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Asymptotically optimal quantum circuits for d-level systems.

Stephen S Bullock1, Dianne P O'Leary, Gavin K Brennen

  • 1Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8910, USA.

Physical Review Letters
|August 11, 2005
PubMed
Summary
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Quantum algorithm complexity for d-level systems (qudits) is now understood. Researchers established a precise scaling law for entangling gates, crucial for building scalable quantum computers.

Area of Science:

  • Quantum Information Science
  • Computational Complexity Theory
  • Many-Body Physics

Background:

  • Scalable quantum computation relies on processing information across multiple subsystems.
  • The relationship between quantum algorithm complexity (entangling gates) and subsystem size (qudit dimension) remains an open question.

Purpose of the Study:

  • To determine the precise scaling of quantum circuit complexity with subsystem size for universal quantum computation.
  • To establish bounds on the number of two-qudit gates required for computation.

Main Methods:

  • Analysis of quantum circuit complexity for many-d-level systems (qudits).
  • Derivation of both lower and upper bounds for the number of two-qudit gates.

Main Results:

Related Experiment Videos

  • A sharp asymptotic scaling of Theta(d^(2n)) gates is proven for universal computation on n qudits.
  • This complexity bound holds even for systems with locality constraints, such as nearest-neighbor interactions.

Conclusions:

  • The quantum circuit complexity question for finite-dimensional qudit systems is now resolved.
  • The established optimal asymptotic scaling provides a fundamental limit for designing efficient quantum algorithms.