Related papers: Quantum hashing based on symmetric groups

Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…

Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an…

Fully homomorphic encryption (FHE) enables an entity to perform arbitrary computation on encrypted data without decrypting the ciphertexts. An ongoing group-theoretical approach to construct an FHE scheme uses a certain "compression"…

The most general examples of quantum learning advantages involve data labeled by cryptographic or intrinsically quantum functions, where classical learners are limited by the infeasibility of evaluating the labeling functions using…

The idea of using a sequence of finite dimensional algebras to approach a quantum linear group (i.e., a quantum $\mathfrak{gl}_n$) was first introduced by Beilinson-Lusztig-MacPherson [BLM]. In their work, the algebras are convolution…

We give a construction of public key quantum money, and even a strengthened version called quantum lightning, from abelian group actions, which can in turn be constructed from suitable isogenies over elliptic curves. We prove security in…

A generic approach for compiling any classical block compression algorithm into a quantum block compression algorithm is presented. Using this technique, compression asymptoticaly approaching the von Neumann entropy of a qubit source can be…

A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…

Quantum computing enables quantum neural networks (QNNs) to have great potentials to surpass artificial neural networks (ANNs). The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various…

Hashing has been widely used for efficient similarity search based on its query and storage efficiency. To obtain better precision, most studies focus on designing different objective functions with different constraints or penalty terms…

A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.

In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…

A general class of authentication schemes for arbitrary quantum messages is proposed. The class is based on the use of sets of unitary quantum operations in both transmission and reception, and on appending a quantum tag to the quantum…

Many qubit implementations are afflicted by correlated noise not captured by standard theoretical tools that are based on Markov approximations. While independent gate operations are a key concept for quantum computing, it is actually not…

Hard Attention Mechanisms (HAMs) effectively filter essential information discretely and significantly boost the performance of machine learning models on large datasets. Nevertheless, they confront the challenge of non-differentiability,…

Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this…

Starting from the one-way group action framework of Brassard and Yung (Crypto '90), we revisit building cryptography based on group actions. Several previous candidates for one-way group actions no longer stand, due to progress both on…

Quantum computing poses fundamental risks to classical blockchain systems by undermining widely used cryptographic primitives. In response, two major research directions have emerged: post-quantum blockchains, which integrate…

We propose to analyse quantum protocols by applying formal verification techniques developed in classical computing for the analysis of communicating concurrent systems. One area of successful application of these techniques is that of…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…