The vacuum provides quantum advantage to otherwise simulatable architectures

Abstract

We consider a computational model composed of ideal Gottesman-Kitaev-Preskill stabilizer states, Gaussian operations - including all rational symplectic operations and all real displacements -, and homodyne measurement. We prove that such architecture is classically efficiently simulatable, by explicitly providing an algorithm to calculate the probability density function of the measurement outcomes of the computation. We also provide a method to sample when the circuits contain conditional operations. This result is based on an extension of the celebrated Gottesman-Knill theorem, via introducing proper stabilizer operators for the code at hand. We conclude that the resource enabling quantum advantage in the universal computational model considered by B.Q. Baragiola et al. [Phys. Rev. Lett. 123, 200502 (2019)], composed of a subset of the elements given above augmented with a provision of vacuum states, is indeed the vacuum state.

arXiv comment21 pages, 6 figures

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• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Classical simulation of non-Gaussian bosonic circuits
• Sufficient condition for universal quantum computation using bosonic circuits
• Classical simulation and quantum resource theory of non-Gaussian optics
• End-to-end switchless architecture for fault-tolerant photonic quantum computing
• Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
• Resourcefulness of non-classical continuous-variable quantum gates
• Sequential information theoretic protocols in continuous variable systems