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Добірка наукової літератури з теми "Toffoli gate"

Автор: Grafiati
Опубліковано: 7 липня 2024

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Зміст

  1. Статті в журналах
  2. Дисертації
  3. Частини книг
  4. Тези доповідей конференцій

Статті в журналах з теми "Toffoli gate":

1

Song, G., and A. Klappenecker. "Optimal realizations of simplified Toffoli gates." Quantum Information and Computation 4, no. 5 (September 2004): 361–72. http://dx.doi.org/10.26421/qic4.5-2.

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A simplified Toffoli gate coincides with the Toffoli gate except that the result is allowed to differ on one computational basis state by a phase factor. We prove that the simplified Toffoli gate implementation by Margolus is optimal, in the sense that it attains a lower bound of {\em three} controlled-not gates, and subject to that, a sharp lower bound of {\em four} single-qubit gates. We also discuss optimal implementations of other simplified Toffoli gates, and explain why the phase factor $-1$ invariably occurs in such implementations.
2

FANG, BAO-LONG, ZHEN YANG, and LIU YE. "SCHEME FOR IMPLEMENTING AN N-QUBIT CONTROLLED NOT GATE WITH SUPERCONDUCTING QUANTUM INTERFERENCE DEVICES IN CAVITY QED." International Journal of Quantum Information 08, no. 08 (December 2010): 1337–45. http://dx.doi.org/10.1142/s0219749910006307.

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We present a scheme for implementing a Toffoli gate. The superconducting quantum interference devices are coupled to a resonant cavity with nonidentical SQUID–cavity coupling constants. So only one interaction between SQUID and cavity is required, and a Toffoli gate can be obtained. The method can be generalized to the N-qubit case easily and the scheme is insensitive to systematic coupling error.
3

Guan, Zhi Jin, Wei Ping Ding, and Xue Yun Cheng. "Cascade Network in Reversible Logic Gate Based on Series Connection." Applied Mechanics and Materials 241-244 (December 2012): 3075–79. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.3075.

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This paper analyzes and proves that the relationship between the output results of the homotypic Toffoli gate which is series cascade and the number of the gates which are series cascade. In order to guarantee the convergence of the process of the series cascade, we gave the counting results of the series cascade network for Toffoli gates, and proved that in the input vector (0, 1, …, 2n-1), the number of the bit vectors with Hamming weight H(w)≥n-1 is equal to the bit number of bit vectors plus 1, and obtained the conclusion that there are (n+1)! kinds of transformation for Toffoli gate series cascade network. Simultaneously we provide the series cascade network algorithm of the Toffoli gates. The reversible network cascade system designed by the above algorithm verified the validity of this algorithm.
4

Trivedi, Amit Ranjan, and S. Bandyopadhyay. "Single spin Toffoli–Fredkin logic gate." Journal of Applied Physics 103, no. 10 (May 15, 2008): 104311. http://dx.doi.org/10.1063/1.2937200.

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5

Huang, He-Liang, Wan-Su Bao, Tan Li, Feng-Guang Li, Xiang-Qun Fu, Shuo Zhang, Hai-Long Zhang, and Xiang Wang. "Deterministic linear optical quantum Toffoli gate." Physics Letters A 381, no. 33 (September 2017): 2673–76. http://dx.doi.org/10.1016/j.physleta.2017.06.034.

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6

Sarkar, Angik, and T. K. Bhattacharyya. "Universal Toffoli gate in ballistic nanowires." Applied Physics Letters 90, no. 17 (April 23, 2007): 173101. http://dx.doi.org/10.1063/1.2731521.

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7

Backens, Miriam, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering, and Sal Wolffs. "Completeness of the ZH-calculus." Compositionality 5 (July 12, 2023): 5. http://dx.doi.org/10.32408/compositionality-5-5.

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There are various gate sets used for describing quantum computation. A particularly popular one consists of Clifford gates and arbitrary single-qubit phase gates. Computations in this gate set can be elegantly described by the ZX-calculus, a graphical language for a class of string diagrams describing linear maps between qubits. The ZX-calculus has proven useful in a variety of areas of quantum information, but is less suitable for reasoning about operations outside its natural gate set such as multi-linear Boolean operations like the Toffoli gate. In this paper we study the ZH-calculus, an alternative graphical language of string diagrams that does allow straightforward encoding of Toffoli gates and other more complicated Boolean logic circuits. We find a set of simple rewrite rules for this calculus and show it is complete with respect to matrices over Z[12], which correspond to the approximately universal Toffoli+Hadamard gateset. Furthermore, we construct an extended version of the ZH-calculus that is complete with respect to matrices over any ring R where 1+1 is not a zero-divisor.
8

Liu, Wen, Yangzhi Li, Zhirao Wang, and Yugang Li. "A New Quantum Private Protocol for Set Intersection Cardinality Based on a Quantum Homomorphic Encryption Scheme for Toffoli Gate." Entropy 25, no. 3 (March 16, 2023): 516. http://dx.doi.org/10.3390/e25030516.

