Chapter 1
... and embedded computing is Evolutionary Hardware, which models Darwinian Evolution directly in special hardware processors to solve decision or optimization problems. Similarly, as the Data Mining and Machine Learning methods will be used in these areas, we will observe the synergism of research in a ...
... and embedded computing is Evolutionary Hardware, which models Darwinian Evolution directly in special hardware processors to solve decision or optimization problems. Similarly, as the Data Mining and Machine Learning methods will be used in these areas, we will observe the synergism of research in a ...
Reply to criticism of the ‘Orch OR qubit’ – ‘Orchestrated... reduction’ is scientifically justified
... Ambient energy, electric fields and mechanical vibrations pump coherence (as occurs in photosynthesis, and as suggested by Fröhlich). Most importantly, apparent quantum coherence up to 10−4 s has been shown by Bandyopadhyay’s group [10,11] to occur in single microtubules at warm temperature, which m ...
... Ambient energy, electric fields and mechanical vibrations pump coherence (as occurs in photosynthesis, and as suggested by Fröhlich). Most importantly, apparent quantum coherence up to 10−4 s has been shown by Bandyopadhyay’s group [10,11] to occur in single microtubules at warm temperature, which m ...
Quantum Error Correction (QEC) - ETH E
... and Toffoli gates.(The Toffoli gate is a CNOT with two control qubits and one target qubit.) We will see in section four that all of this gates can be implemented fault-tolerantly. The Hadamard and T gate are used to approximate any single qubit unitary operation. The CNOT allows us to approximate m ...
... and Toffoli gates.(The Toffoli gate is a CNOT with two control qubits and one target qubit.) We will see in section four that all of this gates can be implemented fault-tolerantly. The Hadamard and T gate are used to approximate any single qubit unitary operation. The CNOT allows us to approximate m ...
Synthesizing arbitrary quantum states in a superconducting resonator
... been rotated to match theory, compensating for a phase delay between the qubit and resonator microwave lines; the measured area is bounded by a dotted white line. The bottom row displays the calculated (grey) and measured (black) values for the resonator density matrix r, projected onto ...
... been rotated to match theory, compensating for a phase delay between the qubit and resonator microwave lines; the measured area is bounded by a dotted white line. The bottom row displays the calculated (grey) and measured (black) values for the resonator density matrix r, projected onto ...
A Bird`s-Eye View of Density-Functional Theory
... This paper is the outgrowth of lectures the author gave at the Physics Institute and the Chemistry Institute of the University of São Paulo at São Carlos, Brazil, and at the VIII’th Summer School on Electronic Structure of the Brazilian Physical Society. It is an attempt to introduce density-funct ...
... This paper is the outgrowth of lectures the author gave at the Physics Institute and the Chemistry Institute of the University of São Paulo at São Carlos, Brazil, and at the VIII’th Summer School on Electronic Structure of the Brazilian Physical Society. It is an attempt to introduce density-funct ...
The Automorphic Universe
... if T −1 B = B (mod 0). In this case, there exist a T − invariant set B e = B (mod 0). A function f : X → R is T −invariant if UT f = f , that B i.e. f ◦ T = T . In this case, f is constant on every trajectory of the map T . Again, if T preserves a measure µ, then we say that f is T −invariant (mod 0 ...
... if T −1 B = B (mod 0). In this case, there exist a T − invariant set B e = B (mod 0). A function f : X → R is T −invariant if UT f = f , that B i.e. f ◦ T = T . In this case, f is constant on every trajectory of the map T . Again, if T preserves a measure µ, then we say that f is T −invariant (mod 0 ...
J. Phys. Chem. B 106, 8271, 2002
... |40-〉, and |31-〉 initial states of H2O, and the |00+〉, |01-〉, and |10-〉 initial states of DOH. The comparison demonstrates that the TS SC-IVR of ref 1 is able to describe the H2O spectroscopy as well as the complete photodissociation dynamics, including the isotopic substitution effects, in excellen ...
... |40-〉, and |31-〉 initial states of H2O, and the |00+〉, |01-〉, and |10-〉 initial states of DOH. The comparison demonstrates that the TS SC-IVR of ref 1 is able to describe the H2O spectroscopy as well as the complete photodissociation dynamics, including the isotopic substitution effects, in excellen ...
Introduction CHAPTER 1
... diffusivity. This equation also describes heat conduction in incompressible liquids if the convective term is negligibly small compared to the conductive term and is the case when the liquid is at rest or the temperature of the liquid changes much faster than the liquid flows. The heat conduction eq ...
... diffusivity. This equation also describes heat conduction in incompressible liquids if the convective term is negligibly small compared to the conductive term and is the case when the liquid is at rest or the temperature of the liquid changes much faster than the liquid flows. The heat conduction eq ...
Module P11.1 Reflection and transmission at steps and barriers
... 2 Reflection & transmission at a potential step when E > V 2.1 Classical description of the problem 2.2 The time-independent Schrödinger eqn & its solutions 2.3 Relations imposed by the boundary conditions 2.4 The wavefunctions in each region and the physical interpretation 2.5 Defining particle flu ...
... 2 Reflection & transmission at a potential step when E > V 2.1 Classical description of the problem 2.2 The time-independent Schrödinger eqn & its solutions 2.3 Relations imposed by the boundary conditions 2.4 The wavefunctions in each region and the physical interpretation 2.5 Defining particle flu ...
On Quantum Simulators and Adiabatic Quantum Algorithms
... classical search algorithms and Hallgren’s quantum algorithm [6] for Pell’s equation1 which is exponentially faster than any known classical algorithm. Quantum mechanics, in so far as it is a complete natural theory, describes every physical computing device and, so, even classical computers. Theref ...
... classical search algorithms and Hallgren’s quantum algorithm [6] for Pell’s equation1 which is exponentially faster than any known classical algorithm. Quantum mechanics, in so far as it is a complete natural theory, describes every physical computing device and, so, even classical computers. Theref ...
Band-gap structure and chiral discrete solitons in optical lattices with
... Taking into account the atom-atom interaction, although the quasi-momentum k is still a good quantum number, it is difficult to directly diagonalize the eigenequations for each k. However, one can obtain the dispersion relation by using the variational method, which request to give an initial guess ...
... Taking into account the atom-atom interaction, although the quasi-momentum k is still a good quantum number, it is difficult to directly diagonalize the eigenequations for each k. However, one can obtain the dispersion relation by using the variational method, which request to give an initial guess ...
Stone`s Theorem and Applications
... absolute convergence implies convergence. Thus the power series converges. (A submultiplicative norm was chosen, but on Cn×n all norms are equivalent.) So, we have extended1 the function exp : C → C to a function expm : Mn (C) → Mn (C). In the following we will for simplicity always write exp (and n ...
... absolute convergence implies convergence. Thus the power series converges. (A submultiplicative norm was chosen, but on Cn×n all norms are equivalent.) So, we have extended1 the function exp : C → C to a function expm : Mn (C) → Mn (C). In the following we will for simplicity always write exp (and n ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.