COntinuous variable Measurement Based quantum computing – COMB

Our project aims at proposing theoretically and demonstrating experimentally quantum computation protocols in the optical domain. Quantum information is a pluridisciplinary field of research whose goal is to benefit from the specific properties of quantum mechanics to provide original communication and calculation protocols. These protocols can provide for instance security advantages or computational speed-up. While quantum computation is very promising, it still lacks a clear roadmap to perform relevant calculations, that is calculations undoable on classical computers. We propose here to benefit from the skills of two communities, namely physicists and computer scientists, to explore the advantages of a specific computation protocol, Measurement-Based Quantum Computing (MBQC), using the frequency spectrum of light.
MBQC is based on the availability of a large, multipartite entangled state on which a series of measurements are performed. For each operation to implement, a specific entangled state as well as a specific measurement order are used. The output of the computation is given by a set of one or more qubits which are to be measured in the end. The advantage of this protocol lies mainly on the absence of requirement of two qubits gates, which are probably the hardest to implement faithfully experimentally. The difficulty then lies mainly in producing a suitable entangled state. The solution which will be studied in this project uses the frequency spectrum of light beams produced by parametric down-conversion.
Parametric down-conversion, a nonlinear optical process by which a pump field is split in two coherent fields, is well known to produce nonclassical states of light. In particular, within an optical cavity, entangled beams are produced. We will base our study on parametric down conversion occurring in an optical cavity pumped by a femtosecond frequency comb. We will not consider standard variables, like polarization or intensity, but rather field quadratures of different frequency component of the light spectrum. Indeed, it can be shown that, while the standard variables can be described by bipartite entanglement, multipartite entanglement can be produced in both regimes in the frequency spectrum. This system produces multipartite entanglement which is the key ingredient for MBQC. The advantage of using the frequency spectrum of short light pulses is that it can involve hundreds of thousands of frequency components that are mutually coherent at the classical level and that are likely to be entangled at the quantum level, which makes the scalability to many qubits an easier task than in other possible schemes that are presently under study.
The goal of this project is to determine and demonstrate how such entangled states can be used in a way that puts in evidence an advantage of the MBQC approach over the standard quantum circuit model in terms of the number of operations for instance. This goal is relevant both in the physics community where this model is little explored for the moment and in the computer science community where the difference of the MBQC and quantum circuit models are not yet fully quantified and demonstrated.
Reaching this ambitious objective requires several steps. Firstly, there is a need to devise proper measurements schemes which can detect the multipartite entanglement present in such states and in particular characterize its dimensionality. Indeed, one of the crucial aspects of this project lies in the number of modes which can be entangled. Then we will show that we are able to tailor at will such a multimode entangled state. Once these steps have been taken, we will design and then implement basic quantum operations such as Fourier transform. Finally, we will tackle the more ambitious part of the project that is demonstrating a protocol with a clear advantage of MBQC protocols over the standard circuit model.