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Comment on "Realization of a scalable Shor algorithm".

Zhengjun Cao, Lihua Liu

Published Jan 1, 2015• 1 citation
OpenAlex

Abstract

Abstract. Recently, Monz, et al. [arXiv:1507.08852] have reported the demon-stration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. We remark that the report is flawed because there are three flaws in the proposed circuit diagram of Shor algorithm. We also remark that the principles be-hind the demonstration have not been explained properly, including its correctness and complexity.

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•Jan 1, 2015•3 citations

Realization of a scalable Shor algorithm

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Realization of Shor's Algorithm at Room Temperature

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Shor's algorithm can find prime factors of a large number more efficiently than any known classical algorithm. Understanding the properties that gives the speedup is essential for a general and scalable construction. Here we present a realization of Shor's algorithm, that does not need any of the simplifications presently needed in current experiments and also gives smaller systematic errors than any former experimental implementation. Our realization is based on classical pass-transistor logic, runs at room temperature, and uses the same amount of resources as a scalable quantum computer. In this paper, the focus is not on the result of the factorization, but to compare our realization with current state-of-the-art experiment, factoring 15. Our result gives further insight to the resources needed for quantum computation, aiming for a true understanding of the subject.

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Experimental realization of a Shor-type quantum algorithm

Isaac L. Chuang

I will describe our recent implementation of a five-qubit NMR quantum computer capable of executing a quantum algorithm for order-finding. This is the first demonstration of a quantum algorithm with the structure of Shor's algorithm for efficient prime factorization, a key step in the experimental realization of quantum computers because its structure appears to be common to all quantum algorithms that achieve an exponential speed-up over their classical counterparts. The experiment was made possible by the synthesis of a 5-spin molecule with remarkable NMR properties, and by the introduction of new techniques for state initialization and quantum control.

Optical Fiber Communication Conference•Jan 1, 2001•1 citation
Abstract. Recently, Monz, et al. [arXiv:1507.08852] have reported the demon-stration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. We remark that the report is flawed because there are three flaws in the proposed circuit diagram of Shor algorithm. We also remark that the principles be-hind the demonstration have not been explained properly, including its correctness and complexity.
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%.
An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark that some experimental demonstrations of Shor's algorithm are misleading, because they violate the necessary condition that the selected number q=2sq=2^sq=2s, where sss is the number of qubits used in the first register, must satisfy n2≤q<2n2n^2 \leq q < 2n^2n2≤q<2n2, where nnn is the large number to be factored.
Shor's algorithm can find prime factors of a large number more efficiently than any known classical algorithm. Understanding the properties that gives the speedup is essential for a general and scalable construction. Here we present a realization of Shor's algorithm, that does not need any of the simplifications presently needed in current experiments and also gives smaller systematic errors than any former experimental implementation. Our realization is based on classical pass-transistor logic, runs at room temperature, and uses the same amount of resources as a scalable quantum computer. In this paper, the focus is not on the result of the factorization, but to compare our realization with current state-of-the-art experiment, factoring 15. Our result gives further insight to the resources needed for quantum computation, aiming for a true understanding of the subject.
I will describe our recent implementation of a five-qubit NMR quantum computer capable of executing a quantum algorithm for order-finding. This is the first demonstration of a quantum algorithm with the structure of Shor's algorithm for efficient prime factorization, a key step in the experimental realization of quantum computers because its structure appears to be common to all quantum algorithms that achieve an exponential speed-up over their classical counterparts. The experiment was made possible by the synthesis of a 5-spin molecule with remarkable NMR properties, and by the introduction of new techniques for state initialization and quantum control.