Spin-orbit implementation of Solovay-Kitaev decomposition of single-qubit channels

TL;DR

This paper demonstrates a method to implement any single-qubit quantum channel using a spin-orbit approach with photons, combining the Solovay-Kitaev theorem and optical components for universal quantum operations.

Contribution

It introduces a novel optical implementation of single-qubit channels using spin-orbit coupling and a minimal ancillary system, expanding quantum simulation capabilities.

Findings

Successful implementation of arbitrary single-qubit channels on photon polarization.

Use of spin-orbit CNOT gate and optical elements for universal quantum operations.

Feasibility of encoding ancillary qubits in the transverse mode of light.

Abstract

The Solovay-Kitaev theorem allows us to approximate any single-qubit gate to arbitrary accuracy with a finite sequence of fundamental operations from a universal set of gates. Inspired by this decomposition, we present a quantum channel simulator capable of implementing any completely positive trace-preserving map. Our realization consists of one ancillary qubit, encoded in the transverse mode of a laser beam (orbital degree of freedom), one qubit system, encoded in its polarization (spin), one spin-orbit CNOT gate and four single-qubit operations performed with prisms and polarization components. Our results describe the implementation of arbitrary single-qubit channels on the photon polarization using the transverse mode as the ancillary qubit.