Realization of a scalable Shor algorithm

By Thomas Monz, Daniel Nigg, E. Martinez, M. F. Brandl, Philipp Schindler, Rich Rines, Shannon X. Wang, Isaac L. Chuang, Rainer Blatt. Science, 2015

467 citations recorded by the source corpus.

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. Science, this issue p. 1068 Integer factorization is implemented in a scalable trapped-ion–based quantum computer. 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%.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c0d338701221232040f24f51ae05391338af07d1

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Citations in the corpus

The Road Towards 6G: A Comprehensive Survey (2021, background): “ematician Peter Shor [117] revealed that quantum computers can solve such problems efficiently, which makes all these public-key schemes completely broken.”
Demonstration of a small programmable quantum computer with atomic qubits (2016, methodology): “These algorithms have been implemented in experiments using a semi-classical version of the QFT that consists of single-qubit rotations based on classical feed-forward and qubit recycling which reduces the required register size [5, 10, 30].”
Experimental comparison of two quantum computing architectures (2017, background): “Recently, two architectures, superconducting transmon qubits [3–7] and trapped ions [2, 8], have reached a new level of maturity.”
Quantum optimization using variational algorithms on near-term quantum devices (2017, background): “es and physical qubit realizations are being considered. While quantum systems based on superconducting qubits [56,57,58, 34,59,60,61] at the moment seem to be leading the way, ion-trap-based systems [62,63] are close competitors. Furthermore, semiconductor-based spin qubits [64,65,66] and other qua”