Beginning with the work of Dinur, Lin, and Vidick (FOCS, 2024), tensor codes with constant product expansion have been foundational to recent advances in quantum locally testable codes (qLTCs) based on cubical complexes. Informally, product expansion says that any low-weight parity check of the tensor code can be written as ... more >>>

We give the first exponential quantum advantage in the general interactive three-party Number-on-Forehead (NOF) model for a decision problem. Previous separations hold only for restricted protocols like one-way communication for a relation. We construct an explicit partial Boolean function, the Interleaved Unitary Product problem, that requires only $O(\log n)$ quantum ... more >>>

The Noisy Linear Equations problem involves finding the solution to a random linear system over a finite field given noisy evaluations. This is a generalisation of various learning problems widely used in cryptography, including Learning with Errors (LWE), Learning with Rounding (LWR), and Learning Parity with Noise (LPN).

We present ... more >>>