Efficient Classical Simulation and Benchmarking of Quantum Processes in the Weyl Basis.

Area of Science:

• Quantum computing
• Quantum information science
• Computational complexity

Background:

• Scalable quantum computer development requires identifying noise sources causing quantum evolution errors.
• Hardware-specific noise and decoherence complicate error detection in diverse quantum implementations.

Purpose of the Study:

• To develop a randomized benchmarking algorithm for efficient identification and learning of mixed error models in quantum computations.
• To provide an efficiently computable estimate of overhead for noisy quantum circuit output analysis.
• To establish analytic noise bounds for efficient classical simulability.

Main Methods:

• Development of a randomized benchmarking algorithm utilizing Weyl unitaries.
• Efficient computation of overhead estimates based on interaction locality.
• Derivation of analytic noise bounds.

Main Results:

• The algorithm efficiently identifies and learns mixtures of error models.
• Overhead for analyzing noisy circuit outputs decreases with increasing noise rate.
• Analytic noise bounds are derived, indicating regimes for efficient classical simulation.

Conclusions:

• The developed methods enable efficient classical simulation of quantum computations under certain noise conditions.
• Application to variational quantum eigensolver ansatz circuits establishes bounds on classical simulation complexity as a function of noise.