Teaching Quantum Computing to High-School-Aged Youth: A Hands-On Approach

Quantum computing is aninterdisciplinary field that lies at the intersection of mathematics, quantum physics, and computer science, and finds applications in areas including optimization, machine learning, and simulation of chemical, physical, and biological systems. It has the potential to help solve problems that so far have no satisfying method solving them, and to provide significant […]

Pricing Multi-Asset Derivatives by Finite-Difference Method on a Quantum Computer

Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this article, we focus on derivative pricing based on solving the Black–Scholes partial differential equation by the finite-difference method (FDM), which is a suitable approach for some types of derivatives but suffers from the […]

Hash Function Based on Controlled Alternate Quantum Walks With Memory (September 2021)

We propose a Quantum inspired Hash Function using controlled alternate quantum walks with Memory on cycles (QHFM), where the j th message bit decides whether to run quantum walk with one-step memory or to run quantum walk with two-step memory at the j th time step, and the hash value is calculated from the resulting probability distribution of the […]

Quantum Radon Transforms and Their Applications

This article extends the Radon transform, a classical image-processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called the quantum periodic discrete Radon transform (QPRT), is proposed. The quantum implementation of QPRT based on the amplitude encoding method is exponentially faster than the […]

Efficient Construction of a Control Modular Adder on a Carry-Lookahead Adder Using Relative-Phase Toffoli Gates

Control modular addition is a core arithmetic function, and we must consider the computational cost for actual quantum computers to realize efficient implementation. To achieve a low computational cost in a control modular adder, we focus on minimizingKQ (where K is the number of logical qubits required by the algorithm, and Q is the elementary […]

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 […]

Grover on KATAN: Quantum Resource Estimation

This article presents the cost analysis of mounting Grover’s key search attack on the family of KATAN block cipher. Several designs of the reversible quantum circuit of KATAN are proposed. Owing to the National Insitute of Standards and Technology’s (NIST) proposal for postquantum cryptography standardization, the circuits are designed focusing on minimizing the overall depth. […]

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 […]

Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this article, inspired by the variational quantum eigensolver (VQE), we propose an iterative layer VQE (L-VQE) approach. We present a large-scale numerical study, simulating circuits with […]