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

There is an increasing interest in quantum algorithms for problems of integer programming
and combinatorial optimization. Classical solvers for such problems employ relaxations …

The weighted MAX k k-CUT problem consists of finding ak-partition of a given weighted
undirected graph G (V, E), such that the sum of the weights of the crossing edges is …

We study the quantum moment problem: given a conditional probability distribution together
with some polynomial constraints, does there exist a quantum state rho and a collection of …

In this paper we obtain violations of general bipartite Bell inequalities of order n\log n with n
inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a …

We establish the first hardness results for the problem of computing the value of one-round
games played by a verifier and a team of provers who can share quantum entanglement. In …

We consider one-round games between a classical verifier and two provers who share
entanglement. We show that when the constraints enforced by the verifier are “unique” …

In this work we show that bipartite quantum states with local Hilbert space dimension n can
violate a Bell inequality by a factor of order\rm Ω\left (n\log^ 2n\right) when observables with …

This paper presents three results on the power of two-prover one-round interactive proof
systems based on oracularization under the existence of prior entanglement between …

We study the projective tensor norm as a measure of the largest Bell violation of a quantum
state. In order to do this, we consider a truncated version of a well-known SDP relaxation for …