Quantum search algorithms, quantum wireless, and a low-complexity maximum likelihood iterative quantum multi-user detector design

The high complexity of numerous optimal classic communication schemes, such as the maximum likelihood (ML) multiuser detector (MUD), often prevents their practical implementation. In this paper, we present an extensive review and tutorial on quantum search algorithms (QSA) and their potential applications, and we employ a QSA that finds the minimum of a function in order to perform optimal hard MUD with a quadratic reduction in the computational complexity when compared to that of the ML MUD. Furthermore, we follow a quantum approach to achieve the same performance as the optimal soft-input soft-output classic detectors by replacing them with a quantum algorithm, which estimates the weighted sum of a function’s evaluations. We propose a soft-input soft-output quantum-assisted MUD (QMUD) scheme, which is the quantum-domain equivalent of the ML MUD. We then demonstrate its application using the design example of a direct-sequence code division multiple access system employing bit-interleaved coded modulation relying on iterative decoding, and compare it with the optimal ML MUD in terms of its performance and complexity. Both our extrinsic information transfer charts and bit error ratio curves show that the performance of the proposed QMUD and that of the optimal classic MUD are equivalent, but the QMUD’s computational complexity is significantly lower

Simulación clásica de un algoritmo cuántico

Classical computing there are multiple algorithms to efficiently locate a certain element within a disorganized database; however, quantum computing can be applied more assertively in the face of problems in which it is complicated to verify a solution and at the same time to test multiple and possible solutions. Therefore, this article presents an introduction to Quantum Computing, developing some concepts of quantum formalism, and then approach Grover's algorithm which exploits the principle of superposition to the maximum. Finally, a classic simulation of this algorithm is performed, and the results obtained are compared with classical algorithms such as sequential search and binary search method. A 95% is obtained as a result of greater effectiveness in times -when solving the same search-, revealing the potential advantages of quantum computing.En la computación clásica existen múltiples algoritmos para localizar de manera eficiente un determinado elemento dentro de una base de datos desorganizada; sin embargo, la computación cuántica puede aplicarse de manera más asertiva frente a tales problemas cuando es complejo verificar una solución y a la vez probar múltiples y posibles soluciones. Por lo anterior, en este artículo se presenta una introducción a la Computación Cuántica -desarrollando algunos conceptos del formalismo cuántico-, y luego se aborda el algoritmo de Grover el cual explota al máximo el principio de superposición. Finalmente se realiza una simulación clásica de dicho algoritmo, y los resultados obtenidos se comparan con otros algoritmos clásicos como el método de búsqueda lineal y búsqueda binaria. Se obtiene como resultado un %95 de mayor efectividad en tiempos -a la hora de resolver la misma búsqueda- logrando poner de manifiesto las ventajas potenciales de la computación cuántica

Zero and Low Energy Thresholds in Quantum Simulation

Quantum simulation is the process of simulating a quantum mechanical system using either a quantum or a classical computer. Because quantum mechanical systems contain a large number of entangled particles, they are hard to simulate on a classical computer. It is the task of computational complexity theorists to estimate the amount of resources to do the same number of operations on either classical or quantum devices. This report first summarizes the state of the art in the field of quantum computing, and gives an example of a model of quantum computer and examples of quantum algorithms that are currently being researched. Then our own research about k-local quantum Hamiltonians is discussed. We developed programs to determine if a particular kind of k-local Hamiltonian has zero-energy solutions. First, to familiarize ourselves with quantum algorithms, we implemented a recently discovered polynomial-time 2-QSAT algorithm called SolveQ. Then we wrote several versions of brute force 7-variable 3-QSAT solvers and conducted experiments for the threshold of satisfiability. We empirically determined that the thresholds for the four versions, Versions 3, 4, 5, and 6, are 0.741, 1.714, 1.714, and 0.571, respectively. In addition, experiments were conducted involving the 6-qubit Ising model, working on which caused us to realize how inefficient the classical computer really is at simulating quantum mechanical systems. Our conclusion is that quantum simulation is much less feasible than classical simulation on a classical computer

Low-gate Quantum Golden Collision Finding

International audienceThe golden collision problem asks us to find a single, special collision among the outputs of a pseudorandom function. This generalizes meet-in-the-middle problems, and is thus applicable in many contexts, such as cryptanalysis of the NIST post-quantum candidate SIKE. The main quantum algorithms for this problem are memory-intensive, and the costs of quantum memory may be very high. The quantum circuit model implies a linear cost for random access, which annihilates the exponential advantage of the previous quantum collision-finding algorithms over Grover's algorithm or classical van Oorschot-Wiener. Assuming that quantum memory is costly to access but free to maintain, we provide new quantum algorithms for the golden collision problem with high memory requirements but low gate costs. Under the assumption of a two-dimensional connectivity layout, we provide better quantum parallelization methods for generic and golden collision finding. This lowers the quantum security of the golden collision and meet-in-the-middle problems, including SIKE

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD

Towards a table top quantum computer

Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 1999.Includes bibliographical references (leaves 135-139).In the early 1990s, quantum computing proved to be an enticing theoretical possibility but a extremely difficult experimental challenge. Two advances have made experimental quantum computing demonstrable: Quantum error correction; and bulk, thermal quantum computing using nuclear magnetic resonance (NMR). Simple algorithms have been implemented on large, commercial NMR spectrometers that are expensive and cumbersome. The goal of this project is to construct a table-top quantum computer that can match and eventually exceed the performance of commercial machines. This computer should be an inexpensive, easy-to-use machine that can be considered more a computer than its "supercomputer" counterparts. For this thesis, the goal is to develop a low-cost, table-top quantum computer capable of implementing simple quantum algorithms demonstrated thus far in the community, but is also amenable to the many scaling issues of practical quantum computing. Understanding these scaling issues requires developing a theoretical understanding of the signal enhancement techniques and fundamental noise sources of this powerful but delicate system. Complementary to quantum computing, this high performance but low cost NMR machine will be useful for a number of medical, low cost sensing and tagging applications due the unique properties of NMR: the ability to sense and manipulate the information content of materials on macroscopic and microscopic scales.Yael G. Maguire.S.M