Constraint satisfaction problems are a central pillar of modern computational complexity
theory. This survey provides an introduction to the rapidly growing field of Quantum …

The calculation of ground-state energies of physical systems can be formalized as the k-
local Hamiltonian problem, which is a natural quantum analogue of classical constraint …

The problem of determining whether a given quantum state is entangled lies at the heart of
quantum information processing. Despite the many methods—such as the positive partial …

In recent years we have seen the birth of a new field known as Hamiltonian complexity lying
at the crossroads between computer science and theoretical physics. Hamiltonian …

Quantum computation appears to offer significant advantages over classical computation
and this has generated a tremendous interest in the field. In this thesis we study the …

Finding the ground-state energy of electrons subject to an external electric field is a
fundamental problem in computational chemistry. While the theory of QMA-completeness …

Estimating the ground state energy of a local Hamiltonian is a central problem in quantum
chemistry. In order to further investigate its complexity and the potential of quantum …

We provide several advances to the understanding of the class of quantum Merlin--Arthur
(QMA) proof systems, the quantum analogue of NP. Our central contribution is proving a …

In quantum chemistry, the price paid by all known efficient model chemistries is either the
truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science …

Despite significant effort, the quantum machine learning community has only demonstrated
quantum learning advantages for artificial cryptography-inspired datasets when dealing with …