Deterministic quantum gate between photons in a next-generation light-matter interface

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Engineered nanoscale systems that provide access to the quantum properties of matter are heralding a revolution in physics and technology. Control over single quantum objects, such as a single electron or photon, and over interactions between them provides the means to engineer the correlations that make quantum technologies a revolutionary advance over their current counterparts. An interface between a stationary matter and a flying optical quantum bit (qubit) is a fundamental building block of the inter-connects that will make quantum technologies useful on a large scale. Solid-state devices have shown strongly coupled light-matter interfaces, efficient light collection, and quantum control of coherent matter nodes. Progress on fabrication techniques to enhance spin and optical coherence properties, combined with important theoretical efforts on modelling complex environments, have yielded significant gains in these areas. Indeed, recent demonstrations using optically addressable spins in semiconductors include a loophole-free test of Bell's inequalities, the generation of photonic states involved in measurement-based quantum computation, and the realisation of quantum internet primitives. Alongside ultracold atoms and superconducting circuits, such optically active solid-state platforms provide developments with distinct long-term advantages due to their ease of integration with combined classical optical and electrical elements. This project will put together a next-generation solid-state quantum networking node that combines the latest developments in the quantum optical research community -- optical device integration, all-optical electron spin control, and nuclear spin coherence and control -- to deliver a platform that outperforms other candidate technologies on the combined metrics of optical coherence and efficiency, quantum bit control, and quantum memory lifetime. This proposal consists of realising this combination by leveraging two recent breakthroughs in a system already known as the best single photon source - III-V semiconductor quantum dots: (1) open optical microcavities as a versatile interface to reach a strong light-matter coupling and high collection efficiency, and (2) strain-free GaAs quantum dots, as host for a coherent matter quantum bit, and on which preliminary measurements indicate a two orders of magnitude improvement in coherence time over the state of the art (InAs quantum dots). As a first major benchmark and the major deliverable of this proposal, a deterministic quantum gate will be performed between two photon qubits, leveraging the optical and spin coherence of this new generation of quantum dots. This proposal aims to reach beyond 1MHz entanglement rate between two photon qubits while achieving a few-percent error rate - a more than four orders of magnitude improvement of the rate-fidelity product over previous attempts in the optical domain. This will serve as a proof-of-concept to establish this platform as the optimal choice for investment towards large-scale arrays of quantum optical devices.Finally, developing this GaAs quantum dot platform promises to equip the leading commercial single-photon emitters with a long-lived nuclear-spin memory, the missing piece for this otherwise exquisite photonics platform. This addition would allow the demonstration of long-lived entanglement across distant quantum nodes, a crucial step en route to a quantum internet where such entanglement can be used as a resource for communication and computation.