Related papers: Span Program for Non-binary Functions

This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…

The quest for effective quantum feature maps for data encoding presents significant challenges, particularly due to the flat training landscapes and lengthy training processes associated with parameterised quantum circuits. To address these…

Being able to identify functions of interest in cross-architecture software is useful whether you are analysing for malware, securing the software supply chain or conducting vulnerability research. Cross-Architecture Binary Code Similarity…

We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts…

Binary code analysis allows analyzing binary code without having access to the corresponding source code. A binary, after disassembly, is expressed in an assembly language. This inspires us to approach binary analysis by leveraging ideas…

Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…

In this brief we investigate the generalization properties of a recently-proposed class of non-parametric activation functions, the kernel activation functions (KAFs). KAFs introduce additional parameters in the learning process in order to…

We study classical query algorithms with post-selection, and find that they are closely connected to rational functions with nonnegative coefficients. We show that the post-selected classical query complexity of a Boolean function is equal…

We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

We prove that all 'gradient span algorithms' have asymptotically deterministic behavior on scaled Gaussian random functions as the dimension tends to infinity. In particular, this result explains the counterintuitive phenomenon that…

In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…

In this paper, we study a class of nonsmooth fractional programs {\rm (FP, for short)} with SOS-convex semi-algebraic functions. Under suitable assumptions, we derive a strong duality result between the problem (FP) and its semidefinite…

We propose a quantum algorithm for training nonlinear support vector machines (SVM) for feature space learning where classical input data is encoded in the amplitudes of quantum states. Based on the classical SVM-perf algorithm of Joachims,…

Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into…

Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…

Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding…

Efficient estimation of nonlinear functions of quantum states is crucial for various key tasks in quantum computing, such as entanglement spectroscopy, fidelity estimation, and feature analysis of quantum data. Conventional methods using…

Consider a Bayesian inference problem where a variable of interest does not take values in a Euclidean space. These "non-standard" data structures are in reality fairly common. They are frequently used in problems involving latent discrete…

In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…