Related papers: Towards a practical, theoretically sound algorithm…
We introduce a new constructive recognition algorithm for finite special linear groups in their natural representation. Given a group $G$ generated by a set of $d\times d$ matrices over a finite field $\mathbb{F}_q$, known to be isomorphic…
We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its…
Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in…
Quantum random number generator harnesses the power of quantum mechanics to generate true random numbers, making it valuable for various scientific applications. However, real-world devices often suffer from imperfections that can undermine…
We consider the minimal k-grouping problem: given a graph G=(V,E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent…
The accurate and efficient energy estimation of quantum Hamiltonians consisting of Pauli observables is an essential task in modern quantum computing. We introduce a Resource-Optimized Grouping Shadow (ROGS) algorithm, which optimally…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
This note deals with the computation of the factorization number $F_2(G)$ of a finite group $G$. By using the M\"{o}bius inversion formula, explicit expressions of $F_2(G)$ are obtained for two classes of finite abelian groups, improving…
Quantum random number generation exploits inherent randomness of quantum mechanical processes and measurements. Real-time generation rate of quantum random numbers is usually limited by electronic bandwidth and data processing rates. Here…
We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the n^(log_p n + O(1)) generator-enumeration algorithm. In previous work…
Quantum many-body systems provide a unique platform for exploring the rich interplay between chaos, randomness, and complexity. In a recently proposed paradigm known as deep thermalization, random quantum states of system A are generated by…
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
We present a random number generation scheme based on measuring the phase fluctuations of a laser with a simple and compact experimental setup. A simple model is established to analyze the randomness and the simulation result based on this…
We present a random number generation scheme that uses broadband measurements of the vacuum field contained in the radio-frequency sidebands of a single-mode laser. Even though the measurements may contain technical noise, we show that…
Meta-Black-Box Optimization (MetaBBO) garners attention due to its success in automating the configuration and generation of black-box optimizers, significantly reducing the human effort required for optimizer design and discovering…
Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…
We prove that $d(G) \log |G| = O(n^2 \log q)$ for irreducible subgroups $G$ of GL$(n,q)$, and estimate the associated constants. The result is motivated by attempts to bound the complexity of computing the automorphism groups of various…
Brakerski et. al [BCM+18] introduced the model of cryptographic testing of a single untrusted quantum device and gave a protocol for certifiable randomness generation. We use the leakage resilience properties of the Learning With Errors…
Let $p ,r $ and $n $ be positive integers. Then the O-Fibonacci $(p,r)$-cube $O\Gamma^{(p,r)}_{n}$ is the subgraph of $Q_{n}$ induced on the binary words in which there is at least $p-1$ zeros between any two $1$s and there is at most $r$…
Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with…