Proof-of-principle demonstration of compiled Shor’s algorithm using a quantum dot single-photon source

Duan, Z.-C.; Li, Jin Peng; Qin, Jian; Yu, Ying; Huo, Yongheng; Höfling, Sven; Lu, Chao‐Yang; Liu, Nai Le; Chen, Kai; Pan, Jian-Wei

doi:10.1364/oe.390209

Cited by 19 publications

(6 citation statements)

References 36 publications

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“…Construction of 15A Factoring circuit with (a, N ) = (7, 15) is traditionally discussed in Vandersypen et al [34] and recently, Monz et al [12] and Duan et al [45] reported experiments with using semi-classical QFT. Our circuit (Figure 15) follows [34].…”

Section: F Construction Of Our Factoring Circuitsmentioning

confidence: 99%

The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers

Aono

Liu

Tanaka

et al. 2022

IEEE Trans. Quantum Eng.

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The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor's work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical post-processing algorithm. The theoretical result corresponds the situation where a quantum device working with a medium number of qubits of very small errors can solve DLP. However, all the quantum devices that we can use have a limited number of noisy qubits, as of the noisy intermediate-scale quantum (NISQ) era. Thus, evaluating the instance size that the latest quantum device can solve, and give a future prediction of the size along the progress of quantum devices are emerging research topics. This paper contains two proposal to discuss the performance of quantum devices against DLP in the NISQ era. (1) A quantitative measure based on the success probability of the post-processing algorithm to determine whether an experiment on a quantum device (or a classical simulator) succeeded. (2) A procedure to modify bit strings observed from a Shor's circuit to increase the success probability of a lattice-based post-processing algorithm. We conducted our experiments with the ibm_kawasaki device and discovered that the simplest circuit (7 qubits) from a 2-bit DLP instance achieves a sufficiently high success probability to proclaim the experiment successful. Experiments on another circuit from a slightly harder 2-bit DLP instance, on the other hand, did not succeed, and we determined that reducing the noise level by half is required to achieve a successful experiment. Finally, we give a near-term prediction based on required noise levels to solve some selected small DLP and integer factoring instances.

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Section: F Construction Of Our Factoring Circuitsmentioning

confidence: 99%

The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers

Aono

Liu

Tanaka

et al. 2022

IEEE Trans. Quantum Eng.

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“…However, recent advances in computational resources and quantum computing, may potentially jeopardize these cyrptobased solutions [145][146][147][148]. This has motivated the community to explore alternative approaches, a popular one is: Physical Layer Security.…”

Section: A a Primer On Information Securitymentioning

confidence: 99%

Security of Underwater and Air-Water Wireless Communication

Aman¹,

Al-Kuwari²,

Kumar³

et al. 2022

Preprint

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We present a first detailed survey that focuses on the security challenges faced by the underwater and air-water (A-W) wireless communication networks (WCNs), as well as the countermeasures proposed to date. Specifically, we provide a detailed literature review of the various kinds of active and passive attacks which hamper the confidentiality, integrity, authentication and availability of both underwater and A-W WCNs. For clarity of exposition, this survey paper is mainly divided into two parts. The first part of the paper is essentially a primer on underwater and A-W WCNs whereby we outline the benefits and drawbacks of the three promising underwater and A-W candidate technologies: radio frequency (RF), acoustic, and optical, along with channel modelling. To this end, we also describe the indirect (relay-aided) and direct mechanisms for the A-W WCNs along with channel modelling. This sets the stage for the second part (and main contribution) of the paper whereby we provide a thorough comparative discussion of a vast set of works that have reported the security breaches (as well as viable countermeasures) for many diverse configurations of the underwater and A-W WCNs. Finally, we highlight some research gaps in the open literature and identify some open problems for the future work.

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“…The construction of U f is the most challenging part when implementing Shor's algorithm. It is usually based on controlled modular multiplier blocks, individually designed for each choice of a and M [63,64]. In terms of tensor products, however, we can construct an explicit representation for any base and modulus.…”

Section: Shor's Algorithmmentioning

confidence: 99%

Low-rank tensor decompositions of quantum circuits

Gelß¹,

Klus²,

Shakibaei³

et al. 2022

Preprint

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Low-rank tensor decompositions of quantum circuitsQuantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation, optimization, and physical realization of quantum circuits is of utmost importance for designing novel algorithms. We show how matrix product states (MPSs) and matrix product operators (MPOs) can be used to express not only the state of the system but also quantum gates and entire quantum circuits as low-rank tensors. This allows us to analyze and simulate complex quantum circuits on classical computers and to gain insight into the underlying structure of the system. We present different examples to demonstrate the advantages of MPO formulations and provide a new perspective on the construction of quantum algorithms.

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Proof-of-principle demonstration of compiled Shor’s algorithm using a quantum dot single-photon source

Cited by 19 publications

References 36 publications

The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers

The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers

Security of Underwater and Air-Water Wireless Communication

Low-rank tensor decompositions of quantum circuits

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