From the 1 of 9 linked papers with an AI index.
9 papers
The Kikuchi Hierarchy is Sharp for XOR
Alexander Schmidhuber, Matthew B. Hastings
Planted noisy XOR and the strong refutation of random XOR are governed by a conjectured trade-off between signal strength and time: Level of the Kikuchi hierarchy shou…
A Spectral Proof of the Hypergraph Moore Bound
Alexander Schmidhuber, Matthew B. Hastings
The paper proves Feige's hypergraph Moore bound conjecture, showing that any sufficiently dense k‑uniform hypergraph contains a small even cover, using new spectral bounds for Kiku…
Accelerating Classical and Quantum Tensor PCA
Matthew B. Hastings
Spectral methods are a leading approach for tensor PCA with a ``spiked" Gaussian tensor. The methods use the spectrum of a linear operator in a vector space with exponentially high…
Roadmap to fault tolerant quantum computation using topological qubit arrays
David Aasen, Morteza Aghaee, Zulfi Alam +179
We describe a concrete device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap e…
Geometrically Enhanced Topological Quantum Codes
David Aasen, Jeongwan Haah, Matthew B. Hastings +1
We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric…
A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes
David Aasen, Matthew B. Hastings, Vadym Kliuchnikov +8
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance o…