{"title":"On quantum codes derived from quasi-cyclic codes over a non-chain ring","authors":"Shivanshu Benjwal, Maheshanand Bhaintwal, Raj Kumar","doi":"10.1007/s11128-024-04514-7","DOIUrl":"10.1007/s11128-024-04514-7","url":null,"abstract":"<div><p>This paper presents a study on the structure of 1-generator quasi-cyclic (QC) codes over the non-chain ring <span>(R=mathbb {F}_{q}+umathbb {F}_{q}+vmathbb {F}_{q}+uvmathbb {F}_{q})</span>, where <span>(u^2=v^2=0,~ uv=vu)</span>, and <span>(mathbb {F}_q)</span> is a finite field of cardinality <span>(q=p^r)</span>; <i>p</i> is a prime. A minimal spanning set and size of these codes are determined. A sufficient condition for 1-generator QC codes over <i>R</i> to be free is given. BCH-type bounds on the minimum distance of free QC codes over <i>R</i> are also presented. Some optimal linear codes over <span>(mathbb {F}_q)</span> are obtained as the Gray images of quasi-cyclic codes over <i>R</i>. Some characterizations of the Gray images of QC codes over <i>R</i> in <span>(mathbb {F}_q)</span> and <span>(mathbb {F}_q+umathbb {F}_q~(u^2=0))</span> are done. As an application, we consider self-orthogonal subcodes of the Gray images of QC codes over <i>R</i> to obtain new and better quantum codes than those are available in the literature.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Geometric genuine N-partite entanglement measure for arbitrary dimensions","authors":"Hui Zhao, Pan-Wen Ma, Shao-Ming Fei, Zhi-Xi Wang","doi":"10.1007/s11128-024-04501-y","DOIUrl":"10.1007/s11128-024-04501-y","url":null,"abstract":"<div><p>We present proper genuine multipartite entanglement (GME) measures for arbitrary multipartite and dimensional systems. By using the volume of concurrence regular polygonal pyramid, we first derive the GME measure of four-partite quantum systems. From our measure, it is verified that the GHZ state is more entangled than the W state. Then, we study the GME measure for multipartite quantum states in arbitrary dimensions. A well-defined GME measure is constructed based on the volume of the concurrence regular polygonal pyramid. Detailed example shows that our measure can characterize better the genuine multipartite entanglements.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Measurement-device-independent multi-party quantum secure direct communication","authors":"Ran Guo, Ri-Gui Zhou, Xiao-Xue Zhang","doi":"10.1007/s11128-024-04505-8","DOIUrl":"10.1007/s11128-024-04505-8","url":null,"abstract":"<div><p>As one of the most important branches of quantum information science, quantum communication is known for its unconditional security and efficiency. Nevertheless, the practical security of quantum key distribution protocols and quantum secure direct communication protocols is challenged due to the imperfections in experimental devices. Despite significant progress in theoretical and experimental research on the MDI-QSDC Protocol, challenges and unresolved issues remain. For example, further enhancing the scalability and system complexity of the protocol to meet the demands of large-scale quantum networks is necessary. In this paper, we propose a multi-party MDI-QSDC scheme based on multi-degree-of-freedom hyperentangled photons. Compared to the original MDI-QSDC protocol, our protocol allows multiple parties to participate in the information transmission process. For example, for four communicating parties, we can encode the information of three independent degrees of freedom so that each photon of each degree of freedom can transmit 2 bits of information. Moreover, all measurement tasks are performed by the fifth party, which can be untrusted or even completely controlled by eavesdroppers. The protocol is resistant to all possible attacks from imperfect measurement devices. It can eventually be extended to arbitrary degrees of freedom, allowing multiple parties to participate.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implementing multi-controlled X gates using the quantum Fourier transform","authors":"Vladimir V. Arsoski","doi":"10.1007/s11128-024-04511-w","DOIUrl":"10.1007/s11128-024-04511-w","url":null,"abstract":"<div><p>Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to implement these algorithms usually require multi-controlled gates as fundamental building blocks, where the multi-controlled Toffoli stands out as the primary example. For implementation in quantum hardware, these gates should be decomposed into many elementary gates, which results in a large depth of the final quantum circuit. However, even moderately deep quantum circuits have low fidelity due to decoherence effects and, thus, may return an almost perfectly uniform distribution of the output results. This paper proposes a different approach for efficient cost multi-controlled gates implementation using the quantum Fourier transform. We show how the depth of the circuit can be significantly reduced using only a few ancilla qubits, making our approach viable for application to noisy intermediate-scale quantum computers. This quantum arithmetic-based approach can be efficiently used to implement many complex quantum gates.