Subuniversal models of quantum computation in continuous variables
Last updated May 26, 2019 by Alessandro Ferraro
Wednesday, May 15th 2019, 04:00 PM, MAPTC/0G/006
Speaker: G Ferrini (Chalmers University)
In the recent years we have witnessed an increasing interest in quantum circuits that define subuniversal models of quantum computation [1]. These models lie somewhere inbetween classical and universal quantum computing, in the sense that, although not possessing the full computational power of a universal quantum computer, they allow for the outperformance of classical computational capabilities with respect to specific problems. Beyond their conceptual relevance, the reason for this interest is that these models require less experimental resources than universal quantum computers do. Therefore, they may enable experimental demonstration of quantum advantage, i.e. the predicted speedup of quantum devices over classical ones for some computational tasks. These models are often associated with sampling problems for which the task is to draw random numbers according to a specific probability distribution. Some of these probability distributions are likely to be hard to sample for classical computers, assuming widely accepted conjectures in computer science; it is the case, for instance, of the celebrated Boson Sampling model [1].
In parallel, ContinuousVariable (CV) systems are being recognized as a promising alternative to the use of qubits, as they allow for the deterministic generation of unprecedented large quantum states, and also offer detection techniques, such as homodyne detection, with high efficiency and reliability.
I will present two different models of subuniversal quantum computers in continuous variables, namely ContinuousVariable Instantaneous Quantum Computing (CV IQP) [2,3], and ContinuousVariable Sampling from photonadded or photonsubtracted squeezed states (CVS) [3]. The main ingredients composing these circuits are: squeezed states or photonadded or photonsubtracted squeezed states, linear optics evolution, homodyne or heterodyne detection. I will detail how, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their exact output probability distribution can be shown to be hard to simulate by a classical computer, and discuss potential experimental implementations.
[1] S. Aaronson and A. Arkhipov, Theory of Computing 9, 143 (2013).
[2] T. Douce, D. Markham, E. Kashefi, E. Diamanti, T. Coudreau, P. Milman, P. van Loock and G. Ferrini, Phys. Rev. Lett. 118, 070503 (2017)
[3] T. Douce, D. Markham, E. Kashefi, P. van Loock and G. Ferrini, Phys. Rev. A 99, 012344 (2019)
[4] U. Chabaud, T. Douce, D. Markham, P. van Loock, E. Kashefi and G. Ferrini, Phys. Rev. A 96, 062307 (2017).

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