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Optimal Universal Programming of Unitary Gates.

Yuxiang Yang1, Renato Renner1, Giulio Chiribella2,3,4,5

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Physical Review Letters
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Summary
This summary is machine-generated.

We determined the scaling of quantum program size with approximation error for universal quantum processors. Our findings connect quantum programming to metrology, establishing an equivalence between programming, learning, and estimating quantum gates.

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Area of Science:

  • Quantum Computing
  • Quantum Information Science
  • Quantum Metrology

Background:

  • Universal quantum processors aim to execute arbitrary quantum gates on data registers.
  • Perfect universal quantum processors are unattainable; research focuses on approximate implementations.
  • A key challenge is understanding how program size relates to approximation error.

Purpose of the Study:

  • To determine the scaling law between quantum program size and approximation error for universal quantum processors.
  • To design a protocol achieving this bound in the asymptotic limit.
  • To explore the connection between quantum programming and quantum metrology.

Main Methods:

  • Proving a theoretical bound on the size of quantum programs required for approximate universal quantum computation.
  • Developing a concrete protocol that achieves this bound asymptotically.
  • Establishing a link between optimal quantum programming and the Heisenberg limit in quantum metrology.

Main Results:

  • A proven bound on the smallest quantum program size as a function of approximation error.
  • A protocol demonstrating that this bound can be attained in the asymptotic limit.
  • An established asymptotic equivalence between quantum programming, quantum learning, and quantum state/gate estimation.

Conclusions:

  • The study quantifies the fundamental limits of approximate universal quantum computation.
  • The findings bridge quantum programming with quantum metrology, revealing deeper theoretical connections.
  • This work provides a framework for understanding and designing efficient quantum processors.