Classical simulation of Gaussian quantum circuits with non-Gaussian input states

Abstract

We consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of continuous-variable quantum states to the multimode setting and relate the stellar rank of the input non-Gaussian states, a recently introduced measure of non-Gaussianity, to the cost of evaluating classically the output probability densities of these circuits. Our results have consequences for the strong simulability of a large class of near-term continuous-variable quantum circuits.

8+6 pages, 3 figures. Comments welcome!

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• Correlation-pattern-based Continuous-variable Entanglement Detection through Neural Networks
• Simulation of quantum optics by coherent state decomposition
• Classical simulation of non-Gaussian bosonic circuits
• Hierarchical Verification of Non-Gaussian Coherence in Bosonic Quantum States
• Quantum Kernel Machine Learning With Continuous Variables
• Multicopy observables for the detection of optically nonclassical states
• Classical simulation and quantum resource theory of non-Gaussian optics
• Boson Sampling for Generalized Bosons
• Superselection rules and bosonic quantum computational resources
• Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator
• Continuous Variable Quantum Advantages and Applications in Quantum Optics
• Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
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• The symplectic rank of non-Gaussian quantum states
• Classical algorithms for measurement-adaptive Gaussian circuits
• Non-Gaussianity from superselection rules