Resilience-runtime tradeoff relations for quantum algorithms

Area of Science:

• Quantum Computing
• Algorithm Design
• Computational Science

Background:

• Minimizing operations is a standard approach in algorithm design, particularly in quantum computing.
• Noise in quantum systems rapidly degrades performance, making gate implementation challenging.

Purpose of the Study:

• To investigate the impact of minimizing operations on quantum algorithm error rates.
• To develop a framework for characterizing quantum algorithm resilience to noise.
• To identify optimal algorithm compilations for noise mitigation.

Main Methods:

• Developed a framework to quantify algorithm resilience against various perturbative noises.
• Analyzed the relationship between the number of operations and noise sensitivity.
• Included coherent errors, dephasing, and depolarizing noise in the analysis.

Main Results:

• Minimizing operations in quantum algorithms can paradoxically increase noise sensitivity and errors.
• Demonstrated that some compilations are resilient to specific noises but not others.
• Established a trade-off relationship between operation count and noise resilience.

Conclusions:

• The intuitive approach of minimizing operations may be counterproductive for quantum algorithm reliability.
• The developed framework aids in selecting quantum algorithm compilations that better withstand environmental noise.
• Optimizing quantum algorithms requires balancing operation count with noise resilience.