9,980 research outputs found
A Quantum Interior Point Method for LPs and SDPs
We present a quantum interior point method with worst case running time
for
SDPs and for LPs, where the output of our algorithm is a pair of matrices
that are -optimal -approximate SDP solutions. The factor
is at most for SDPs and for LP's, and is
an upper bound on the condition number of the intermediate solution matrices.
For the case where the intermediate matrices for the interior point method are
well conditioned, our method provides a polynomial speedup over the best known
classical SDP solvers and interior point based LP solvers, which have a worst
case running time of and respectively. Our results
build upon recently developed techniques for quantum linear algebra and pave
the way for the development of quantum algorithms for a variety of applications
in optimization and machine learning.Comment: 32 page
State estimation in quantum homodyne tomography with noisy data
In the framework of noisy quantum homodyne tomography with efficiency
parameter , we propose two estimators of a quantum state whose
density matrix elements decrease like , for
fixed known and . The first procedure estimates the matrix
coefficients by a projection method on the pattern functions (that we introduce
here for ), the second procedure is a kernel estimator of the
associated Wigner function. We compute the convergence rates of these
estimators, in risk
Choice of Measurement Sets in Qubit Tomography
Optimal generalized measurements for state estimation are well understood.
However, practical quantum state tomography is typically performed using a
fixed set of projective measurements and the question of how to choose these
measurements has been largely unexplored in the literature. In this work we
develop theoretical asymptotic bounds for the average fidelity of pure qubit
tomography using measurement sets whose axes correspond to vertices of Platonic
solids. We also present complete simulations of maximum likelihood tomography
for mixed qubit states using the Platonic solid measurements. We show that
overcomplete measurement sets can be used to improve the accuracy of
tomographic reconstructions.Comment: 13 Pages, 6 figure
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