相关论文: A New Algorithm for Computing Branch Number of Non…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference. This work introduces a segmentation-based regression method tailored to quantum neural networks…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…
This note describes a technique for generating large non-singular matrices with blocks of full rank. Our motivation to construct such matrices arises in the white-box implementation of cryptographic algorithms with S-boxes.
We introduce a general framework to construct multi-emission kernels for parton branching algorithms at the amplitude level and across different soft and collinear limits. We highlight the connection of kinematic parameterizations and…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
Differential cryptanalysis is one of the most popular methods in attacking block ciphers. However, there still some limitations in traditional differential cryptanalysis. On the other hand, researches of quantum algorithms have made great…
It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
The paper proposes a numerically stable recursive algorithm for the exact computation of the linear-chain conditional random field gradient. It operates as a forward algorithm over the log-domain expectation semiring and has the purpose of…
We consider the problem of interpolating a sparse multivariate polynomial over a finite field, represented with a black box. Building on the algorithm of Ben-Or and Tiwari for interpolating polynomials over rings with characteristic zero,…
With the tremendous benefits of internet and advanced communications, there is a serious threat from the data security perspective. There is a need of secure and robust encryption algorithm that can be implemented on each and diverse…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
Mathematically constructed S-boxes arise from algebraic structures and finite field theory to ensure strong, provable cryptographic properties. These mathematically grounded constructions allow for generation of thousands of S-Boxes with…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
In this paper, we propose two new interpolation algorithms for sparse multivariate polynomials represented by a straight-line program(SLP). Both of our algorithms work over any finite fields $F_q$ with large characteristic. The first one is…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…