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Quantum Advantage from Sequential-Transformation Contextuality.

Shane Mansfield1, Elham Kashefi1,2

  • 1Sorbonne Université, CNRS, Laboratoire d'Informatique de Paris 6, F-75005 Paris, France.

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Summary
This summary is machine-generated.

We introduce a new concept of sequential transformation contextuality for quantum computation. This contextuality is key for deterministic and probabilistic computation of nonlinear functions, offering a quantifiable advantage.

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Area of Science:

  • Quantum Information Science
  • Foundations of Quantum Mechanics
  • Computational Complexity Theory

Background:

  • Existing notions of contextuality (Bell-Kochen-Specker, Spekkens) are primarily applied to state-based or measurement-based scenarios.
  • Quantum computation models often rely on understanding the role of contextuality in information processing.
  • The computational power of quantum systems is linked to non-classical features like contextuality.

Purpose of the Study:

  • To introduce and define a novel concept: sequential-transformation contextuality.
  • To investigate the necessity and sufficiency of this contextuality for deterministic and probabilistic computation of nonlinear functions within a transformation-based quantum computation model.
  • To establish a quantitative relationship between the degree of contextuality and computational advantage.

Main Methods:

  • Development of a transformation-based model for quantum computation.
  • Formal definition of sequential-transformation contextuality, distinguishing it from prior notions.
  • Analysis of computational tasks (deterministic and probabilistic nonlinear function computation) under specific classical component restrictions (mod2 linearity, matching constraints).

Main Results:

  • Strong sequential-transformation contextuality is proven to be necessary and sufficient for deterministic computation of nonlinear functions under the given constraints.
  • Sequential-transformation contextuality is necessary and sufficient for achieving advantage in probabilistic computation of nonlinear functions.
  • The degree of advantage in probabilistic computation is shown to be directly quantifiable by the degree of contextuality.

Conclusions:

  • Sequential-transformation contextuality represents a distinct and crucial resource in quantum computation.
  • This framework provides a new perspective on the role of contextuality in computational advantage.
  • The findings offer a pathway to understand and potentially enhance quantum computational capabilities through tailored contextual properties.