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Phase transitions in random circuit sampling.

A Morvan1, B Villalonga1, X Mi1

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Quantum processors face noise challenges. This study reveals two phase transitions in random circuit sampling, demonstrating a computationally complex phase achievable with current quantum hardware.

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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.