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New optimized Lcd codes and quantum codes using constacyclic codes over a non-local collection of rings ({{varvec{A}}}_{{varvec{k}}})","authors":"Pooja Soni, Manju Pruthi","doi":"10.1007/s11128-024-04489-5","DOIUrl":"10.1007/s11128-024-04489-5","url":null,"abstract":"<div><p>In this article, we find several novel and efficient quantum error-correcting codes (<span>(boldsymbol{mathcal{Q}})</span><b>ecc</b>) by studying the structure of constacyclic (<span>(boldsymbol{{mathcal{C}}{mathcalligra{cc}}})</span>), cyclic (<span>(boldsymbol{{mathcal{C}}{mathcalligra{c}}})</span>), and negacyclic codes (<b>N</b><span>(boldsymbol{{mathcal{C}}{mathcalligra{c}}})</span>) over the ring <span>({A}_{k}={Z}_{p}left[{r}_{1},{r}_{2},dots ,{r}_{k}right])</span>/<span>(langle {{(r}_{b}}^{({m}_{b}+1)}-{r}_{b}), {r}_{l}{r}_{b}={r}_{b}{r}_{l}=0, bne lrangle )</span>, where <span>(p={q}^{m})</span> for m, <span>({m}_{b}in {mathbb{N}})</span>, <span>({m}_{b} | left(-1+qright))</span> <span>(forall b, l in left{1, text{to}, kright})</span>, <span>(qge 3)</span> is a prime, <span>({Z}_{p})</span> is a finite field. We define distance-preserving gray map <span>({delta }_{k})</span>. Moreover, we determine the quantum singleton defect (<span>(mathcal{Q})</span>SD) of <span>(boldsymbol{mathcal{Q}})</span><b>ecc</b>, which indicates their overall quality. We compare our codes with existing codes in recent publications. The rings discussed by Kong et al. (EPJ Quantum Technol 10:1–16, 2023), Suprijanto et al. (Quantum codes constructed from cyclic codes over the ring<span>(F_{text{q}}+{text{vF}}_{text{q}}+{v}^{2}F_{text{q}}+{v}^{3}F_{text{q}}+{v}^{4}F_{text{q}})</span>, pp 1–14, 2021. arXiv: 2112.13488v2 [cs.IT]), and Dinh et al. (IEEE Access 8:194082–194091, 2020) are specific cases of our work. Furthermore, we construct several novel and optimum linear complementary dual (Lcd) codes over <span>({A}_{k}.)</span></p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum image edge detection based on Haar wavelet transform","authors":"Guoling Wang, Weiqian Zhao, Ping Zou, Jindong Wang, Haibing Yin, Yafei Yu","doi":"10.1007/s11128-024-04513-8","DOIUrl":"10.1007/s11128-024-04513-8","url":null,"abstract":"<div><p>Quantum edge detection offers a promising avenue for real-time image analysis, addressing constraints faced by classical algorithms. However, existing quantum edge detection methods often rely on classical edge detection operators, leading to the loss of intricate edge details, especially in high-resolution images. Here, we present a novel quantum image edge detection algorithm. Our approach involves transforming the image into the wavelet domain through wavelet transform, performing edge detection, and obtaining the edge image via inverse wavelet transform. This innovative method not only mitigates edge information loss but also enhances precision in delineation. Through comprehensive simulations on a classical computing platform, employing peak signal-to-noise ratio (PSNR) and Edge Preservation Index (EPI) evaluations, our proposed scheme demonstrates superior edge information and heightened accuracy. These results underscore the potential of our approach in advancing image processing techniques.