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The complexity of NISQ.

Sitan Chen1,2, Jordan Cotler3, Hsin-Yuan Huang4,5

  • 1Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA. sitan@seas.harvard.edu.

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|September 26, 2023
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Summary
This summary is machine-generated.

We introduce the NISQ (Noisy Intermediate-Scale Quantum) complexity class for problems solvable with noisy quantum circuits. Our findings show NISQ offers limited advantages over classical methods for search but excels in specific tasks like the Bernstein-Vazirani problem.

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Area of Science:

  • Quantum Computing
  • Computational Complexity Theory

Background:

  • The rise of Noisy Intermediate-Scale Quantum (NISQ) devices necessitates understanding their computational capabilities.
  • Classical computation and fault-tolerant quantum computation represent established computational paradigms.

Purpose of the Study:

  • To define and analyze the NISQ complexity class.
  • To compare the computational power of NISQ devices against classical and fault-tolerant quantum computers.
  • To investigate NISQ's performance on specific computational problems.

Main Methods:

  • Definition of the NISQ complexity class.
  • Establishing super-polynomial complexity separations using modified Simon's problems.
  • Analysis of NISQ performance on unstructured search, Bernstein-Vazirani problem, and quantum state learning.

Main Results:

  • Super-polynomial separations demonstrated between classical, NISQ, and fault-tolerant quantum computation.
  • NISQ devices do not provide a Grover-like quadratic speedup for unstructured search.
  • NISQ offers a significant advantage for the Bernstein-Vazirani problem, requiring logarithmic queries.
  • NISQ is exponentially weaker than noiseless quantum circuits for quantum state learning.

Conclusions:

  • The NISQ complexity class offers a framework for understanding near-term quantum devices.
  • NISQ's capabilities are problem-dependent, showing limitations in search but potential in other areas.
  • Significant differences in computational power exist across classical, NISQ, and fault-tolerant quantum computing models.