# PhD position: Theory of Quantum Computation with Continuous Variables

contact: Giulia Ferrini; email address: giulia.ferrini@gmail.com

Starting date: early 2018. Duration: 5 years.

Quantum computers, i.e. devices in which quantum information can be encoded, processed and read out, are expected to solve certain computational tasks faster than classical computers. This property is referred to as quantum advantage. Despite the optimism towards the possible forthcoming achievements in quantum technologies, a conclusive experimental evidence of quantum advantage is still lacking: it has not yet been possible to build a quantum computer with a number of qubits that is large enough to practically beat classical machines.

The Continuous-Variable (CV) approach is emerging as a promising alternative to the use of qubits for information encoding. While qubits are encoded on two-level quantum systems, the CV approach relies on quantized variables with a continuous spectrum: for instance, the position and momentum of a particle, or the amplitude (q) and phase (p) quadratures of the quantized electromagnetic field. Up to one-million optical modes have been entangled in CV in 2016, which represents a striking progress with respect to DV systems, where only a few tens of qubits can be entangled nowadays. Therefore, CV systems are promising to overcome the problem of scalability. Furthermore, CV implementations beyond the purely optical realm are started to being studied, namely in opto-mechanics, or with microwaves coupled to superconducting devices.

The goal of this PhD project is to explore the origins of quantum advantage for computation in CV architectures, and to assess whether simple criteria can be provided. A particular focus will be given on sub-universal models of quantum computation [1, 2], that allow one to efficiently sample from a probability distribution that cannot be efficiently sampled with a classical computer.

For this project, we seek for a motivated student with interests and possibly expertises at the cross-over between quantum physics and computer science. The PhD will be carried at Chalmers University of Technology in Gothenburg, where regular exchanges with experimentalist and theorists working on superconducting qubits (Per Delsing, Göran Johansson) are in order. Further collaborations are planned with the computer science group of Elham Kashefi in Paris.

[1] Continuous-Variable Instantaneous Quantum Computing is hard to sample, T. Douce, D. Markham, E. Kashefi, E. Diamanti, T. Coudreau, P. Milman, P. van Loock, and G. Ferrini, Phys. Rev. Lett. 118, 070503 (2017).

[2] Continuous-Variable Sampling, U. Chabaud, T. Douce, D. Markham, P. van Loock, E. Kashefi, and G. Ferrini, preprint at arXiv:1707.09245 (2017).