Quantum annealing-based computed tomography using variational approach for a real-number image reconstruction

Objective: Despite recent advancements in quantum computing, the limited number of available qubits has hindered progress in CT reconstruction. This study investigates the feasibility of utilizing quantum annealing-based computed tomography (QACT) with current quantum bit levels. Approach: The QACT algorithm aims to precisely solve quadratic unconstrained binary optimization (QUBO) problems. Furthermore, a novel approach is proposed to reconstruct images by approximating real numbers using the variational method. This approach allows for accurate CT image reconstruction using a small number of qubits. The study examines the impact of projection data quantity and noise on various image sizes ranging from 4x4 to 24x24 pixels. The reconstructed results are compared against conventional reconstruction algorithms, namely maximum likelihood expectation maximization (MLEM) and filtered back projection (FBP). Main result: By employing the variational approach and utilizing two qubits for each pixel of the image, accurate reconstruction was achieved with an adequate number of projections. Under conditions of abundant projections and lower noise levels, the image quality in QACT outperformed that of MLEM and FBP. However, in situations with limited projection data and in the presence of noise, the image quality in QACT was inferior to that in MLEM. Significance: This study developed the QACT reconstruction algorithm using the variational approach for real-number reconstruction. Remarkably, only 2 qubits were required for each pixel representation, demonstrating their sufficiency for accurate reconstruction.Comment: 14 pages, 8 figure

Curve fitting on a quantum annealer for an advanced navigation method

We explore the applicability of quantum annealing to the approximation task of curve fitting. To this end, we consider a function that shall approximate a given set of data points and is written as a finite linear combination of standardized functions, e.g., orthogonal polynomials. Consequently, the decision variables subject to optimization are the coefficients of that expansion. Although this task can be accomplished classically, it can also be formulated as a quadratic unconstrained binary optimization problem, which is suited to be solved with quantum annealing. Given the size of the problem stays below a certain threshold, we find that quantum annealing yields comparable results to the classical solution. Regarding a real-word use case, we discuss the problem to find an optimized speed profile for a vessel using the framework of dynamic programming and outline how the aforementioned approximation task can be put into play.Comment: 12 pages, 5 figures, 4 table

Two quantum Ising algorithms for the shortest-vector problem

Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardized for the postquantum era, and a significant proportion of these rely on the hardness of problems like the shortest-vector problem to a quantum adversary. In this paper we describe two variants of a quantum Ising algorithm to solve this problem. One variant is spatially efficient, requiring only O ( N log 2 N ) qubits, where N is the lattice dimension, while the other variant is more robust to noise. Analysis of the algorithms' performance on a quantum annealer and in numerical simulations shows that the more qubit-efficient variant will outperform in the long run, while the other variant is more suitable for near-term implementation

Algoritmos cuánticos y Quantum Ant Colony Optimization

[EN] I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization. Quantum computation is on the verge of becoming the new technology for solving time- and energy-consuming problems. To make use of the full potential of quantum computers one must implement algorithms that are significantly different from the ones used on digital computers. This work serves as an introduction to both quantum computing and algorithms. Starting from the basis of the quantum physics, I expose each of the steps needed to understand the mathematics beneath this topic. Using this basis, I develope one quantum algorithm from scratch. Based on a previously proposed Quantum Ant Colony Optimization (QACO) algorithm, I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization.[ES] La computación cuántica está a punto de convertirse en la nueva tecnología para resolver problemas de tiempo y consumo de energía. Para hacer uso del potencial completo de las computadoras cuánticas uno debe implementar algoritmos que son significativamente diferentes de los utilizados en las computadoras digitales. Este trabajo sirve como introducción a la computación cuántica y algoritmos. A partir de la base de la física cuántica, expongo cada uno de los pasos necesarios para entender las matemáticas bajo este tema. Usando esta base, desarrollo un algoritmo cuántico desde cero. Basado en un algoritmo previamente propuesto de Optimización de Colonias de Hormigas Cuánticas (QACO), propongo un algoritmo mejorado que se puede implementar en un ordenador cuántico real con una nueva estrategia de exploración guiada. Los puntos de referencia realizados al simular el circuito cuántico muestran que el tiempo para resolver un problema utilizando QACO podría superar en gran medida otros algoritmos bioinspirados clásicos, en particular el QACO se basa en la Ant Colony Optimization

Algoritmos cuánticos y Quantum Ant Colony Optimization

[EN] I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization. Quantum computation is on the verge of becoming the new technology for solving time- and energy-consuming problems. To make use of the full potential of quantum computers one must implement algorithms that are significantly different from the ones used on digital computers. This work serves as an introduction to both quantum computing and algorithms. Starting from the basis of the quantum physics, I expose each of the steps needed to understand the mathematics beneath this topic. Using this basis, I develope one quantum algorithm from scratch. Based on a previously proposed Quantum Ant Colony Optimization (QACO) algorithm, I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization.[ES] La computación cuántica está a punto de convertirse en la nueva tecnología para resolver problemas de tiempo y consumo de energía. Para hacer uso del potencial completo de las computadoras cuánticas uno debe implementar algoritmos que son significativamente diferentes de los utilizados en las computadoras digitales. Este trabajo sirve como introducción a la computación cuántica y algoritmos. A partir de la base de la física cuántica, expongo cada uno de los pasos necesarios para entender las matemáticas bajo este tema. Usando esta base, desarrollo un algoritmo cuántico desde cero. Basado en un algoritmo previamente propuesto de Optimización de Colonias de Hormigas Cuánticas (QACO), propongo un algoritmo mejorado que se puede implementar en un ordenador cuántico real con una nueva estrategia de exploración guiada. Los puntos de referencia realizados al simular el circuito cuántico muestran que el tiempo para resolver un problema utilizando QACO podría superar en gran medida otros algoritmos bioinspirados clásicos, en particular el QACO se basa en la Ant Colony Optimization

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma