrate the application and benefits of SOSSA on a representative strongly correlated system.

Main Methods:

• Developed the SOSSA framework for quantum simulation.
• Designed quantum algorithms for energy and phase estimation utilizing SOSSA.
• Applied SOSSA to the Sachdev-Ye-Kitaev (SYK) model for analysis.

Main Results:

• SOSSA framework significantly improves quantum simulation for low-energy problems.
• Achieved fast quantum algorithms for energy and phase estimation, outperforming prior art.
• Demonstrated asymptotic speedups by a factor of the square root of system size on the SYK model.

Conclusions:

• SOSSA provides a powerful approach for enhancing quantum simulations.
• The framework offers substantial computational advantages for strongly correlated systems.
• Results align with and reinforce previous findings on SOSSA's efficacy in quantum chemistry.