Closed-Form Expressions for the Matrix Exponential
... exp B = A, as shown by Dattoli, Mari and Torre [2]. These authors used essentially the same tools as we do here and presented some of the results that we will show below, but leaving them in an implicit form. The aforementioned authors belong to a group that has extensively dealt with our subject ma ...
... exp B = A, as shown by Dattoli, Mari and Torre [2]. These authors used essentially the same tools as we do here and presented some of the results that we will show below, but leaving them in an implicit form. The aforementioned authors belong to a group that has extensively dealt with our subject ma ...
Chapter 6 Euclidean Path Integral
... where|Ωi denotes the ground state. We subtracted the groundstate energy from H such that|Ωi has zero energy and H becomes a non-negative operator. The W (n) are not symmetric in their arguments, since the position operators at different times do not commute. We may analytically continue the W (n) to ...
... where|Ωi denotes the ground state. We subtracted the groundstate energy from H such that|Ωi has zero energy and H becomes a non-negative operator. The W (n) are not symmetric in their arguments, since the position operators at different times do not commute. We may analytically continue the W (n) to ...
Statistical Mechanics: An overview
... Thermodynamics deals with the thermal properties of macroscopic system by determining the relationship between different thermodynamic parameters of the system. In order to determine different relationships between the system parameters, the internal structure of matter is completely ignored in ther ...
... Thermodynamics deals with the thermal properties of macroscopic system by determining the relationship between different thermodynamic parameters of the system. In order to determine different relationships between the system parameters, the internal structure of matter is completely ignored in ther ...
What Has Quantum Mechanics to Do With Factoring?
... Quantum computer gives smallest r with ar − 1 divisible by N = pq First piece of luck: r even. Then (ar/2 − 1)(ar/2 + 1) divisible by N . but ar/2 − 1 is not divisible by N (since r is smallest number with ar − 1 divisible by N .) Second piece of luck: ar/2 + 1 is also not divisible by N . Then pro ...
... Quantum computer gives smallest r with ar − 1 divisible by N = pq First piece of luck: r even. Then (ar/2 − 1)(ar/2 + 1) divisible by N . but ar/2 − 1 is not divisible by N (since r is smallest number with ar − 1 divisible by N .) Second piece of luck: ar/2 + 1 is also not divisible by N . Then pro ...
Posterior distributions on certain parameter spaces obtained by using group theoretic methods adopted from quantum physics
... The use of group theoretic methods in statistical inference has been investigated from many points of view. Lists of references are provided, for example, in Eaton(1989), Barndorff-Nielsen et al.(1982), Kass and Wasserman(1996), and Diaconis(1988). Helland(1999 and 2003a, b) provides a scheme for em ...
... The use of group theoretic methods in statistical inference has been investigated from many points of view. Lists of references are provided, for example, in Eaton(1989), Barndorff-Nielsen et al.(1982), Kass and Wasserman(1996), and Diaconis(1988). Helland(1999 and 2003a, b) provides a scheme for em ...
Quantum error correcting codes and Weyl commutation relations
... subspace C admits a recovery operation R so that (C, R) is a quantum N -correcting code we then say that C, or equivalently, the orthogonal projection P on C is a quantum N -correcting code. The dimension of C or tr P is called the size of the code. The Knill-Laflamme theorem [5] gives a necessary a ...
... subspace C admits a recovery operation R so that (C, R) is a quantum N -correcting code we then say that C, or equivalently, the orthogonal projection P on C is a quantum N -correcting code. The dimension of C or tr P is called the size of the code. The Knill-Laflamme theorem [5] gives a necessary a ...
Documentation
... gate has to be reversible, i.e., input and output must always correspond uniquely to one another. In particular, the number of input and output qubits have to be equal. This is different than in the Boolean case, where most gates have two input bits and only one output bit. In fact, all basic binary ...
... gate has to be reversible, i.e., input and output must always correspond uniquely to one another. In particular, the number of input and output qubits have to be equal. This is different than in the Boolean case, where most gates have two input bits and only one output bit. In fact, all basic binary ...
Schumacher Compression
... Given access to many uses of a noiseless classical channel, what is the best that a sender and receiver can make of this resource for compressed data transmission? Shannon’s compression theorem demonstrates that the Shannon entropy is the fundamental limit for the compression rate in the IID setting ...
... Given access to many uses of a noiseless classical channel, what is the best that a sender and receiver can make of this resource for compressed data transmission? Shannon’s compression theorem demonstrates that the Shannon entropy is the fundamental limit for the compression rate in the IID setting ...
The quantum does not reduce to discrete bits
... I worry that we don't really understand quantum phenomena. … But there is another possibility: that quantum mechanics does not provide an explanation for what happens in individual phenomena because it is incomplete, because it simply leaves out aspects of nature needed for a true description. This ...
... I worry that we don't really understand quantum phenomena. … But there is another possibility: that quantum mechanics does not provide an explanation for what happens in individual phenomena because it is incomplete, because it simply leaves out aspects of nature needed for a true description. This ...
Many-body theory
... the same momentum by introducing the occupational number, nq giving the number of particles with wave vector q, ...
... the same momentum by introducing the occupational number, nq giving the number of particles with wave vector q, ...
Quantum Information—S. Lloyd, L. Levitov, T. Orlando, J. H. Shapiro, N.C. Wong
... Lin Tian, William Kaminsky, Aram Harrow Superconducting systems present a variety of opportunities for quantum information processing. In collaboration with Delft Institute of Technology, we have demonstrated the first macroscopic quantum superposition of circulating supercurrents, and have designed ...
... Lin Tian, William Kaminsky, Aram Harrow Superconducting systems present a variety of opportunities for quantum information processing. In collaboration with Delft Institute of Technology, we have demonstrated the first macroscopic quantum superposition of circulating supercurrents, and have designed ...
slides
... Theoretical approach to the problem of thermoelectric current and thermopower in the presence of microwaves. Presentation of results, discussion, conclusions. ...
... Theoretical approach to the problem of thermoelectric current and thermopower in the presence of microwaves. Presentation of results, discussion, conclusions. ...