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Measurement-based classical computation.

Matty J Hoban1, Joel J Wallman2, Hussain Anwar3

  • 1ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain.

Physical Review Letters
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Summary
This summary is machine-generated.

We introduce a classical analog of measurement-based quantum computation (MBQC), revealing complex computational structures. This work explores quantum computational nonclassicality in classical analogs of MBQC.

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Area of Science:

  • Quantum Information Science
  • Computational Complexity Theory
  • Classical Analogues of Quantum Computation

Background:

  • Measurement-based quantum computation (MBQC) is a quantum computing model equivalent to the circuit model.
  • The classical analogues of MBQC are not well-studied, limiting understanding of their computational properties.
  • Existing research on quantum computation often focuses on the circuit model, leaving MBQC's classical parallels underexplored.

Purpose of the Study:

  • To present a classical analogue of measurement-based quantum computation (MBQC).
  • To explore the computational complexity and structure within this classical analogue.
  • To identify quantum computational tasks that are classically hard to simulate but efficiently implementable within the MBQC framework.

Main Methods:

  • Identification of uniform families of quantum computations based on refined circuit models.
  • Efficient implementation of these circuit families within the MBQC model, notably without adaptive measurements.
  • Utilizing quantum-mechanically generated probability distributions as resource states in the classical analogue.

Main Results:

  • A classical analogue of MBQC with a rich computational complexity structure was developed.
  • Specific quantum computation families were identified as classically hard to simulate (sample).
  • These families were shown to be efficiently implementable in the MBQC model, even without adaptive measurements.

Conclusions:

  • The study establishes a classical analogue of MBQC, demonstrating its potential for complex computations.
  • Quantum-generated probability distributions, while not violating Bell inequalities, can exhibit nonclassical computational properties.
  • This research bridges quantum computation and classical complexity, highlighting the subtle imprint of quantum origins on computational resources.