105 research outputs found
Direct Fidelity Estimation from Few Pauli Measurements
We describe a simple method for certifying that an experimental device prepares a desired quantum state ρ. Our method is applicable to any pure state ρ, and it provides an estimate of the fidelity between ρ and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of d, the dimension of the state space, and extends easily and naturally to quantum channels
The Optical Frequency Comb as a One-Way Quantum Computer
In the one-way model of quantum computing, quantum algorithms are implemented
using only measurements on an entangled initial state. Much of the hard work is
done up-front when creating this universal resource, known as a cluster state,
on which the measurements are made. Here we detail a new proposal for a
scalable method of creating cluster states using only a single multimode
optical parametric oscillator (OPO). The method generates a continuous-variable
cluster state that is universal for quantum computation and encoded in the
quadratures of the optical frequency comb of the OPO. This work expands on the
presentation in Phys. Rev. Lett. 101, 130501 (2008).Comment: 20 pages, 8 figures. v2 corrects minor error in published versio
Detecting Topological Order with Ribbon Operators
We introduce a numerical method for identifying topological order in
two-dimensional models based on one-dimensional bulk operators. The idea is to
identify approximate symmetries supported on thin strips through the bulk that
behave as string operators associated to an anyon model. We can express these
ribbon operators in matrix product form and define a cost function that allows
us to efficiently optimize over this ansatz class. We test this method on spin
models with abelian topological order by finding ribbon operators for
quantum double models with local fields and Ising-like terms. In
addition, we identify ribbons in the abelian phase of Kitaev's honeycomb model
which serve as the logical operators of the encoded qubit for the quantum
error-correcting code. We further identify the topologically encoded qubit in
the quantum compass model, and show that despite this qubit, the model does not
support topological order. Finally, we discuss how the method supports
generalizations for detecting nonabelian topological order.Comment: 15 pages, 8 figures, comments welcom
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