7,285 research outputs found
Iterative maximum-likelihood reconstruction in quantum homodyne tomography
I propose an iterative expectation maximization algorithm for reconstructing
a quantum optical ensemble from a set of balanced homodyne measurements
performed on an optical state. The algorithm applies directly to the acquired
data, bypassing the intermediate step of calculating marginal distributions.
The advantages of the new method are made manifest by comparing it with the
traditional inverse Radon transformation technique
Iterative algorithm for reconstruction of entangled states
An iterative algorithm for the reconstruction of an unknown quantum state
from the results of incompatible measurements is proposed. It consists of
Expectation-Maximization step followed by a unitary transformation of the
eigenbasis of the density matrix. The procedure has been applied to the
reconstruction of the entangled pair of photons.Comment: 4 pages, no figures, some formulations changed, a minor mistake
correcte
Online quantum mixture regression for trajectory learning by demonstration
In this work, we present the online Quantum Mixture Model (oQMM), which combines the merits of quantum mechanics and stochastic optimization. More specifically it allows for quantum effects on the mixture states, which in turn become a superposition of conventional mixture states. We propose an efficient stochastic online learning algorithm based on the online Expectation Maximization (EM), as well as a generation and decay scheme for model components. Our method is suitable for complex robotic applications, where data is abundant or where we wish to iteratively refine our model and conduct predictions during the course of learning. With a synthetic example, we show that the algorithm can achieve higher numerical stability. We also empirically demonstrate the efficacy of our method in well-known regression benchmark datasets. Under a trajectory Learning by Demonstration setting we employ a multi-shot learning application in joint angle space, where we observe higher quality of learning and reproduction. We compare against popular and well-established methods, widely adopted across the robotics community
Efficient Computation of the Quantum Rate-Distortion Function
The quantum rate-distortion function plays a fundamental role in quantum
information theory, however there is currently no practical algorithm which can
efficiently compute this function to high accuracy for moderate channel
dimensions. In this paper, we show how symmetry reduction can significantly
simplify common instances of the entanglement-assisted quantum rate-distortion
problems. This allows for more efficient computation regardless of the
numerical algorithm being used, and provides insight into the quantum channels
which obtain the optimal rate-distortion tradeoff. Additionally, we propose an
inexact variant of the mirror descent algorithm to compute the quantum
rate-distortion function with provable sublinear convergence rates. We show how
this mirror descent algorithm is related to Blahut-Arimoto and
expectation-maximization methods previously used to solve similar problems in
information theory. Using these techniques, we present the first numerical
experiments to compute a multi-qubit quantum rate-distortion function, and show
that our proposed algorithm solves faster and to higher accuracy when compared
to existing methods.Comment: 37 pages, 2 figures, 2 tables. v2: Minor edits to introduction,
abstract, and notatio
Diluted maximum-likelihood algorithm for quantum tomography
We propose a refined iterative likelihood-maximization algorithm for
reconstructing a quantum state from a set of tomographic measurements. The
algorithm is characterized by a very high convergence rate and features a
simple adaptive procedure that ensures likelihood increase in every iteration
and convergence to the maximum-likelihood state.
We apply the algorithm to homodyne tomography of optical states and quantum
tomography of entangled spin states of trapped ions and investigate its
convergence properties.Comment: v2: Convergence proof adde
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