Automated Discovery of Non-local Photonic Gates

TL;DR

This work shows that non-local photonic gates can be realized without photon interactions or pre-shared entanglement by exploiting indistinguishability through path identity. Using a graph-based representation, the authors (via the AI system PyTheus) discover SWAP, CNOT, TOFFOLI, and FREDKIN gate schemes that operate on spatially separated photons, relying on coherent superpositions of photon-pair origins and path indistinguishability rather than entangled ancillas. The proposals demonstrate generic patterns and high-dimensional generalizations, with four ancilla photons sufficing in many cases, and include path-identity teleportation and path-information erasure teleportation concepts. The results advance practical distributed quantum information processing and illustrate how automated discovery can contribute novel ideas in physics, with clear experimental feasibility given existing technologies.

Abstract

Interactions between quantum systems enable quantum gates, the building blocks of quantum information processing. In photonics, direct photon-photon interactions are too weak to be practically useful, so effective interactions are engineered with linear optics and measurement. A central challenge is to realize such interactions non-locally, i.e., between photons that remain spatially separated. We present experimental proposals for several essential non-local multiphoton quantum gates that act on spatially separated photons, in both qubit and high-dimensional qudit systems. All solutions were discovered by the AI-driven discovery system called PyTheus. Rather than using pre-shared entanglement or Bell state measurements, our gates use as a resource quantum indistinguishability by path identity - a technique that exploits coherent superpositions of the photon pair origins. While analyzing these solutions, we uncovered a new mechanism that mimics much of the properties of quantum teleportation, without shared entanglement or Bell state measurements. Technically, our results establish path indistinguishability as a practical resource for distributed quantum information processing; conceptually, they demonstrate how automated discovery systems can contribute new ideas and techniques in physics.

Figures (4)

• Figure 1: Quantum teleportation as a core component of the SWAP gate. (a) The standard quantum teleportation protocol, based on a shared entangled pair and a Bell-state measurement bennett1993teleportingbouwmeester1997experimental. (b) A variant based on path identity (PI) wang2024entangling, where the quantum information of a photon is transferred to the output, while the photon itself does not propagate to the output but is instead measured. This variation was discovered accidentally during the automated search for a SWAP gate. (c) The detector click patterns corresponding to the PI analogue of teleportation in (b). (d) A variation of the PI-based teleportation, enabled by removing the path information through quantum erasure (we label as PE teleportation). (e) A high-dimensional generalization of PE teleportation. (f-h) All corresponding solutions were discovered by PyTheusruiz2023digital using the graph-based representation of quantum optics krenn2017quantumgu2019quantum. These graphs represent the underlying logic of the quantum correlations encoded in the experiments.
• Figure 2: Photonic SWAP gate. (a) A trivial way to perform a SWAP operation, where both photons are physically exchanged by sending each over the whole distance. (b) A SWAP gate realized through two quantum teleportations siddiqui2023swap, without direct transmission of the photons. (c) A path-identity (PI) analogue of teleportation used to construct a SWAP gate. (d) An alternative scheme employing path-information quantum erasure (PE). (e-f) A three-dimensional generalization of the SWAP gate, shown as a graph representation and as an extension of the experiment in (d).
• Figure 3: Photonic CNOT gates. (a) The standard implementation of a photonic CNOT gate, in which an entangled photon pair is shared between the two sides gasparoni2004realization. (b) An alternative scheme based on path identity that do not need shared entanglement between the input photons. (c) A new experimental blueprint for a CNOT gate realized via path-information erasure. (d) The original qubit CNOT solution discovered by PyTheus. The perfect matchings of the corresponding graph (shown below) illustrate the intrinsic working principle of the gate. (e) High-dimensional CNOT gates discovered by PyTheus. (f) Manually constructed graphs based on a generalizable pattern we identified from the machine-discovered gates. Analogous to Figs. \ref{['fig:teleport']} and \ref{['fig:swap']}, the graphs can be directly translated into implementations based on path identity or path-information erasure.
• Figure 4: Experimental proposals for three-photon gates. (a-b) A qubit and qutrit TOFFOLI gate, each requiring four ancilla photons. (c) A qubit FREDKIN gate implemented with four ancilla photons.