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[Reducing quantum overhead] A quantum computer is expected to outperform its classical counterpart in certain tasks. One such task is the factorization of large integers, the technology that underpins the security of bank cards and online privacy. Using a small-scale quantum computer comprising five trapped calcium ions, Monz et al. implement a scalable version of Shor's factorization algorithm. With the function of ions being recycled and the architecture scalable, the process is more efficient than previous implementations. The approach thus provides the potential for designing a powerful quantum computer, but with fewer resources. [Abstract] Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four '' cache qubits'' and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99\,%.

@article{monzRealizationScalableShor2015, title = {Realization of a Scalable {{Shor}} Algorithm}, author = {Monz, T. and Nigg, D. and Martinez, E. A. and Brandl, M. F. and Schindler, P. and Rines, R. and Wang, S. X. and Chuang, I. L. and Blatt, R.}, year = {2015}, month = mar, volume = {351}, pages = {1068--1070}, issn = {0036-8075}, doi = {10.1126/science.aad9480}, abstract = {[Reducing quantum overhead] A quantum computer is expected to outperform its classical counterpart in certain tasks. One such task is the factorization of large integers, the technology that underpins the security of bank cards and online privacy. Using a small-scale quantum computer comprising five trapped calcium ions, Monz et al. implement a scalable version of Shor's factorization algorithm. With the function of ions being recycled and the architecture scalable, the process is more efficient than previous implementations. The approach thus provides the potential for designing a powerful quantum computer, but with fewer resources. [Abstract] Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four '' cache qubits'' and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99\,\%.}, archivePrefix = {arXiv}, eprint = {1507.08852}, eprinttype = {arxiv}, journal = {Science}, keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-13967666,~to-add-doi-URL,algorithmics,computational-science,quantum-computing}, lccn = {INRMM-MiD:c-13967666}, number = {6277} }

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