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A quantum circuit design of AES requiring fewer quantum qubits and gate operations

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Frontiers of physics 2022年第4期17卷 99-105页

作者： Ze-Guo Wang Shi-Jie Wei Gui-Lu Long State Key Laboratory of Low-Dimensional quantum Physics and Department of Physics Tsinghua UniversityBeijing 100084China Beijing Academy of quantum Information Sciences Beijing 100193China Beijing National Research Center for Information Science and Technology and School of Information Tsinghua University Beijing 100084China Frontier Science Center for quantum Information Beijing 100084China

Advanced Encryption Standard(AES)is one of the most widely used block ciphers nowadays,and has been established as an encryption standard in 2001.Here we design AES-128 and the sample-AES(S-AES)quantum circuits for deciphering.In the quantum circuit of AES-128,we perform an affine transformation for the SubBytes part to solve the problem that the initial state of the output qubits in SubBytes is not the|0⟩⊗8 state.After that,we are able to encode the new round sub-key on the qubits encoding the previous round sub-key,and this improvement reduces the number of qubits used by 224 compared with Langenberg et al.’s implementation.For S-AES,a complete quantum circuit is presented with only 48 qubits,which is already within the reach of existing noisy intermediate-scale quantum computers.

关键词： AES S-AES quantum circuit quantum attack

Integer multiple quantum image scaling based on NEQR and bicubic interpolation

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Chinese Physics B 2024年第4期33卷 259-273页

作者：蔡硕周日贵罗佳陈思哲 College of Information Engineering Shanghai Maritime UniversityShanghai 201306China Research Center of Intelligent Information Processing and quantum Intelligent Computing Shanghai 201306China College of Merchant Marine Shanghai Maritime UniversityShanghai 201306China School of Mathematics and Computational Science Shangrao Normal UniversityShangrao 334001China

As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.

关键词： quantum image processing image scaling bicubic interpolation quantum circuit

Proposal for sequential Stern-Gerlach experiment with programmable quantum processors

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Chinese Physics B 2024年第2期33卷 131-136页

作者：胡孟军缪海兴张永生 Beijing Academy of quantum Information Sciences Beijing 100193China State Key Laboratory of Low Dimensional quantum Physics Department of PhysicsTsinghua UniversityBeijing 100084China Laboratory of quantum Information University of Science and Technology of ChinaHefei 230026China Synergetic Innovation Center of quantum Information and quantum Physics University of Science and Technology of ChinaHefei 230026China Hefei National Laboratory University of Science and Technology of ChinaHefei 230088China

The historical significance of the Stern–Gerlach(SG)experiment lies in its provision of the initial evidence for space quantization.Over time,its sequential form has evolved into an elegant paradigm that effectively illustrates the fundamental principles of quantum theory.To date,the practical implementation of the sequential SG experiment has not been fully achieved.In this study,we demonstrate the capability of programmable quantum processors to simulate the sequential SG experiment.The specific parametric shallow quantum circuits,which are suitable for the limitations of current noisy quantum hardware,are given to replicate the functionality of SG devices with the ability to perform measurements in different directions.Surprisingly,it has been demonstrated that Wigner’s SG interferometer can be readily implemented in our sequential quantum circuit.With the utilization of the identical circuits,it is also feasible to implement Wheeler’s delayed-choice experiment.We propose the utilization of cross-shaped programmable quantum processors to showcase sequential experiments,and the simulation results demonstrate a strong alignment with theoretical predictions.With the rapid advancement of cloud-based quantum computing,such as BAQIS Quafu,it is our belief that the proposed solution is well-suited for deployment on the cloud,allowing for public accessibility.Our findings not only expand the potential applications of quantum computers,but also contribute to a deeper comprehension of the fundamental principles underlying quantum theory.

