Phase transitions in random circuit sampling

Area of Science:

• Quantum Information Science
• Quantum Computing
• Condensed Matter Physics

Background:

• Quantum processors are susceptible to environmental noise, degrading performance and limiting computational capabilities.
• Cross-entropy benchmarking (XEB) is used to estimate the effective size of the Hilbert space in quantum processors.
• Noise can compromise quantum algorithms, making them vulnerable to classical simulation.

Purpose of the Study:

• To experimentally demonstrate and theoretically explain two observable phase transitions in random circuit sampling using cross-entropy benchmarking.
• To introduce a weak-link model for analyzing the interplay between noise and coherent evolution.
• To establish the existence of a computationally complex phase accessible with current quantum processors.

Main Methods:

• Implementation of a random circuit sampling algorithm.
• Experimental observation of two phase transitions using cross-entropy benchmarking.
• Theoretical explanation using a statistical model and a weak-link model.
• Execution of a large-scale random circuit sampling experiment on a 67-qubit processor.

Main Results:

• Two phase transitions were experimentally observed: a dynamical transition with circuit depth and a quantum phase transition controlled by error rate.
• A weak-link model was developed to analytically and experimentally identify the quantum phase transition.
• A 67-qubit, 32-cycle random circuit sampling experiment demonstrated computational complexity exceeding classical supercomputers.

Conclusions:

• The study establishes the existence of phase transitions in quantum computation, offering insights into noise resilience.
• A computationally complex phase is shown to be reachable with current quantum processors, paving the way for practical quantum advantage.
• The findings provide a framework for understanding and mitigating noise in quantum computing.