We propose the first fully homomorphic encryption scheme, solving an old open problem.
Such a scheme allows one to compute arbitrary functions over encrypted data without the …

We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker
coefficients in the context of the geometric complexity theory program to prove a variant of …

A large class of problems in symbolic computation can be expressed as the task of
computing some polynomials; and arithmetic circuits form the most standard model for …

The status of the P versus NP problem Page 1 78 commuNicaTioNS of The acm |
SePteMber 2009 | voL. 52 | No. 9 review articles Doi:10.1145/1562164.1562186 It’s one of …

What is the minimal size quantum circuit required to exactly implement a specified n-qubit
unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the …

The P vs NP problem arose from the question of whether exhaustive search is necessary for
problems with short verifiable solutions. We still do not know if even a slight algorithmic …

Two central problems in computer science are P vs NP and the complexity of matrix
multiplication. The first is also a leading candidate for the greatest unsolved problem in …

The computational complexity of a quantum state quantifies how hard it is to make.
Complexity geometry, first proposed by Nielsen, is an approach to defining computational …

Abstract In 1950, John Nash sent a remarkable letter to the National Security Agency, in
which—seeking to build theoretical foundations for cryptography—he all but formulated what …

We propose a new second-order method for geodesically convex optimization on the natural
hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling …