Integrated Optics as a Platform for Continuous Variable Measurement Based Quantum Computing

Recently there have been demonstrations of squeezing using Lithium Niobate and Silicon-based integrated chip architectures[5]. These results have been claimed to be useful for quantum computing, however the squeezing levels achieved so far are low. Also recently, extremely large 2D continuous variable cluster states have been generated using bulk optics[1,2]. A key element of these demonstrations were large temporal delays to enable the use of time-bin encoding. Increasing the number of input modes in the cluster requires an increase in the delay, constraining the scalability of an input register. This PhD aims to explore the generation of CV cluster states using integrated optical technology with the view to designing a scalable integrated platform.
A key experimental challenge to be addressed is the reconciliation of the squeezing levels required for cluster state verification (~3-5dB) and full fault tolerance (~15-17dB [7]) with current integrated results of ~1-2dB. A first stage of the PhD would therefore be to use commercially available lithium niobite modules coupled into a chip with integrated Homodyne detectors to observe the minimum 3dB of squeezing required. The PhD is sufficiently flexible to pivot and use demonstrated silicon and silicon-nitride based squeezing if they meet requirements.
Once this has been achieved, a milestone of the PhD will be to understand the theory of, design, construct and verify a 1D integrated massive cluster state generation platform based upon existing bulk schemes[3]. A stretch goal of this project would then be to implement gaussian operations on the cluster state to demonstrate a computing proof of concept following recently established techniques[4]. A second targeted project will be to extend the cluster state to 2D. However, due to the large delays required (and associated losses) in the double time-bin encoding method an alternative platform using frequency and/or spatial modes will need to be explored[6]. This sub theme of the PhD will constitute multiple possibilities for projects, including performing state teleportation between two spectrally separate frequency modes and using the generated experiments for multi-partite entanglement demonstrations. Finally, an alternate direction for the PhD would be to look at optical generation of required non gaussian states for fault tolerance in CV computation.
In addition to the experimental projects, the PhD will also consist of a significant theory component relating to Fault Tolerance for Universal CV-MBQC. To take advantage of error correction techniques, a bosonic code is needed to embed a qubit within the continuous system. Furthermore, to enable universality a Non-Gaussian operation is needed. Both of these challenges can be resolved by the use of 'GKP' qubits which are injected into the cluster states[8]. A collaborative effort with Nicolas Menicucci is proposed to directly address some of these challenges by studying mixed Gaussian / GKP encoding schemes. The proposed collaboration will involve a secondment at RMIT within Nick's group for 3-6 months to develop this project.

1. Deterministic generation of a two-dimensional cluster state https://science.sciencemag.org/content/366/6463/369
2. Generation of time-domain-multiplexed two-dimensional cluster state https://science.sciencemag.org/content/366/6463/373
3. Generation of one-million- mode continuous-variable cluster state by unlimited time-domain multiplexing https://aip.scitation.org/doi/10.1063/1.4962732[4].
4. One-hundred step measurement-based quantum computation multiplexed in the time domain with 25 MHz clock frequency https://arxiv.org/pdf/2006.11537.pdf
5. Single-mode quadrature squeezing using dual-pump four-wave mixing in a nanophotonic device https://arxiv.org/abs/2001.09474
6. https://arxiv.org/pdf/1912.11215
7. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.010301
8. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.200502