N-qubit universal quantum logic with a photonic qudit and O(N) linear optics elements

TL;DR

This paper introduces a linear-optics-based method for deterministic N-qubit quantum logic using a single photonic qudit, significantly reducing complexity compared to previous approaches, and discusses scalable integration with matter qubits for quantum networks.

Contribution

It presents a linear-optics scheme for N-qubit logic in a single photonic qudit with O(N) elements, enabling scalable quantum processing and interfacing with matter qubits.

Findings

Deterministic generation and manipulation of N-qubit states in a single time-bin qudit.

Linear scaling of optical elements with N, reducing complexity.

Feasibility of interfacing photonic qudits with matter qubits for scalable quantum networks.

Abstract

High-dimensional quantum units of information, or qudits, can carry more than one quantum bit of information in a single degree of freedom, and can therefore be used to boost the performance of quantum communication and quantum computation protocols. A photon in a superposition of $2^N$ time bins - a time-bin qudit - contains as much information as N qubits. Here, we show that N-qubit states encoded in a single time-bin qudit can be arbitrarily and deterministically generated, manipulated and measured using a number of linear optics elements that scales linearly with N, as opposed with prior proposals of single-qudit implementation of N-qubit logic, which typically requires $O(2^N)$ elements. The simple and cost-effective implementation we propose can be used as a small-scale quantum processor. We then demonstrate a path towards scalability by interfacing distinct qudit processors to a matter qubit (atom or quantum dot spin) in an optical resonator. Such a cavity QED system allows for more advanced functionalities, such as single-qubit nondemolition measurement and two-qubit gates between distinct qudits. It could also enable quantum interfaces with other matter quantum nodes in the context of quantum networks and distributed quantum computing.