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Set Intersection Cardinality (SI-CA) computes the intersection cardinality of two parties’ sets, which has many important and practical applications such as data mining and data analysis. However, in the face of big data sets, it is difficult for two parties to execute the SI-CA protocol repeatedly. In order to reduce the execution pressure, a Private Set Intersection Cardinality (PSI-CA) protocol based on a quantum homomorphic encryption scheme for the Toffoli gate is proposed. Two parties encode their private sets into two quantum sequences and encrypt their sequences by way of a quantum homomorphic encryption scheme. After receiving the encrypted results, the semi-honest third party (TP) can determine the equality of two quantum sequences with the Toffoli gate and decrypted keys. The simulation of the quantum homomorphic encryption scheme for the Toffoli gate on two quantum bits is given by the IBM Quantum Experience platform. The simulation results show that the scheme can also realize the corresponding function on two quantum sequences.
9

Lei, Peng, Yang Zhang, Jiong Cheng, and Wen-Zhao Zhang. "Quantum Toffoli gate in hybrid optomechanical system." Results in Physics 35 (April 2022): 105338. http://dx.doi.org/10.1016/j.rinp.2022.105338.

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10

Samanta, Debajyoti. "Implementation of polarization-encoded quantum Toffoli gate." Journal of Optics 48, no. 1 (December 6, 2018): 70–75. http://dx.doi.org/10.1007/s12596-018-0496-4.

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Статті в журналах

Дисертації з теми "Toffoli gate":

1

Ashkarin, Ivan. "Few-body Förster resonances in Rydberg atoms for the implementation of quantum computing." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASP199.

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L'application des résonances de Förster à plusieurs corps est étudiée pour réaliser des circuits de portes quantiques multi-qbits. Deux nouveaux types de transitions borroméennes à trois atomes utilisant un atome relais ont été proposées et étudiées numériquement. En particulier, une résonance de Förster à trois atomes non isolée et contrôlée par effet Stark entre des états S et P de niveaux élevés n = 80, 81, 82 avec des atomes de Rb isolés dans des pièges optiques a été modélisée. Une résonance de Förster isolée à trois atomes a également été démontrée pour les états n = 70, 71 des atomes Rb. Les résonances ont été étudiées dans une configuration spatiale fixe, ce qui nous a permis de démontrer l'évolution cohérente de la population et de la phase des états collectifs impliqués. Des schémas de portes de Toffoli à trois qubits ont été développés et modélisés numériquement sur la base des résonances démontrées dans des ensembles à trois atomes. En outre, un schéma généralisé de porte de phase doublement contrôlée CCPHASE a été développé sur la base de la résonance de Förster à trois corps induite par radiofréquence. De plus, un schéma de porte quantique similaire a été proposé sur la base de la résonance de Förster induite par radiofréquence à deux atomes avec un déplacement contrôlé par interaction avec le troisième. Les performances rapides et la grande fidélité des schémas proposés, ainsi que leur robustesse potentielle aux erreurs, nous permettent d'espérer le succès d'une réalisation expérimentale prochainement
Application of few-body Förster resonances for implementation of multiqubit quantum gate circuits has been investigated. New types of three-atom Borromean transitions based on the relay atom have been proposed and numerically studied. In particular, a Stark-controlled non-isolated three-atom Förster resonance between high-lying n = 80, 81, 82 S − P states of Rb atoms isolated in individual optical traps has been modeled. Isolated three-atom Förster resonance has also been demonstrated for n = 70, 71 states of Rb atoms. The resonances were investigated in a fixed spatial configuration, allowing us to demonstrate the coherent population and phase dynamics of the collective states involved. Three-qubit Toffoli gates schemes have been developed and numerically modeled based on the demonstrated resonances. Also, a generalized doubly controlled phase CCPHASE gate scheme has been developed based on the radiofrequency-induced three-body Förster resonance. Additionally, a similar quantum gate scheme has been proposed based on two-atom RF-induced Förster resonance with controlled displacement. The fast performance and high fidelity of the proposed schemes, as well as their potential robustness to errors, allow us to expect a successful experimental implementation in the near future
2

Mohammad, Kazemi Mehdi [Verfasser], Arnulf [Akademischer Betreuer] [Gutachter] Materny, Ulrich [Gutachter] Kleinekathöfer, and Johannes [Gutachter] Kiefer. "Application of Nonlinear Optical Techniques: Probing Ultrafast Dynamics in Ionic Liquids and Realization of an Ultrafast Toffoli Logic Gate / Mehdi Mohammad Kazemi ; Gutachter: Arnulf Materny, Ulrich Kleinekathöfer, Johannes Kiefer ; Betreuer: Arnulf Materny." Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2016. http://d-nb.info/1116080303/34.

