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- Anargyros Papageorgiou, Iasonas Petras
- J. Complexity
- 2009

It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem to be weakly tractable in the worst case. The complexity of linear tensor product problems in the worst case depends on the eigenvalues {λ i } i∈N of a certain operator. It is known that if λ 1 = 1 and λ 2 ∈ (0, 1) then λ n = o((ln n) −2), as n →… (More)

The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error ε. We assume we are given a superposition of function… (More)

- Anargyros Papageorgiou, Iasonas Petras, Joseph F. Traub, Chi Zhang
- Math. Comput.
- 2013

Estimating the ground state energy of a multiparticle system with relative error ε using deterministic classical algorithms has cost that grows exponentially with the number of particles. The problem depends on a number of state variables d that is proportional to the number of particles and suffers from the curse of dimensionality. Quantum computers can… (More)

- Anargyros Papageorgiou, Iasonas Petras
- J. Complexity
- 2014

- Anargyros Papageorgiou, Iasonas Petras
- J. Complexity
- 2011

It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem S = {S d } in the average case setting to be weakly tractable but not polynomially tractable. As a result of the tensor product structure , the eigenvalues of the covariance operator of the induced measure in the one dimensional problem… (More)

- Mihir K. Bhaskar, Stuart Hadfield, Anargyros Papageorgiou, Iasonas Petras
- Quantum Information & Computation
- 2016

Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly scalable and reversible (unitary), and that can be implemented efficiently. We present quantum algorithms and circuits for… (More)

- Anargyros Papageorgiou, Iasonas Petras
- J. Complexity
- 2014

In 2011, the fundamental gap conjecture for Schrödinger operators was proven. This can be used to estimate the ground state energy of the time-independent Schrödinger equation with a convex potential and relative error ε. Classical deterministic algorithms solving this problem have cost exponential in the number of its degrees of freedom d. We show a… (More)

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