Probability in quantum computation and quantum computational logics: a survey

2014 ◽  
Vol 24 (3) ◽  
Author(s):  
MARIA LUISA DALLA CHIARA ◽  
ROBERTO GIUNTINI ◽  
GIUSEPPE SERGIOLI
Keyword(s):  
Quantum Computation ◽  
Logic Gates ◽  
Point Of View ◽  
Quantum Processes ◽  
Classical Probability ◽  
Quantum Logic Gates ◽  
Quantum Computational Logics ◽  
Probability Spaces ◽  
Formal Point ◽  
Standard Probability

Quantum computation and quantum computational logics give rise to some non-standard probability spaces that are interesting from a formal point of view. In this framework, events represent quantum pieces of information (qubits, quregisters, mixtures of quregisters), while operations on events are identified with quantum logic gates (which correspond to dynamic reversible quantum processes). We investigate the notion of Shi–Aharonov quantum computational algebra. This structure plays the role for quantum computation that is played by σ-complete Boolean algebras in classical probability theory.

scholarly journals Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States

Micromachines ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1111
Author(s):  
Meng Li ◽  
Qian Zhang ◽  
Yang Chen ◽  
Xifeng Ren ◽  
Qihuang Gong ◽  
...  
Keyword(s):  
Femtosecond Laser ◽  
Quantum Computation ◽  
Logic Gates ◽  
Quantum Circuit ◽  
Bell States ◽  
Direct Writing ◽  
Laser Direct Writing ◽  
Quantum Logic Gates ◽  
Complex Circuits ◽  
Computation Algorithms

Integrated photonic quantum chip provides a promising platform to perform quantum computation, quantum simulation, quantum metrology and quantum communication. Femtosecond laser direct writing (FLDW) is a potential technique to fabricate various integrated photonic quantum chips in glass. Several quantum logic gates fabricated by FLDW have been reported, such as polarization and path encoded quantum controlled-NOT (CNOT) gates. By combining several single qubit gates and two qubit gates, the quantum circuit can realize different functions, such as generating quantum entangled states and performing quantum computation algorithms. Here we demonstrate the FLDW of integrated photonic quantum chips composed of one Hadamard gate and one CNOT gate for generating all four path-encoded Bell states. The experimental results show that the average fidelity of the reconstructed truth table reaches as high as 98.8 ± 0.3%. Our work is of great importance to be widely applied in many quantum circuits, therefore this technique would offer great potential to fabricate more complex circuits to realize more advanced functions.

scholarly journals Designs for a two-dimensional Si quantum dot array with spin qubit addressability

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Masahiro Tadokoro ◽  
Takashi Nakajima ◽  
Takashi Kobayashi ◽  
Kenta Takeda ◽  
Akito Noiri ◽  
...  
Keyword(s):  
Quantum Dot ◽  
Quantum Computation ◽  
Quantum Logic ◽  
Large Scale ◽  
Scale Up ◽  
Logic Gates ◽  
Two Dimensional ◽  
Device Design ◽  
Quantum Logic Gates ◽  
Novel Structure

AbstractElectron spins in Si are an attractive platform for quantum computation, backed with their scalability and fast, high-fidelity quantum logic gates. Despite the importance of two-dimensional integration with efficient connectivity between qubits for medium- to large-scale quantum computation, however, a practical device design that guarantees qubit addressability is yet to be seen. Here, we propose a practical 3 × 3 quantum dot device design and a larger-scale design as a longer-term target. The design goal is to realize qubit connectivity to the four nearest neighbors while ensuring addressability. We show that a 3 × 3 quantum dot array can execute four-qubit Grover’s algorithm more efficiently than the one-dimensional counterpart. To scale up the two-dimensional array beyond 3 × 3, we propose a novel structure with ferromagnetic gate electrodes. Our results showcase the possibility of medium-sized quantum processors in Si with fast quantum logic gates and long coherence times.

scholarly journals Holistic logical arguments in quantum computation

2016 ◽  
Vol 66 (2) ◽  
Author(s):  
Maria Luisa Dalla Chiara ◽  
Roberto Giuntini ◽  
Roberto Leporini ◽  
Giuseppe Sergioli
Keyword(s):  
Quantum Information ◽  
Quantum Computation ◽  
Essential Role ◽  
Circuit Theory ◽  
Logical Connectives ◽  
Quantum Computational Logics

AbstractQuantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters), while logical connectives correspond to (quantum logical) gates that transform quantum information in a reversible way. The characteristic holistic features of the quantum theoretic formalism (which play an essential role in entanglement-phenomena) can be used in order to develop a

Review of: Рикёр П. Genesis, essence and substance in Plato and Aristotle. Course taught at the University of Strasbourg in 1953-1954 / transl. from french G. V. Vdovina. Moscow: Publishing house of humanitarian literature, 2019. 286 p. ISBN 978-5-87121-051-2

2019 ◽  
pp. 279-287
Author(s):  
Алексей Михайлович Гагинский
Keyword(s):  
20Th Century ◽  
Publishing House ◽  
Point Of View ◽  
History Of ◽  
The University ◽  
Formal Point

Курс лекций П. Рикёра, прочитанный более полувека назад, интересен по ряду причин. Во-первых, потому что он посвящён крайне важной теме — античной онтологии; во-вторых, потому что он был прочитан одним из ведущих философов XX в.; в-третьих, потому что этот философ был крупнейшим представителем герменевтического направления, вследствие чего особенно любопытно проследить, как он читает тексты, без преувеличения, самых важных философов в истории человечества. Впрочем, с формальной точки зрения есть некоторые сомнения в возожности исполнения замысла работы: П. Рикёр всё-таки не антиковед, его знание греческого языка, что видно из текста, весьма скромного уровня; кроме того, изданный текст представляет собой курс лекций, автор которых, как кажется, не столько хочет донести до слушателей результаты кропотливых исследований и продуманных идей, сколько разобраться вместе со студентами в античной онтологии. P. Ricoeur's course of lectures, delivered more than half a century ago, is interesting for a number of reasons. Firstly, because it is devoted to an extremely important topic - ancient ontology; secondly, because it was read by one of the leading philosophers of the 20th century; thirdly, because this philosopher was the biggest representative of the hermeneutic direction, so it is especially interesting to trace how he reads texts of, without exaggeration, the most important philosophers in the history of mankind. However, from the formal point of view, there are some doubts about the feasibility of the idea of the work: Ricoeur is not an antiquarian and his knowledge of Greek, as the text shows, is rather modest; besides, the published text is a course of lectures, the author of which seems to want not so much to convey the results of laborious research and elaborated ideas to his students, as to understand ancient ontology together with the students.

Quantum logic gates by adiabatic passage

2006 ◽  
Vol 135 (1) ◽  
pp. 209-210 ◽  
Author(s):  
X. Lacour ◽  
N. Sangouard ◽  
S. Guérin ◽  
H. R. Jauslin
Keyword(s):  
Quantum Logic ◽  
Logic Gates ◽  
Adiabatic Passage ◽  
Quantum Logic Gates

The geometry and algebra of the representations of the Lorentz group

1968 ◽  
Vol 303 (1474) ◽  
pp. 381-396 ◽  
Keyword(s):  
Projective Space ◽  
Lorentz Group ◽  
Point Of View ◽  
Normal Curve ◽  
Geometrical Representation ◽  
Spinor Space ◽  
Dimensional Projective Space ◽  
And Algebra ◽  
Rational Normal Curve ◽  
Formal Point

In this paper a (2j + l)-spinor analysis is developed along the lines of the 2-spinor and 3-spinor ones. We define generalized connecting quantities A μv (j) which transform like (j, 0) ⊗ (j -1, 0) in spinor space and like second rank tensors under transformations in space-time. The general properties of the A uv are investigated together with algebraic relations involving the Lorentz group generators, J μv . The connexion with 3j symbols is discussed. From a purely formal point of view we introduce a geometrical representation of a (2j +1)-spinor as a point in a 2j dimensional projective space. Then, for example, the charge con­jugate of a (2j + l)-spinor is just the polar of the corresponding point with respect to a certain rational, normal curve in the projective space. It is suggested that this representation will prove useful.

scholarly journals Efficient implementation of coupled logic gates for quantum computation

2000 ◽  
Vol 61 (4) ◽  
Author(s):  
Debbie W. Leung ◽  
Isaac L. Chuang ◽  
Fumiko Yamaguchi ◽  
Yoshihisa Yamamoto
Keyword(s):  
Quantum Computation ◽  
Logic Gates ◽  
Efficient Implementation
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