tgd as a generalized number theory

... 3.4.2 Prime Hilbert spaces and infinite primes . . . . . . . . . . . . . . . . . . . . . . 191 3.4.3 Do infinite hyper-octonionic primes represent quantum numbers associated with Fock states? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 3.4.4 The physical interpret ...

... 3.4.2 Prime Hilbert spaces and infinite primes . . . . . . . . . . . . . . . . . . . . . . 191 3.4.3 Do infinite hyper-octonionic primes represent quantum numbers associated with Fock states? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 3.4.4 The physical interpret ...

Primality Test Via Quantum Factorization

... The situation is completely different after Shor’s discovery. As shown in the Appendix A, Shor’s algorithm requires O((log M)2 (log log M)2 log log log M) elementary q-bit operations2 to find a factor of a composite number M, provided that M is not in the form of pn or 2pn for some odd prime number ...

... The situation is completely different after Shor’s discovery. As shown in the Appendix A, Shor’s algorithm requires O((log M)2 (log log M)2 log log log M) elementary q-bit operations2 to find a factor of a composite number M, provided that M is not in the form of pn or 2pn for some odd prime number ...

Novel Systems and Methods for Quantum

... Precise control over quantum systems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators that can elucidate the physics of complex condensed matter systems. However, the fragility of quantum eﬀects makes it very diﬃcult to h ...

... Precise control over quantum systems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators that can elucidate the physics of complex condensed matter systems. However, the fragility of quantum eﬀects makes it very diﬃcult to h ...

Individual Trapped Atoms for Cavity QED Quantum

... the individual atoms into a high finesse cavity. Inside this optical cavity, atoms are cooled and non-destructively observed for up to 10 seconds. ...

... the individual atoms into a high finesse cavity. Inside this optical cavity, atoms are cooled and non-destructively observed for up to 10 seconds. ...

Quantum dynamics and isotope effects of hydrogen

... interaction time that is exceptionally long in order to get this small energy indeterminacy required for the state to be stationary [2]. However, there is another difficulty that is connected to the fact the constituents of a macroscopic body are subject to interaction with each other. For example, ...

... interaction time that is exceptionally long in order to get this small energy indeterminacy required for the state to be stationary [2]. However, there is another difficulty that is connected to the fact the constituents of a macroscopic body are subject to interaction with each other. For example, ...

Two-dimensional quantum mechanical modeling of nanotransistors A. Svizhenko, M. P. Anantram,

... to fully quantum mechanical approaches, and can also include ballistic effects and the role of quantized energy levels in the MOSFET inversion layer in an approximate manner.29–31 Discussing the relative merits of various approaches and quantum-corrected drift-diffusion approaches is important. In f ...

... to fully quantum mechanical approaches, and can also include ballistic effects and the role of quantized energy levels in the MOSFET inversion layer in an approximate manner.29–31 Discussing the relative merits of various approaches and quantum-corrected drift-diffusion approaches is important. In f ...

Quantum dots on bilayer graphene made on a substrate of boron

... excitation spectrum. A quantum dot has another characteristic called the charging energy; this is the energy required to add or remove a single electron from the dot [1]. The ability to control current through these dots at the single-electron level make it an interesting object. A future applicatio ...

... excitation spectrum. A quantum dot has another characteristic called the charging energy; this is the energy required to add or remove a single electron from the dot [1]. The ability to control current through these dots at the single-electron level make it an interesting object. A future applicatio ...

reactive molecular collisions

... body of sophisticated and detailed experimental data, upon which the theory must be built. Experiments are discussed in many reviews, including Bernstein’s AMCT chapter (6). The most recent experimental review is given by Levy (7), and includes a truly exhaustive compilation of data. for every atom- ...

... body of sophisticated and detailed experimental data, upon which the theory must be built. Experiments are discussed in many reviews, including Bernstein’s AMCT chapter (6). The most recent experimental review is given by Levy (7), and includes a truly exhaustive compilation of data. for every atom- ...

Thèse de doctorat - IMJ-PRG

... Vincent Calvez, Lingyan Guo, Yong Lu, Christophe Prange, Botao Qin et Fei Sun. Cette période m’a aussi donner l’occasion de saluer mes compagnons en route : R3 à Ulm et 7C à Chevaleret. Merci donc à Alfredo, Benben, Daniel, Dragoş, Elodie, Farid, Haoran, Hoël, Huafeng, Ismaël, Jialin, Jiao, Johan, J ...

... Vincent Calvez, Lingyan Guo, Yong Lu, Christophe Prange, Botao Qin et Fei Sun. Cette période m’a aussi donner l’occasion de saluer mes compagnons en route : R3 à Ulm et 7C à Chevaleret. Merci donc à Alfredo, Benben, Daniel, Dragoş, Elodie, Farid, Haoran, Hoël, Huafeng, Ismaël, Jialin, Jiao, Johan, J ...

Quantum teleportation is a process by which quantum information (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle) from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location. Because it depends on classical communication, which can proceed no faster than the speed of light, it cannot be used for faster-than-light transport or communication of classical bits. It also cannot be used to make copies of a system, as this violates the no-cloning theorem. While it has proven possible to teleport one or more qubits of information between two (entangled) atoms, this has not yet been achieved between molecules or anything larger.Although the name is inspired by the teleportation commonly used in fiction, there is no relationship outside the name, because quantum teleportation concerns only the transfer of information. Quantum teleportation is not a form of transportation, but of communication; it provides a way of transporting a qubit from one location to another, without having to move a physical particle along with it.The seminal paper first expounding the idea was published by C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters in 1993. Since then, quantum teleportation was first realized with single photons and later demonstrated with various material systems such as atoms, ions, electrons and superconducting circuits. The record distance for quantum teleportation is 143 km (89 mi).