The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the ...

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability ...

We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement ...

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects ...