Resources for bosonic quantum computational advantage

Abstract

Quantum computers promise to dramatically outperform their classical counterparts. However, the non-classical resources enabling such computational advantages are challenging to pinpoint, as it is not a single resource but the subtle interplay of many that can be held responsible for these potential advantages. In this work, we show that every bosonic quantum computation can be recast into a continuous-variable sampling computation where all computational resources are contained in the input state. Using this reduction, we derive a general classical algorithm for the strong simulation of bosonic computations, whose complexity scales with the non-Gaussian stellar rank of both the input state and the measurement setup. We further study the conditions for an efficient classical simulation of the associated continuous-variable sampling computations and identify an operational notion of non-Gaussian entanglement based on the lack of passive separability, thus clarifying the interplay of bosonic quantum computational resources such as squeezing, non-Gaussianity and entanglement.

Published version, 6+14 pages, 2 figures. Comments are welcome!

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• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Classical models may be a better explanation of the Jiuzhang 1.0 Gaussian Boson Sampler than its targeted squeezed light model
• Correlation-pattern-based Continuous-variable Entanglement Detection through Neural Networks
• Simulation of quantum optics by coherent state decomposition
• Page curves and typical entanglement in linear optics
• Classical simulation of non-Gaussian bosonic circuits
• Phase-space negativity as a computational resource for quantum kernel methods
• Seeding Gaussian boson samplers with single photons for enhanced state generation
• Certification of non-Gaussian Einstein-Podolsky-Rosen Steering
• Quantum Kernel Machine Learning With Continuous Variables
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Clifford operations and homological codes for rotors and oscillators
• Classical simulation and quantum resource theory of non-Gaussian optics
• On Quantum Steering and Wigner Negativity
• Nonlinear squeezing generation via multimode PDC and single photon measurement
• Superselection rules and bosonic quantum computational resources
• Transition of Anticoncentration in Gaussian Boson Sampling
• Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator
• Graphical Framework for Non-Gaussian Quantum States
• Adapting coherent-state superpositions in noisy channels
• The Second Moment of Hafnians in Gaussian Boson Sampling
• Adaptive Non-Gaussian Quantum State Engineering
• Complexity of quantum tomography from genuine non-Gaussian entanglement
• Husimi phase distribution in non-Gaussian operations
• Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
• Non-Gaussian state teleportation with a nonlinear feedforward
• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources
• Adding Photonic Entanglement to Superradiance by Using Multilevel Atoms
• Continuous-variable spatio-spectral quantum networks in nonlinear photonic lattices
• Configurable photonic simulator for quantum field dynamics
• Variational Tensor Network Simulation of Gaussian Boson Sampling and Beyond
• Majorization theoretical approach to entanglement enhancement via local filtration
• Detecting strongly non-Gaussian entanglement
• Non-Gaussianity from superselection rules
• Classical algorithms for measurement-adaptive Gaussian circuits
• Resourcefulness of non-classical continuous-variable quantum gates
• The symplectic rank of non-Gaussian quantum states