This article surveys quantum computational complexity, with a focus on three fundamental
notions: polynomial-time quantum computations, the efficient verification of quantum proofs …

Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms,
make use of restricted tomography of the quantum state that measures the reduced density …

The classical PCP theorem is arguably the most important achievement of classical
complexity theory in the past quarter century. In recent years, researchers in quantum …

This is a set of lecture notes suitable for a Master's course on quantum computation and
information from the perspective of theoretical computer science. The first version was …

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 …

A bstract Conformal truncation is a powerful numerical method for solving generic strongly-
coupled quantum field theories based on purely field-theoretic technics without introducing …

Given a renormalization scheme, we show how to formulate a tractable convex relaxation of
the set of feasible local density matrices of a many-body quantum system. The relaxation is …

We construct a constant-round zero-knowledge classical argument for NP secure against
quantum attacks. We assume the existence of Quantum Fully-Homomorphic Encryption and …

Verifying equivalence between two quantum circuits is a hard problem, that is nonetheless
crucial in compiling and optimizing quantum algorithms for real-world devices. This paper …

Clarifying the relation between the whole and its parts is crucial for many problems in
science. In quantum mechanics, this question manifests itself in the quantum marginal …