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arXiv · 1607.07605

Continuous-Variable Instantaneous Quantum Computing is hard to sample

T. Douce·D. Markham·E. Kashefi·E. Diamanti·T. Coudreau·P. Milman·P. van Loock·G. Ferrini
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Abstract

Instantaneous quantum computing is a sub-universal quantum complexity class, whose circuits have proven to be hard to simulate classically in the Discrete-Variable (DV) realm. We extend this proof to the Continuous-Variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of post-selected circuits. In order to treat post-selection in CVs we consider finitely-resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator GKP encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render post-selected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

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T. Douce, D. Markham, E. Kashefi, E. Diamanti, T. Coudreau, P. Milman, P. van Loock, G. Ferrini. 2016-07-26. Continuous-Variable Instantaneous Quantum Computing is hard to sample. https://doi.org/10.1103/physrevlett.118.070503

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