6 papers · 1 filter
A quantum algorithm to solve nonlinear differential equations
Sarah K. Leyton, Tobias J. Osborne
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic a…
Unifying variational methods for simulating quantum many-body systems
Christopher M. Dawson, Jens Eisert, Tobias J. Osborne
We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over qu…
Approximate locality for quantum systems on graphs
Tobias J. Osborne
In this Letter we make progress on a longstanding open problem of Aaronson and Ambainis [Theory of Computing 1, 47 (2005)]: we show that if A is the adjacency matrix of a sufficien…
A Finite de Finetti Theorem for Infinite-Dimensional Systems
Christian D'Cruz, Tobias J. Osborne, Ruediger Schack
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is vali…
The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
Tobias J. Osborne
We study families H_n of 1D quantum spin systems, where n is the number of spins, which have a spectral gap ΔE between the ground-state and first-excited state energy that scales,…
General entanglement scaling laws from time evolution
Jens Eisert, Tobias J. Osborne
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy…