Towards Photonic Non-Abelian Quantum Gates

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Quantum information science, a field that has emerged over the past several decades, addresses the question of whether harnessing quantum mechanical effects through storing, processing and transmitting information encoded in inherently quantum mechanical systems can lead to new phenomena, functionalities, and devices. Quantum information is both fundamental science and a progenitor for new technologies. Photonic quantum systems provide many advantages, reaching from low levels of decoherence to precise single-particle quantum control and being mobile. Laser-written integrated photonic waveguides provide the unique capability of designing complex, stable quantum information circuitry with unprecedented flexibility. For example, non-Abelian geometric phases associated with non-Abelian synthetic gauge fields have recently been successfully implemented. Such phases are crucial for topological quantum computation, non-Abelian anyon statistics, and the quantum simulation of Yang–Mills theories. The aim of our proposal is to promote the implementation of photonic non-Abelian U(N) holonomies in integrated waveguide architectures with the vision to establish a basis for new quantum information processing applications in the framework of noisy intermediate-scale quantum (NISQ) processing. In particular, in the proposed project we will (1) develop the theoretical foundations for and experimentally demonstrate a U(3) holonomy using two indistinguishable photons and a network of four coupled sites, in which the waveguides’ bending geometry has been optimized, (2) develop and demonstrate a conceptual and experimental framework to include non-orthogonal modes and non-adiabatic quantum state evolution in the functionality of our integrated waveguide circuits which will allow us to access larger degenerate subspaces, including a U(4)-holonomy for two photons, and (3) implement various holonomic quantum gates and experimentally demonstrate holonomic quantum computation protocols. The strength of our proposal comes from combining two very fruitful modern research directions: multi-photon-state manipulation and integrated optical circuitry in order to explore fundamental concepts of quantum information processing, for the advancement of fundamental science as well as photonic applications.