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Quantum algorithm for solving linear systems of equations
Aram W. Harrow, Avinatan Hassidim, Seth Lloyd
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x s…
Efficient Quantum Tensor Product Expanders and k-designs
Aram W. Harrow, Richard A. Low
Quantum expanders are a quantum analogue of expanders, and k-tensor product expanders are a generalisation to graphs that randomise k correlated walkers. Here we give an efficient…
Exact universality from any entangling gate without inverses
Aram W. Harrow
This note proves that arbitrary local gates together with any entangling bipartite gate V are universal. Previously this was known only when access to both V and V^{-1} was given,…
Superpolynomial speedups based on almost any quantum circuit
Sean Hallgren, Aram W. Harrow
The first separation between quantum polynomial time and classical bounded-error polynomial time was due to Bernstein and Vazirani in 1993. They first showed a O(1) vs. Omega(n) qu…
Classical and Quantum Tensor Product Expanders
M. B. Hastings, A. W. Harrow
We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the…
A communication-efficient nonlocal measurement with application to communication complexity and bipartite gate capacities
Aram W. Harrow, Debbie W. Leung
Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We…