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Register a new userDissipative evolution of covariance matrix beyond quadratic order
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The covariance matrix contains the complete information about the second-order expectation values of the mode quadratures (position and momentum operators) of the system. Due to its prominence in studies of continuous variable systems, most significantly Gaussian states, special emphasis is put on time evolution models that result in self-contained equations for the covariance matrix. So far, despite not being explicitly implied by this requirement, virtually all such models assume a so-called quadratic, or second-order case, in which the generator of the evolution is at most second-order in the mode quadratures. Here, we provide an explicit model of covariance matrix evolution of infinite order. Furthermore, we derive the solution, including stationary states, for a large subclass of proposed evolutions. Our findings challenge the contemporary understanding of covariance matrix dynamics and may give rise to new methods and improvements in quantum technologies employing continuous variable systems.
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Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant, and are designed such that some subset of the observer and plants expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; Here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer, and find there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement; As they provide estimation of a systems quantum state without explicit use of the measurement postulate in their derivation.
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Evolution-based neural architecture search requires high computational resources, resulting in long search time. In this work, we propose a framework of applying the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to the neural architecture search problem called CMANAS, which achieves better results than previous evolution-based methods while reducing the search time significantly. The architectures are modelled using a normal distribution, which is updated using CMA-ES based on the fitness of the sampled population. We used the accuracy of a trained one shot model (OSM) on the validation data as a prediction of the fitness of an individual architecture to reduce the search time. We also used an architecture-fitness table (AF table) for keeping record of the already evaluated architecture, thus further reducing the search time. CMANAS finished the architecture search on CIFAR-10 with the top-1 test accuracy of 97.44% in 0.45 GPU day and on CIFAR-100 with the top-1 test accuracy of 83.24% for 0.6 GPU day on a single GPU. The top architectures from the searches on CIFAR-10 and CIFAR-100 were then transferred to ImageNet, achieving the top-5 accuracy of 92.6% and 92.1%, respectively.
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