Cyclic permutations for qudits in d dimensions.

Abstract:

:One of the main challenges in quantum technologies is the ability to control individual quantum systems. This task becomes increasingly difficult as the dimension of the system grows. Here we propose a general setup for cyclic permutations Xd in d dimensions, a major primitive for constructing arbitrary qudit gates. Using orbital angular momentum states as a qudit, the simplest implementation of the Xd gate in d dimensions requires a single quantum sorter Sd and two spiral phase plates. We then extend this construction to a generalised Xd(p) gate to perform a cyclic permutation of a set of d, equally spaced values {|[Formula: see text]〉, |[Formula: see text] + p〉, …, |[Formula: see text] + (d - 1)p〉} [Formula: see text] {|[Formula: see text] + p〉, |[Formula: see text] + 2p〉, …, |[Formula: see text]〉}. We find compact implementations for the generalised Xd(p) gate in both Michelson (one sorter Sd, two spiral phase plates) and Mach-Zehnder configurations (two sorters Sd, two spiral phase plates). Remarkably, the number of spiral phase plates is independent of the qudit dimension d. Our architecture for Xd and generalised Xd(p) gate will enable complex quantum algorithms for qudits, for example quantum protocols using photonic OAM states.

journal_name

Sci Rep

journal_title

Scientific reports

authors

Isdrailă TA,Kusko C,Ionicioiu R

doi

10.1038/s41598-019-42708-7

subject

Has Abstract

pub_date

2019-04-19 00:00:00

pages

6337

issue

1

issn

2045-2322

pii

10.1038/s41598-019-42708-7

journal_volume

9

pub_type

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