关键词： sequential Stern-Gerlach quantum circuit quantum processor

Anomalous non-Hermitian dynamical phenomenon on the quantum circuit

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Chinese Physics B 2023年第7期32卷 132-141页

作者：董陈潇杨哲森曾进峰胡江平 Beijing National Laboratory for Condensed Matter Physics and Institute of PhysicsChinese Academy of SciencesBeijing 100190China Kavli Institute for Theoretical Sciences University of Chinese Academy of SciencesBeijing 100190China South Bay Interdisciplinary Science Center Dongguan 523808China Beijing Academy of quantum Information Sciences Beijing 100193China

The anomalous non-Hermitian dynamical phenomenon with the non-Hermitian skin effect(NHSE)attracts wide attention due to its novel physics and promising applications.Here,we propose a new type of non-unitary discrete-time quantum walk system demonstrating the NHSE and anomalous non-Hermitian dynamical phenomena,including the dynamical chiral phenomenon,the funneling phenomenon on the domain wall,and the anomalous reflection on the phase impurity.Furthermore,we design the quantum circuit experiments of these quantum walk systems and numerically simulate them with quantum noises to verify the robustness of the non-Hermitian dynamical phenomenon on the noisy intermediate-scale quantum(NISQ)devices.Our work paves the way for implementing the non-Hermitian dynamical phenomenon on the quantum circuit.

关键词： spectral degeneracy splitting discrete-time quantum walk quantum circuit non-Hermitian skin effect

A general quantum minimum searching algorithm with high success rate and its implementation

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Science China(Physics,Mechanics & Astronomy) 2023年第4期66卷 49-60页

作者： Yi Zeng Ziming Dong Hao Wang Jin He Qijun Huang Sheng Chang School of Physics and Technology Wuhan UniversityWuhan 430072China Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education Wuhan UniversityWuhan 430072China

Finding a minimum is a fundamental calculation in many quantum algorithms.However,challenges are faced in demonstrating it effectively in real quantum computers.In practice,the number of solutions is unknown,and there is no universal encoding method.Besides that,current quantum computers have limited resources.To alleviate these problems,this paper proposes a general quantum minimum searching algorithm.An adaptive estimation method is adopted to calculate the number of solutions,and a quantum encoding circuit for arbitrary databases is presented for the first time,which improves the universality of the algorithm and helps it achieve a nearly 100%success rate in a series of random databases.Moreover,gate complexity is reduced by our simplified Oracle,and the realizability of the algorithm is verified on a superconducting quantum computer.Our algorithm can serve as a subroutine for various quantum algorithms to promote their implementation in the Noisy IntermediateScale quantum era.

关键词： quantum minimum searching algorithm quantum circuit superconducting quantum computer quantum encoding

A quantum Algorithm for Evaluating the Hamming Distance

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Computers, Materials & Continua 2022年第4期71卷 1065-1078页

作者： Mohammed Zidan Manal G.Eldin Mahmoud Y.Shams Mohamed Tolan Ayman Abd-Elhamed Mahmoud Abdel-Aty Department of Artificial Intelligence Hurghada Faculty of Computers and Artificial IntelligenceSouth Valley UniversityEgypt Faculty of Engineering King Salman International UniversitySouth SinaiEgypt Department of Mathematics and Computer Science Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt Department of Machine Learning and Information Retrieval Faculty of Artificial IntelligenceKafrelsheikh UniversityEgypt Mechanical Department Faculty of Technology and EducationSuez UniversitySuezEgypt Faculty of Technological Industries King Salman International UniversitySouth SinaiEgypt Faculty of Engineering at Mataria Helwan UniversityCairoEgypt Department of Mathematics Faculty of SciencesSohag University82524 SohagEgypt

We present a novel quantum algorithm to evaluate the hamming distance between two unknown oracles via measuring the degree of entanglement between two ancillary qubits.In particular,we use the power of the entanglement degree based quantum computing model that preserves at most the locality of interactions within the quantum model structure.This model uses one of two techniques to retrieve the solution of a quantum computing problem at hand.In the first technique,the solution of the problem is obtained based on whether there is an entanglement between the two ancillary qubits or not.In the second,the solution of the quantum computing problem is obtained as a function in the concurrence value,and the number of states that can be generated from the Boolean variables.The proposed algorithm receives two oracles,each oracle represents an unknown Boolean function,then it measures the hamming distance between these two oracles.The hamming distance is evaluated based on the second technique.It is shown that the proposed algorithm provides exponential speedup compared with the classical counterpart for Boolean functions that have large numbers of Boolean variables.The proposed algorithm is explained via a case study.Finally,employing recently developed experimental techniques,the proposed algorithm has been verified using IBM’s quantum computer simulator.

