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Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems,…
A quantum computer has now solved a specialized problem believed to be intractable for supercomputers, suggesting that quantum processors may soon outperform supercomputers on scientifically important problems. But flaws in each quantum…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
Near term quantum computers suffer from the presence of different noise sources. In order to mitigate for this effect and acquire results with significantly better accuracy, there is the urge of designing efficient error correction or error…
Noise dominates every aspect of near-term quantum computers, rendering it exceedingly difficult to carry out even small computations. In this paper we are concerned with the modelling of noise in Noisy Intermediate-Scale Quantum (NISQ)…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid…
This article focuses on the connection between the possibility of quantum computers, the predictability of complex quantum systems in nature, and the issue of free will.
Quantum computers are becoming real, and they have the inherent potential to significantly impact many application domains. We sketch the basics about programming quantum computers, showing that quantum programs are typically hybrid…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
Quantum computers have now appeared in our society and are utilized for the investigation of science and engineering. At present, they have been built as intermediate-size computers containing about fifty qubits and are weak against noise…
Quantum memory systems are vital in quantum information processing for dependable storage and retrieval of quantum states. Inspired by classical reliability theories that synthesize reliable computing systems from unreliable components, we…
Quantum computing promises to help humanity solve problems that would otherwise be intractable on classical computers. Unlike today's machines, quantum computers use a novel computing process that leverages the foundational quantum…
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quantum computation. We consider stochastic models of quantum computation on $n$ qubits subject to noise…
Current experiments are taking the first steps toward noise-resilient logical qubits. Crucially, a quantum computer must not merely store information, but also process it. A fault-tolerant computational procedure ensures that errors do not…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…