What Randomized Benchmarking Actually Measures.

Area of Science:

• Quantum Information Science
• Quantum Computing Error Characterization

Background:

• Randomized benchmarking (RB) is a standard technique for quantifying errors in quantum gate operations.
• The error metric 'r' derived from RB decay is generally assumed to represent the average gate infidelity for Clifford gates.
• This assumption has been challenged for small errors described by process matrices.

Purpose of the Study:

• To investigate the relationship between the randomized benchmarking error rate (r) and average gate infidelity for Clifford gates.
• To develop new theoretical frameworks for understanding RB decay with small errors.
• To determine if the RB error metric accurately reflects physically realizable quantum gate errors.

Main Methods:

• Analysis of randomized benchmarking decay curves for Clifford gates with small errors.
• Development of new theoretical models for RB decay using process matrices.
• Comparison of the computed RB error rate (r) with gate infidelity metrics.

Main Results:

• The quantity 'r' derived from RB does not reliably correspond to the mean gate infidelity for Clifford gates.
• The representation of imperfect and ideal gates significantly impacts the computed error metric.
• New theories confirm RB decay is a simple exponential for small errors describable by process matrices.
• The computed error rate 'r' may differ from the infidelity of physically allowed (completely positive) gate representations by orders of magnitude.

Conclusions:

• The interpretation of randomized benchmarking error rates requires re-evaluation.
• Existing methods for calculating average gate infidelity from RB may be inaccurate.
• New theoretical models provide a more accurate understanding of RB decay and the error metric 'r'.