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3

Daraeizadeh, Saman. "Efficient implementation of multi-control Toffoli gates in linear nearest neighbor arrays." Wichita State University, 2014. http://hdl.handle.net/10057/10952.

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Most promising implementations in quantum computing are based on Linear Nearest Neighbor (LNN) architectures, where qubits only interact with neighbors. Multi-control Toffoli gates are used in many quantum applications such as error correction and algorithms like Shor's factorization. Typically, to implement a multi-control Toffoli gate in an LNN architecture, additional operations called swap gates are required to bring the qubits adjacent to each other. This may increase the total number of quantum gates and computational overhead of the circuit. Here, we propose a new method to implement multi-control Toffoli gates in LNN arrays without using swap gates. The circuit reduction techniques discussed here are based on 3 lemmas. Using the lemmas, we show how to implement multi-control Toffoli gates in LNN arrays with different separations between the control and target qubits. The key feature of our scheme is to involve qubits other than control and target qubits to take part in gate operations. We call these qubits auxiliary" qubits and they are used in our gate decomposition protocols. Auxiliary qubits can be in any arbitrary states, a|0>+beta|1> , and are always restored back to their original states. Since we do not use swap gates to bring qubits adjacent to each other, compared to circuits using swap gates, the total number of gate operations used in our method is decreased, and the quantum cost is lowered. In addition, for implementing multi-control Toffoli gate operations efficiently in LNN arrays, we also show how to extend our protocols to 2D arrays. Here, in addition to translating our gate reduction techniques, directly from 1D to 2D, we use further simplification techniques for particular arrangements of qubits.
Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science
4

Gajewski, David C. "Analysis of Groups Generated by Quantum Gates." Connect to full text in OhioLINK ETD Center, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1250224470.

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5

Tian, Ke-Qun, and 田克群. "Quantum Circuit Design of Modular Exponentiation Computation Using Toffoli Gate." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/91066009297808769652.

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Анотація:
碩士
國立高雄第一科技大學
電腦與通訊工程所
95
The Shor''s quantum algorithm for breaking prime factorization in polynomial time was developed in 1994.This algorithm is mainly composed of two quantum circuits including quantum Fourier transform circuit and quantum modular exponentiation circuit .In this thesis, two methods are proposed for the design quantum modular Exponentiation. One is revision item by item method ,the other is tree structure search. These two methods use Toffoli gate to design modular exponential circuit .The number of quantum elementary gates such as single qubit gate and control NOT gate and chosen as the criterion to study the complexity of the circuit. The complexity of the designed modular exponentiation circuits is compared with the conventional IBM design method and Shannon expansion method .Finally, the advantages and disadvantages of proposed methods are described in details.

Частини книг з теми "Toffoli gate":

1

Luo, Ming-Xing, and Hui-Ran Li. "Distributed Quantum Computation Assisted by Remote Toffoli Gate." In Cloud Computing and Security, 475–85. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48671-0_42.

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2

Bhattacharya, Animesh, Goutam K. Maity, and Amal K. Ghosh. "Optical Quadruple Toffoli and Fredkin Gate Using SLM and Savart Plate." In Communications in Computer and Information Science, 281–95. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6427-2_23.

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3

Mukherjee, Chiradeep, Dip Ghosh, Sayan Halder, Sambhu Nath Surai, Saradindu Panda, Asish Kumar Mukhopadhyay, and Bansibadan Maji. "Implementation of Toffoli Gate Using LTEx Module of Quantum-Dot Cellular Automata." In Advances in Intelligent Systems and Computing, 57–65. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1540-4_7.

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4

Kole, Abhoy, Kamalika Datta, Philipp Niemann, Indranil Sengupta, and Rolf Drechsler. "Exploiting the Benefits of Clean Ancilla Based Toffoli Gate Decomposition Across Architectures." In Reversible Computation, 232–44. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38100-3_15.

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5

Mei, Jingyi, Tim Coopmans, Marcello Bonsangue, and Alfons Laarman. "Equivalence Checking of Quantum Circuits by Model Counting." In Automated Reasoning, 401–21. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-63501-4_21.

