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no code implementations • 3 Mar 2021 • Anurag Anshu, Itai Arad, David Gosset

We first establish that the ground state projector of any locally gapped frustration-free 1D spin system can be approximated to within error $\epsilon$ by a degree $O(\sqrt{n\log(\epsilon^{-1})})$ multivariate polynomial in the interaction terms of the Hamiltonian.

Quantum Physics Strongly Correlated Electrons

2 code implementations • 1 Aug 2018 • Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, Mark Howard

The computational cost of such methods is directly related to the notion of stabilizer rank, which for a pure state $\psi$ is defined to be the smallest integer $\chi$ such that $\psi$ is a superposition of $\chi$ stabilizer states.

Quantum Physics

1 code implementation • 27 Jan 2016 • Sergey Bravyi, David Gosset

The main ingredient of both algorithms is a subroutine for approximating the norm of an n-qubit state which is given as a linear combination of $\chi$ stabilizer states.

Quantum Physics

no code implementations • 16 May 2012 • Andrew M. Childs, David Gosset, Zak Webb

A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk.

Quantum Physics

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