It is proved that every problem that is recursively enumerable, including the Halting problem, can be efficiently verified by a classical probabilistic polynomial-time verifier interacting with two all-powerful but noncommunicating provers sharing entanglement.Expand

This paper focuses on a special family of quantum circuits called the Hamiltonian Variational Ansatz (HVA), which takes inspiration from the quantum approximation optimization algorithm and adiabatic quantum computation and exhibits favorable structural properties and numerically observes that the optimization landscape of HVA becomes almost trap free when the ansatz is over-parameterized.Expand

A device-independent randomness expansion protocol, involving only a constant number of non-signaling quantum devices, that achieves infinite expansion that can produce an unbounded amount of certified randomness that is close to uniform and secure against a quantum adversary.Expand

Three complexity-theoretic applications are described: a proof that the recent breakthrough lower bound of Lee, Raghavendra, and Steurer on the positive semidefinite extension complexity of the correlation and TSP polytopes cannot be improved further, and bounds on the query complexity of quantum algorithms whose expected output approximates such functions.Expand

We show that any language solvable in nondeterministic time exp( exp(⋯exp(n))), where the number of iterated exponentials is an arbitrary function R(n), can be decided by a multiprover interactive… Expand

The first parallel repetition theorem for entangled games involving more than two players, and for games involving quantum outputs is obtained; in particular, this theorem gives a quadratic Grover speed-up for distributed search problems.Expand

It is shown that non-adaptive randomness amplifiers that are robust to noise cannot achieve more than doubly exponential expansion, and that a wide class of protocols based on the use of the CHSH game can only lead to (singly) exponential expansion if adversarial devices are allowed the full power of non-signaling strategies.Expand

The quantum query complexity of this problem is studied, and it is shown that any quantum algorithm that solves this problem with bounded error must make $\Omega(N^{1/5}/\log N)$ queries to the input function.Expand

This paper gives the first proof that the entangled value of a parallel repeated game must converge to 0 for all games whose entangled value is less than 1.Expand