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Cyclic permutations for qudits in d dimensions.

Tudor-Alexandru Isdrailă1, Cristian Kusko2, Radu Ionicioiu3

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Controlling multi-dimensional quantum systems is challenging. This study introduces a general setup for cyclic permutation gates (Xd) using orbital angular momentum states, enabling complex quantum algorithms for qudits.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Quantum Computing

Background:

  • Controlling individual quantum systems is crucial for quantum technologies.
  • System dimensionality significantly increases control complexity.
  • Arbitrary qudit gates are essential for advanced quantum algorithms.

Purpose of the Study:

  • To propose a general setup for cyclic permutation gates (Xd) in d dimensions.
  • To enable the construction of arbitrary qudit gates.
  • To utilize orbital angular momentum states as a qudit.

Main Methods:

  • Implementation of the Xd gate using a single quantum sorter (Sd) and two spiral phase plates.
  • Extension to a generalized Xd(p) gate for cyclic permutations of d equally spaced values.
  • Development of compact Michelson and Mach-Zehnder configurations for the generalized gate.

Main Results:

  • A general setup for cyclic permutation gates (Xd) is proposed.
  • Compact implementations for generalized Xd(p) gates are achieved in Michelson and Mach-Zehnder setups.
  • The number of spiral phase plates required is independent of the qudit dimension d.

Conclusions:

  • The proposed architecture facilitates complex quantum algorithms for qudits.
  • This work enables advanced quantum protocols, particularly using photonic orbital angular momentum states.
  • The dimension-independent nature of spiral phase plates simplifies scalable quantum control.