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We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of…
Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…
We solve the ground state of the deuteron using a variational neural network ansatz for the wave function in momentum space. This ansatz provides a flexible representation of both the $S$ and the $D$ states, with relative errors in the…
To accelerate and compress deep neural networks (DNNs), many network quantization algorithms have been proposed. Although the quantization strategy of any algorithm from the state-of-the-arts may outperform others in some network…
The Quantizer problem is a tessellation optimisation problem where point configurations are identified such that the Voronoi cells minimise the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost…
Vector quantization(VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution presents a theoretical foundation of…
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational…
Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. It is usually formulated as a constrained optimization problem and optimized…
Deep neural networks (DNNs) are quantized for efficient inference on resource-constrained platforms. However, training deep learning models with low-precision weights and activations involves a demanding optimization task, which calls for…
Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate…
The barren plateau phenomenon is one of the main obstacles to implementing variational quantum algorithms in the current generation of quantum processors. Here, we introduce a method capable of avoiding the barren plateau phenomenon in the…
We present an algorithm for boundary approximation in locally-linked sensor networks that communicate with a remote monitoring station. Delaunay triangulations and Voronoi diagrams are used to generate a sensor communication network and…
The inherent noise and complexity of quantum communication networks leads to challenges in designing quantum network protocols using classical methods. To address this issue, we develop a variational quantum optimization framework that…
We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…
Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of…
In this paper, we propose two second-order methods for solving the \(\ell_1\)-regularized composite optimization problem, which are developed based on two distinct definitions of approximate second-order stationary points. We introduce a…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…