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Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of…
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…
Partition refinement is a method for minimizing automata and transition systems of various types. Recently, a new partition refinement algorithm and associated tool CoPaR were developed that are generic in the transition type of the input…
The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…
We present a set of methods to generate less complex error channels by quantum circuit parallelisation. The resulting errors are simplified as a consequence of their symmetrisation and randomisation. Initially, the case of a single error…
The present thesis deals with various methods of quantum error correction. It is divided into two parts. In the first part, dynamical decoupling methods are considered which have the task of suppressing the influence of residual…
This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…
An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…
We consider a version of Shor's quantum factoring algorithm such that the quantum Fourier transform is replaced by an extremely simple one where decomposition coefficients take only the values of $1,i,-1,-i$. In numerous calculations which…
Based on sketching techniques, we propose two randomized algorithms for tensor ring (TR) decomposition. Specifically, by defining new tensor products and investigating their properties, we apply the Kronecker sub-sampled randomized Fourier…
This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…