In order to achieve universal quantum computation using continuous variables, one needs to jump out of the set of Gaussian operations and have a non-Gaussian element, such as the cubic phase gate. However, such a gate is currently very difficult to implement in practice. Here we introduce an experimentally viable 'repeat-untilsuccess' approach to generating the cubic phase gate, which is achieved using sequential photon subtractions and Gaussian operations. We find that our scheme offers benefits in terms of the expected time until success, although we require a primitive quantum memory.

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has led to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuousvariable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on cluster states that is feasible with today's technology.

The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a user's privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits (from a quantum perspective) that could one day allow the potential widespread adoption of this quantum technology in future cloud-based computing networks.

We propose a method to improve the performance of two entanglement-based continuous-variable quantum key distribution protocols using noiseless linear amplifiers. The two entanglement-based schemes consist of an entanglement distribution protocol with an untrusted source and an entanglement swapping protocol with an untrusted relay. Simulation results show that the noiseless linear amplifiers can improve the performance of these two protocols, in terms of maximal transmission distances, when we consider small amounts of entanglement, as typical in realistic setups.

We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable deviceindependent quantum key distribution to this encoding enables a continuous-variable analogue. Since the security of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find that our protocol is valid over the same distances as its discrete-variable counterpart, except that we are able to take advantage of high efficiency commercially available detectors where, for the most part, only homodyne detection is required. This offers the potential of removing the difficulty in closing the loopholes associated with Bell inequalities.