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Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theorys inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future.
Quantum neuromorphic computing physically implements neural networks in brain-inspired quantum hardware to speed up their computation. In this perspective article, we show that this emerging paradigm could make the best use of the existing and near f
The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental importance. Capacities of classical channels are computed using alternating
There are two schools of measurement-only quantum computation. The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an entanglement patter
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary operation
This is a set of lecture notes suitable for a Masters course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years