Efficient Quantum State Preparation for the Cauchy Distribution Based on Piecewise Arithmetic

The benefits of the quantum Monte Carlo algorithm heavily rely on the efficiency of the superposition state preparation. So far, most reported Monte Carlo algorithms use the Grover–Rudolph state preparation method, which is suitable for efficiently integrable distribution functions. Consequently, most reported works are based on log-concave distributions, such as normal distributions. However, non-log-concave distributions […]

A Low-Complexity Quantum Principal Component Analysis Algorithm

In this article, we propose a low-complexity quantum principal component analysis (qPCA) algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting principal components of the data matrix, rather than all components of the data matrix, to quantum registers, so that the samples of measurement required can be reduced considerably. Both our qPCA […]

A Grover Search-Based Algorithm for the List Coloring Problem

Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for k -coloring of graphs on n vertices has runtimes Ω(2n) for k≥5 . The list coloring problem asks the following more general question: given a list of available colors for each vertex in a graph, does it admit a proper coloring? We propose a hybrid classical-quantum algorithm based […]

EP-PQM: Efficient Parametric Probabilistic Quantum Memory With Fewer Qubits and Gates

Machine learning (ML) classification tasks can be carried out on a quantum computer (QC) using probabilistic quantum memory (PQM) and its extension, parametric PQM (P-PQM), by calculating the Hamming distance between an input pattern and a database of r patterns containing z features with a distinct attributes. For PQM and P-PQM to correctly compute the Hamming distance, the feature must be […]

Finding Solutions to the Integer Case Constraint Satisfiability Problem Using Grover’s Algorithm

Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover’s search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high probability for several cases and are illustrated for the cases involving two variables for both 3- and 4-bit numbers. Methods are defined for […]

Quantum Bloom Filter and Its Applications

A quantum Bloom filter is a spatially more efficient data structure which is used to represent a set of n elements by using O(lognk) qubits. In this article, we define and design a quantum Bloom filter and its corresponding algorithms. Due to the reversibility of quantum operators, it can not only add a new element to a quantum Bloom […]

Quantum Attacks on HCTR and Its Variants

Recently, in Asiacrypt 2019, Bonnetain et al. have shown attacks by quantum adversaries on FX construction and Even-Mansour Cipher without using superposition queries to the encryption oracle. In this article, we use a similar approach to mount new attacks on Hash-Counter (HCTR) and Hash-Counter-Hash (HCH) constructions. In addition, we mount attacks on HCTR, tweakable-HCTR, and […]