Quantum mechanics permits certain kinds of non-local effects. This paper demonstrates how these can be used for distributed computation with minimal communication between various processors. The problem considered is that of estimating the mean of N items to a certain precision. First a serial quantum mechanical algorithm for this is presented that is faster than any classical algorithm. Next it is shown how this can be efficiently parallelized with quantum mechanical processors that are remotely located. These processors consist of coupled EPR particles. Each processor has just to communicate one bit of classical information to a central location at the end of its local computation.
Quantum mechanics permits certain kinds of non-local effects. This paper demonstrates how these can be used for distributed computation with minimal communication between various processors. The problem considered is that of estimating the mean of N items to a certain precision. First a serial quantum mechanical algorithm for this is presented that is faster than any classical algorithm. Next it is shown how this can be efficiently parallelized with quantum mechanical processors that are remotely located. These processors consist of coupled EPR particles. Each processor has just to communicate one bit of classical information to a central location at the end of its local computation.
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 advantage is well-established in centralized computing, where quantum algorithms can solve certain problems exponentially faster than classical ones. In the distributed setting, significant progress has been made in bandwidth-limited networks, where quantum distributed networks have shown computational advantages over classical counterparts. However, the potential of quantum computing in networks that are constrained only by large distances is not yet understood. We focus on the LOCAL model of computation (Linial, FOCS 1987), a distributed computational model where computational power and communication bandwidth are unconstrained, and its quantum generalization. In this brief survey, we summarize recent progress on the quantum-LOCAL model outlining its limitations with respect to its classical counterpart: we discuss emerging techniques, and highlight open research questions that could guide future efforts in the field.
Computers today become faster by becoming smaller. By reducing the size of transistors, engineers are able to fit more of them on a given size microprocessor, thus increasing the processor's computational power. This process cannot continue forever. It has been estimated that sometime within the next two decades, at the current rate, engineers will be faced with the problem of building something that is smaller than an atom. This is as far as our current "classical" computing paradigm will take us. Quantum computing is a potential solution to this problem. This paradigm of computing seeks to directly exploit quantum mechanical phenomena to perform calculations or in some way boost computational efficiency. Some problems can theoretically be solved on a quantum computer exponentially faster than on a classical computer. An overview of the subject is provided here with emphasis on quantum information processing and physical realizations of a quantum computer. Included is a brief history of the subject, a discussion of quantum computing notions such as parallelism and entanglement and their use in quantum algorithms, and conjecture on the prospects and pitfalls of this theory.
Richard Feynman's observation that certain quantum mechanical effects cannot be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used these quantum effects. This speculation proved justified when Peter Shor described a polynomial time quantum algorithm for factoring intergers. In quantum systems, the computational space increases exponentially with the size of the system, which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new nontraditional programming techniques. The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to exploiting the power of quantum parallelism are explained. We conclude with a discussion of quantum error correction.
Summary form only given. Quantum mechanics offers the information scientist a new rich resource, which is only recently being tapped to allow for secure communication in the form of quantum cryptography, and for tremendous parallelism in quantum information processing and computing. I will describe developments and prospects for each. Quantum cryptography has already advanced beyond the research laboratory to become a realizable technology with proven secret key distribution for encryption. Quantum computing, although at an earlier stage of development has been recognized as a major new development in physics, enables us (if a quantum computer is realizable) to attack problems previously thought to be too complex for normal computation in a reasonable time. Examples of quantum algorithms involving this kind of advantage are Shor's for fast factorization (in itself a threat to secure communication) and Grover's for database searching. I will discuss the ways quantum mechanics allow such a speed-up, stressing how quantum entanglement is the key resource being exploited, and how quantum gates, networks, and the processors may be implemented in a realistically noisy environment. Simple demonstrators have already been built, and I will discuss prospects for future realization of large-scale processors.
The unique principles of quantum mechanics may one day enable computers to perform operations that would be impossible on a classical computer. Although no one knows whether it will be possible to build a large-scale, functional, and stable quantum computer, researchers can study quantum-mechanical systems and develop algorithms and circuits by simulating quantum systems in software. Performance and memory bottlenecks prevent most current quantum computer simulators from being able to simulate quantum systems that are large enough to be useful. In this thesis, we develop a matrix-free sequential quantum computer simulator to vastly improve both time and memory performance of sequential code on a single processor. Next, we distribute the matrix-free algorithm over multiple parallel processors using the Message Passing Interface in order to simulate quantum systems that are too large to reside wholly within the memory of a single processor. Finally, we simulate various quantum circuits using the Hamming high-performance computing cluster in order to conduct algorithmic analysis.