Algorithms on ensemble quantum computers |
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Authors: | P Oscar Boykin Tal Mor Vwani Roychowdhury Farrokh Vatan |
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Affiliation: | (1) Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA;(2) Computer Science Department, Technion, Haifa, 32000, Israel;(3) Electrical Engineering Department, UCLA, Los Angeles, CA 90095, USA;(4) Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA;; |
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Abstract: | In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead,
only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model
of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy
of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of
some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers,
e.g., on liquid NMR quantum computers. These algorithms are Shor’s factorization algorithm, Grover’s search algorithm (with
several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified
using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to
present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation
of Toffoli and sz1/4,\sigma_{z}^{1/4}, as these operations cannot be implemented “bitwise”, and their standard fault-tolerant implementations require measurement. |
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