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implementation and analysis of quantum-classical hybrid interactive image segmentation algorithm based on quantum annealer","authors":"Kehan Wang, Shuang Wang, Qinghui Chen, Xingyu Qiao, Hongyang Ma, Tianhui Qiu","doi":"10.1007/s11128-024-04512-9","DOIUrl":"10.1007/s11128-024-04512-9","url":null,"abstract":"<div><p>With the development of computer vision and digital image processing technology, image segmentation has become an important part of various image processing and image analysis. Since interactive segmentation can obtain more accurate results than automatic segmentation, the most representative Graph Cuts has gradually become a popular method in image segmentation. However, this algorithm has two significant disadvantages. On the one hand, if the background is complex or very similar to the foreground, the accuracy will be low; on the other hand, the algorithm is slow and the iteration process is complicated. To improve it, this paper proposes a new image segmentation algorithm based on quantum annealing and Graph Cuts. The algorithm beds the classical interactive image segmentation problem into a quantum optimization algorithm and obtains ideal image segmentation results on the D-Wave quantum annealer. Meanwhile, it is compared with the other three methods. Compared with MATLAB, the segmentation results are more beautiful, with an average precision higher than 5.27% and an average recall higher than 5.43%; the quantum annealing time is always lower than the simulated annealing time; and the success probability is more than twice that of the quantum approximate optimization algorithm. Therefore, it is concluded that this method is superior.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The quantum uncertainty relations of quantum channels","authors":"Shi-Yun Kong, Ming-Jing Zhao, Zhi-Xi Wang, Shao-Ming Fei","doi":"10.1007/s11128-024-04510-x","DOIUrl":"10.1007/s11128-024-04510-x","url":null,"abstract":"<div><p>The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first derive the quantum uncertainty relation for quantum channels with respect to the relative entropy of coherence. Then we obtain the quantum uncertainty relation for unitary channels with respect to the <span>(l_1)</span> norm of coherence. Some examples are given in detail.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reduction of the semigroup-action problem on a module to the hidden-subgroup problem","authors":"Huawei Huang, Changgen Peng, Lunzhi Deng","doi":"10.1007/s11128-024-04509-4","DOIUrl":"10.1007/s11128-024-04509-4","url":null,"abstract":"<div><p>The discrete-logarithm problem and related problems are important in public-key cryptography; however, these problems can be reduced to the hidden-subgroup problem (HSP) of an abelian group, for which efficient quantum algorithms exist. This paper more broadly regards these problems as semigroup-action problems (SAPs) on different modules. The results prove that if the action on a module is injective or the cardinality of the hidden subgroup’s least generating set is less than or equal to that of the ring’s least generating set, the corresponding SAP on the module can be reduced to the HSP of an abelian group in polynomial time; therefore, most cryptosystems based on the SAP on a module cannot resist quantum cryptanalysis. The results are applicable to the discrete-logarithm problem and matrix-action problem on a group, along with other SAPs on a module. Such reduction is not be found for the SAP on the semi-module. The cryptographic systems based on SAPs on some semi-modules are likely to resist quantum attacks.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xi-Chen Xu, Yang-Yang Xie, Arapat Ablimit, Zhao-Ming Wang
{"title":"Enhanced adiabatic quantum algorithm in finite-temperature reservoirs via squeezing","authors":"Xi-Chen Xu, Yang-Yang Xie, Arapat Ablimit, Zhao-Ming Wang","doi":"10.1007/s11128-024-04503-w","DOIUrl":"10.1007/s11128-024-04503-w","url":null,"abstract":"<div><p>Adiabatic quantum algorithm always requires that the system is kept in its ground state during the time evolution, but the interaction between the system and its environment often destroys the adiabaticity. In this paper we show that the reservoir engineering, i.e. the squeezing of the environment, can be used to enhance the adiabaticity of the system in the presence of environment noise. We use the non-Markovian quantum state diffusion (QSD) method to solve the system dynamics. Taking the Max-Cut problem as an example, the effects of squeezing strength and squeezing direction on the adiabatic fidelity are investigated. The results show that appropriate squeezing can enhance the fidelity, and this enhancement remains effective as system sizes vary. Moreover, the optimal squeezing direction changes with different temperature and spectrum bandwidth. Our work demonstrate that reservoir engineering is an effective approach to control the dynamics of the system, which can be used to boost the adiabaticity of the quantum algorithm in open systems.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141925790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}