While modern computers are fast, there are still many important practical situations in which we need even faster computations. It turns out that, due to the fact that the speed of all communications is limited by the speed of light, the only way to make computers drastically faster is to drastically decrease the size of computer’s components. When we decrease their size to sizes comparable with micro-sizes of individual molecules, it becomes necessary to take into account specific physics of the micro-world – known as quantum physics. Traditional approach to designing quantum computers – i.e., computers that take effect of quantum physics into account – was based on using quantum analogies of bits (2-state systems). However, it has recently been shown that the use of multi-state quantum systems – called qudits – can make quantum computers even more efficient. When processing data, it is important to take into account that in practice, data always comes with uncertainty. In this paper, we analyze how to represent different types of uncertainty by qudits.
While modern computers are fast, there are still many important practical situations in which we need even faster computations. It turns out that, due to the fact that the speed of all communications is limited by the speed of light, the only way to make computers drastically faster is to drastically decrease the size of computer’s components. When we decrease their size to sizes comparable with micro-sizes of individual molecules, it becomes necessary to take into account specific physics of the micro-world – known as quantum physics. Traditional approach to designing quantum computers – i.e., computers that take effect of quantum physics into account – was based on using quantum analogies of bits (2-state systems). However, it has recently been shown that the use of multi-state quantum systems – called qudits – can make quantum computers even more efficient. When processing data, it is important to take into account that in practice, data always comes with uncertainty. In this paper, we analyze how to represent different types of uncertainty by qudits.
Quantum computation is going to revolutionize the world of computing by enabling the design of massive parallel algorithms that solve hard problems in an efficient way, thanks to the exploitation of quantum mechanics effects, such as superposition, entanglement, and interference. These computational improvements could strongly influence the way how fuzzy systems are designed and used in contexts, such as Big Data, where computational efficiency represents a nonnegligible constraint to be taken into account. In order to pave the way toward this innovative scenario, this article introduces a novel representation of fuzzy sets and operators based on quadratic unconstrained binary optimization problems, so as to enable the implementation of fuzzy inference engines on a type of quantum computers known as quantum annealers.
In many practical problems, the computation speed of modern computers is not sufficient. Due to the fact that all speeds are bounded by the speed of light, the only way to speed up computations is to further decrease the size of the memory and processing cells that form a computational device. At the resulting size level, each cell will consist of a few atoms -- thus, we need to take quantum effects into account. For traditional computational devices, quantum effects are largely a distracting noise, but new quantum computing algorithms have been developed that use quantum effects to speed up computations. In some problems, however, this expected speed-up may not be sufficient. To achieve further speed-up, we need to parallelize quantum computing. For this, we need to be able to transmit a quantum state from the location of one processor to the location of another one; in quantum computing, this process is known as teleportation. A teleportation algorithm is known, but it is not clear how efficient it is: maybe there are other more efficient algorithms for teleportation? In this paper, we show that the existing teleportation algorithm is, in some reasonable sense, unique -- and thus, optimal.
Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem which may be tackled using quantum computing, it is imperative to represent the data used onto a quantum computing system. Depending on the application, many different types of data and data structures occur, including regular numbers, higher-dimensional data structures, e.g., n-dimensional images, up to graphs. This report aims to provide an overview of existing methods for representing these data types on gate-based quantum computers.
In 1959, Nobelist Richard Feynman gave a talk titled “There’s plenty of room at the bottom”, in which he emphasized that, to drastically speed up computations, we need to make computer components much smaller – all the way to the size of molecules, atoms, and even elementary particles. At this level, physics is no longer described by deterministic Newton’s mechanics, it is described by probabilistic quantum laws. Because of this, computer designers started thinking about how to design a reliable computer based on non-deterministic elements – and this thinking eventually led to the modern ideas and algorithms of quantum computing. So, we have a straight path of speeding up computations: by learning how to use molecules, atoms, and then elementary particles as building blocks of a computational device. But what if we reach the size of an elementary particle? At first glance, it may seem that we will then reach an absolute limit of how fast a computer can be. However, as we show in this paper, we can potentially speed up computations even further – by using the internal structure of elementary particles, e.g., the fact that protons and neutrons consist of quarks. Interestingly, the corresponding mathematics is very similar to what is called color optical computing – the use of light of different colors in computations.