How many qubits are needed for quantum computational supremacy?

Quantum supremacy using a programmable superconducting processor

(2019) Frank Arute et al.   NATURE

Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error

(2018) Keisuke Fujii et al.   PHYSICAL REVIEW LETTERS

Architectures for Quantum Simulation Showing a Quantum Speedup

(2018) Juan Bermejo-Vega et al.   Physical Review X

Generalized Kakeya sets for polynomial evaluation and faster computation of fermionants

(2018) Andreas Björklund et al.   ALGORITHMICA

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(2018)   QUANTUM INFORMATION & COMPUTATION

On the complexity and verification of quantum random circuit sampling

(2018) Adam Bouland et al.   Nature Physics

Quantum circuits and low-degree polynomials over $\mathbb{F_\mathsf{2}}$

(2017) Ashley Montanaro   Journal of Physics A-Mathematical and Theoretical

Quantum computational supremacy

(2017) Aram W. Harrow et al.   NATURE

Classical boson sampling algorithms with superior performance to near-term experiments

(2017) Alex Neville et al.   Nature Physics

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(2017)   QUANTUM INFORMATION & COMPUTATION

Average-Case Complexity Versus Approximate Simulation of Commuting Quantum Computations

(2016) Michael J. Bremner et al.   PHYSICAL REVIEW LETTERS

Exponential Time Complexity of the Permanent and the Tutte Polynomial

(2014) Holger Dell et al.   ACM Transactions on Algorithms

Hardness of Classically Simulating the One-Clean-Qubit Model

(2014) Tomoyuki Morimae et al.   PHYSICAL REVIEW LETTERS

A linear-optical proof that the permanent is #P-hard

(2011) S. Aaronson   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

(2010) M. J. Bremner et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Temporally unstructured quantum computation

(2009) D. Shepherd et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES