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We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission…

Quantum Physics · Physics 2007-05-23 Simon Gay , Rajagopal Nagarajan , Nikolaos Papanikolaou

In this paper we propose a tokenization algorithm of Reversible Hybrid type, as defined in PCI DSS guidelines for designing a tokenization solution, based on a block cipher with a secret key and (possibly public) additional input. We…

Cryptography and Security · Computer Science 2019-04-26 Riccardo Longo , Massimiliano Sala , Riccardo Aragona

Tokenization is the task of chopping it up into pieces, called tokens, perhaps at the same time throwing away certain characters, such as punctuation. A token is an instance of token a sequence of characters in some particular document that…

Information Retrieval · Computer Science 2013-03-05 Ahmad Al Badawi , Qasem Abu Al-Haija

Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum…

Quantum Physics · Physics 2022-01-11 Valeria Saggio , Philip Walther

We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…

Cryptography and Security · Computer Science 2007-05-23 Ilia Toli

Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…

Numerical Analysis · Computer Science 2016-09-19 Saskia Metzler , Pauli Miettinen

We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In…

Algebraic Geometry · Mathematics 2017-02-28 Daniel Perrucci , Marie-Françoise Roy

In order to solve the problem of non-ideal training sets (i.e., the less-complete or over-complete sets) and implement one-iteration learning, a novel efficient quantum perceptron algorithm based on unitary weights is proposed, where the…

Quantum Physics · Physics 2024-05-14 Wenjie Liu , Peipei Gao , Yuxiang Wang , Wenbin Yu , Maojun Zhang

A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…

Quantum Physics · Physics 2007-05-23 Guihua Zeng , Carlos Saavedra , Christoph H. Keitel

In practical systems, reliable communication is often accomplished by coding at different network layers. We question the necessity of this approach and examine when it can be beneficial. Through conceptually simple probabilistic models…

Information Theory · Computer Science 2014-11-18 Michael Heindlmaier , Emina Soljanin

The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…

Numerical Analysis · Computer Science 2018-12-03 Pierre Ablin , Jean-François Cardoso , Alexandre Gramfort

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-04-09 Huamin Li , Yuval Kluger , Mark Tygert

Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…

Quantum Physics · Physics 2011-04-27 Yuichiro Fujiwara , Min-Hsiu Hsieh

A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish…

Machine Learning · Statistics 2016-07-06 Tim Leathart , Bernhard Pfahringer , Eibe Frank

Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how to convert a compression…

Information Theory · Computer Science 2023-02-28 Daniel Severo , James Townsend , Ashish Khisti , Alireza Makhzani , Karen Ullrich

We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed…

Computation and Language · Computer Science 2026-05-28 Craig W. Schmidt , Michael Krumdick , Adam Wiemerslage , Seth Ebner , Varshini Reddy , Yuval Pinter , Chris Tanner

Describes a near-linear-time algorithm for a variant of Huffman coding, in which the letters may have non-uniform lengths (as in Morse code), but with the restriction that each word to be encoded has equal probability. [See also ``Huffman…

Data Structures and Algorithms · Computer Science 2015-06-02 Mordecai Golin , Neal E. Young

Ensemble learning combines multiple classifiers in the hope of obtaining better predictive performance. Empirical studies have shown that ensemble pruning, that is, choosing an appropriate subset of the available classifiers, can lead to…

Byte Pair Encoding (BPE) is a widely used tokenization algorithm, whose tokens cannot extend across pre-tokenization boundaries, functionally limiting it to representing at most full words. The BoundlessBPE and SuperBPE algorithms extend…

Computation and Language · Computer Science 2026-04-08 Craig W. Schmidt , Chris Tanner , Yuval Pinter

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…

Quantum Physics · Physics 2017-02-20 Peter W. Shor