关键词： quantum computing quantum algorithm quantum circuit

A new method of constructing adversarial examplesfor quantum variational circuits

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Chinese Physics B 2023年第7期32卷 268-272页

作者：颜金歌闫丽丽张仕斌 School of Cybersecurity Chengdu University of Information TechnologySichuan 610000China Advanced Cryptography and System Security Key Laboratory of Sichuan Province Sichuan 610000China

A quantum variational circuit is a quantum machine learning model similar to a neural network.A crafted adversarial example can lead to incorrect results for the model.Using adversarial examples to train the model will greatly improve its robustness.The existing method is to use automatic differentials or finite difference to obtain a gradient and use it to construct adversarial examples.This paper proposes an innovative method for constructing adversarial examples of quantum variational circuits.In this method,the gradient can be obtained by measuring the expected value of a quantum bit respectively in a series quantum circuit.This method can be used to construct the adversarial examples for a quantum variational circuit classifier.The implementation results prove the effectiveness of the proposed method.Compared with the existing method,our method requires fewer resources and is more efficient.

关键词： quantum variational circuit adversarial examples quantum machine learning quantum circuit

Two-qubit pure state tomography by five product orthonormal bases

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Chinese Physics B 2018年第10期27卷 190-195页

作者：王宇尚云 Institute of Mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing 100190 China MDIS Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100190 China

In this paper, we focus on two-qubit pure state tomography. For an arbitrary unknown two-qubit pure state, separable or entangled, it has been found that the measurement probabilities of 16 projections onto the tensor products of Pauli eigenstates are enough to uniquely determine the state. Moreover, these corresponding product states are arranged into five orthonormal bases. We design five quantum circuits, which are decomposed into the common gates in universal quantum computation, to simulate the five projective measurements onto these bases. At the end of each circuit, we measure each qubit with the projective measurement {｜0〉〈0 ｜,｜1〉,〈1｜ }. Then, we consider the open problem whether three orthonormal bases are enough to distinguish all two-qubit pure states. A necessary condition is given. Suppose that there are three orthonormal bases {B1,B2,B3}. Denote the unitary transition matrices from B1 to {B2,B3 } as U1 and U2. All 32 elements of matrices U1 and U2 should not be zero. If not, these three bases cannot distinguish all two-qubit pure states.

关键词： two-qubit pure state tomography projective measurement quantum circuit

quantum watermarking based on threshold segmentation using quantum informational entropy

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Chinese Physics B 2022年第4期31卷 116-122页

作者：罗佳周日贵胡文文李尧翀罗高峰 College of Information Engineering Shanghai Maritime UniversityShanghai 201306China Research Center of Intelligent Information Processing and quantum Intelligent Computing Shanghai 201306China College of Information Engineering Shaoyang UniversityShaoyang 422000China

We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image.The core idea of this scheme is to embed information into object and background of cover image in different ways.First,a threshold method adopting the quantum informational entropy is employed to determine a threshold value.The threshold value can then be further used for segmenting the cover image to a binary image,which is an authentication key for embedding and extraction information.By a careful analysis of the quantum circuits of the scheme,that is,translating into the basic gate sequences which show the low complexity of the scheme.One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image.Furthermore,the analyses of peak signal-to-noise ratio,histogram and capacity of the scheme are also provided.

关键词： quantum image watermarking threshold segmentation quantum informational entropy quantum circuit