What Has Quantum Mechanics to Do With Factoring?
... Periods −→ factors solely via number-theory. 2. Period-finding is non-trivial for functions that look like random noise within a period. 3. Quantum parallelism doesn’t calculate all values of a function using 10300 computers in parallel universes. 4. Shor’s quantum Fourier transform (QFT) doesn’t tr ...
... Periods −→ factors solely via number-theory. 2. Period-finding is non-trivial for functions that look like random noise within a period. 3. Quantum parallelism doesn’t calculate all values of a function using 10300 computers in parallel universes. 4. Shor’s quantum Fourier transform (QFT) doesn’t tr ...
- Philsci
... it might be better to resist the very inference to the existence of such a property at all. As Hoefer (1999) argues, there is an explanatory itch here, but it is not clear one gains much by scratching it. Space constraints prevent me from saying more about this inference here, but I can point the r ...
... it might be better to resist the very inference to the existence of such a property at all. As Hoefer (1999) argues, there is an explanatory itch here, but it is not clear one gains much by scratching it. Space constraints prevent me from saying more about this inference here, but I can point the r ...
The harmonic oscillator in quantum mechanics: A third way F. Marsiglio
... of many applications in physics. For example, vibrations in solids8 are treated using springs that obey harmonic oscillator potentials. Bose condensation in alkali gases9 utilizes a harmonic trap, and the conventional theory of superconductivity uses electron-ion interactions with harmonic oscillato ...
... of many applications in physics. For example, vibrations in solids8 are treated using springs that obey harmonic oscillator potentials. Bose condensation in alkali gases9 utilizes a harmonic trap, and the conventional theory of superconductivity uses electron-ion interactions with harmonic oscillato ...
Creation of entangled states in coupled quantum dots via adiabatic... C. Creatore, R. T. Brierley, R. T. Phillips,
... It is important to recognize that the requirement of exact degeneracy of the uncoupled transition is relaxed up to the magnitude of the coupling energy. This affords a route to practical realizations of the scheme, as the coupling energy and level splitting can be traded to optimize the probability ...
... It is important to recognize that the requirement of exact degeneracy of the uncoupled transition is relaxed up to the magnitude of the coupling energy. This affords a route to practical realizations of the scheme, as the coupling energy and level splitting can be traded to optimize the probability ...
Quantum circuits for strongly correlated quantum systems
... novel ways of looking at strongly correlated quantum manybody systems. On the one hand, a great deal of theoretical work has been done identifying the basic structure of entanglement in low-energy states of many-body Hamiltonians. This has led, for example, to new interpretations of renormalization- ...
... novel ways of looking at strongly correlated quantum manybody systems. On the one hand, a great deal of theoretical work has been done identifying the basic structure of entanglement in low-energy states of many-body Hamiltonians. This has led, for example, to new interpretations of renormalization- ...
Fractional charge in the fractional quantum hall system
... linearization of the energy spectrum near the Fermi wave vector kF . 1D is a special case because there are only 2 discrete fermi surfaces (points in 1D case). The low energy excitation is only possible for fermions with wave vector k with |k − kF | ¿ 1 or |k − 2kF | ¿ 1. This indicates that as the ...
... linearization of the energy spectrum near the Fermi wave vector kF . 1D is a special case because there are only 2 discrete fermi surfaces (points in 1D case). The low energy excitation is only possible for fermions with wave vector k with |k − kF | ¿ 1 or |k − 2kF | ¿ 1. This indicates that as the ...
Regular Structures
... represented by means of a notational device called a ket, written "| >.” • In general the amplitudes are complex numbers (with both a real and an imaginary part) – but in some examples considered here will be confined to positive and negative real numbers. ...
... represented by means of a notational device called a ket, written "| >.” • In general the amplitudes are complex numbers (with both a real and an imaginary part) – but in some examples considered here will be confined to positive and negative real numbers. ...
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.