Large-Scale Quantum Simulators and Quantum Computers over Continuous Variables: Theory and Experiment*

Continuous-variable (CV) quantum computing [1,2] is based on harmonic-oscillator qumodes such as position and momentum, or the two quadrature amplitudes of the quantized electromagnetic field, rather than on qubit- or qudit-based discrete encodings. It is a viable approach for which error correction [3] and fault tolerance [4] have been elucidated. It is particularly well suited to electromagnetic qumodes, which scale up very well as the resonant modes of a single optical cavity, such as that of an optical parametric oscillator, analogously to the classical optical frequency comb of a femtosecond laser. This allows cluster entangled states, which are quantum-computing ``substrates'' [5] in a sense, to be implemented over CV [6] on very large scales [7] as was experimentally demonstrated in the quantum optical frequency comb of a single OPO (60 entangled qumodes, simultaneously accessible) [8]. Note that sequential time-bin implementations are also possible (one million entangled qumodes, accessible two at a time) [9]. This paves the way to realizing interesting testbeds for bosonic, and possibly more general, quantum simulation [10]. In this talk, I will present the fundamentals of scalable CV cluster state generation in quantum optics, experimental realizations on five different continents, and applications to quantum simulation. [1] S. Lloyd and S.L. Braunstein, PRL \textbf{82}, 1784 (1999) [2] S.D. Bartlett, B.C. Sanders, S.L. Braunstein, K. Nemoto, PRL \textbf{88}, 097904 (2002) [3] D. Gottesman, A. Kitaev, and J. Preskill, PRA \textbf{64}, 012310 (2001) [4] N.C. Menicucci, PRL \textbf{112}, 120504 (2014) [5] R. Raussendorf and H.-J. Briegel, PRL \textbf{86}, 5188 (2001) [6] N.C. Menicucci \textit{et al.}, PRL \textbf{97}, 110501 (2006) [7] O. Pfister \textit{et al.}, PRA \textbf{70}, 020302 (2004) [8] M. Chen, N.C. Menicucci, and O. Pfister, PRL \textbf{112}, 120505 (2014) [9] J.-I. Yoshikawa \textit{et al.}, APL Photonics \textbf{1}, 060801 (2016) [10] K. Marshall, R. Pooser, G. Siopsis, and Ch. Weedbrook, PRA \textbf{92}, 063825 (2015)