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AbstractVerifying equivalence between two quantum circuits is a hard problem, that is nonetheless crucial in compiling and optimizing quantum algorithms for real-world devices. This paper gives a Turing reduction of the (universal) quantum circuits equivalence problem to weighted model counting (WMC). Our starting point is a folklore theorem showing that equivalence checking of quantum circuits can be done in the so-called Pauli-basis. We combine this insight with a WMC encoding of quantum circuit simulation, which we extend with support for the Toffoli gate. Finally, we prove that the weights computed by the model counter indeed realize the reduction. With an open-source implementation, we demonstrate that this novel approach can outperform a state-of-the-art equivalence-checking tool based on ZX calculus and decision diagrams.
6

Kalpana, K., B. Paulchamy, V. V. Teresa, K. Sivakami, S. M. Deepa, and N. Revathi. "Reversible Logic Toffoli Gate Priority Encoder for Effective Nano-Scale Application in QCA Paradigm." In Communications in Computer and Information Science, 205–16. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58607-1_15.

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7

Moraga, Claudio. "OR-Toffoli and OR-Peres Reversible Gates." In Reversible Computation, 266–73. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79837-6_17.

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8

Moraga, Claudio. "Hybrid Control of Toffoli and Peres Gates." In Recent Findings in Boolean Techniques, 167–75. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68071-8_8.

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9

Wong, Hiu Yung. "SWAP, Phase Shift, and CCNOT (Toffoli) Gates." In Introduction to Quantum Computing, 143–53. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-36985-8_16.

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10

James, Rekha K., K. Poulose Jacob, and Sreela Sasi. "Reversible Binary Coded Decimal Adders using Toffoli Gates." In Lecture Notes in Electrical Engineering, 117–31. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-8919-0_9.

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Тези доповідей конференцій з теми "Toffoli gate":

1

Li, Meng, Chu Li, Yang Chen, Lan-Tian Feng, Xi-Feng Ren, Qihuang Gong, and Yan Li. "Femtosecond Laser Direct Writing of Path Encoded Two-qubit and Multiqubit Photonic Quantum Gate Chips." In Conference on Lasers and Electro-Optics/Pacific Rim. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleopr.2022.ctup7b_03.

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We demonstrate the first realization of path encoded two-qubit photonic quantum gate chip for generating Bell states, three-qubit Toffoli gate and four-qubit Controlled-Controlled-Controlled NOT gate via combining logic gates together by femtosecond laser direct writing.
2

Fazel, K., M. A. Thornton, and J. E. Rice. "ESOP-based Toffoli Gate Cascade Generation." In 2007 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing. IEEE, 2007. http://dx.doi.org/10.1109/pacrim.2007.4313212.

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3

Maity, Goutam Kumar, Santi P. Maity, and Jitendra Nath Roy. "TOAD-based Feynman and Toffoli Gate." In Communication Technologies (ACCT). IEEE, 2012. http://dx.doi.org/10.1109/acct.2012.116.

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4

Jia-Lin Chen, Xiao-Ying Zhang, Ling-Li Wang, Xin-Yuan Wei, and Wen-Qing Zhao. "Extended Toffoli gate implementation with photons." In 2008 9th International Conference on Solid-State and Integrated-Circuit Technology (ICSICT). IEEE, 2008. http://dx.doi.org/10.1109/icsict.2008.4734595.

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5

Khan, Mozammel H. A. "Primitive quantum gate realizations of multiple-controlled Toffoli gates." In 2013 16th International Conference on Computer and Information Technology (ICCIT). IEEE, 2014. http://dx.doi.org/10.1109/iccitechn.2014.6997380.

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6

Miller, D. Michael, Robert Wille, and Zahra Sasanian. "Elementary Quantum Gate Realizations for Multiple-Control Toffoli Gates." In 2011 IEEE 41st International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2011. http://dx.doi.org/10.1109/ismvl.2011.54.

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7

Kole, Abhoy, and Kamalika Datta. "Improved NCV Gate Realization of Arbitrary Size Toffoli Gates." In 2017 30th International Conference on VLSI Design and 2017 16th International Conference on Embedded Systems (VLSID). IEEE, 2017. http://dx.doi.org/10.1109/vlsid.2017.11.

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8

Safoev, Nuriddin, Ganiev Abdukhalil, and Karimov Abduqodir Abdisalomovich. "QCA based Priority Encoder using Toffoli gate." In 2020 IEEE 14th International Conference on Application of Information and Communication Technologies (AICT). IEEE, 2020. http://dx.doi.org/10.1109/aict50176.2020.9368637.

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9

Hwang, Ho, Sang-Ho Shin, and Jun-Cheol Jeon. "Reversible Data Hiding Scheme using Toffoli Gate." In The 6th International Conference on Signal Processing, Image Processing and Pattern Recognition. Science & Engineering Research Support soCiety, 2013. http://dx.doi.org/10.14257/astl.2013.29.20.

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10

Miller, D. Michael. "Lower cost quantum gate realizations of multiple-control Toffoli gates." In 2009 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim). IEEE, 2009. http://dx.doi.org/10.1109/pacrim.2009.5291355.

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