Quantum Stat Mech Primer
... system, one has to be careful regarding counting Identical particles are indistinguishable Fermions: Only one particle is allowed in a quantum state Bosons: Any number of particles can occupy a state Assume that the energy levels εi are solved for and the state i is gi fold degenerate There are a to ...
... system, one has to be careful regarding counting Identical particles are indistinguishable Fermions: Only one particle is allowed in a quantum state Bosons: Any number of particles can occupy a state Assume that the energy levels εi are solved for and the state i is gi fold degenerate There are a to ...
Operator methods in quantum mechanics
... the initial state implying that P̂ 2 = 1. Therefore, the eigenvalues of the parity operation (if such exist) are ±1. A wavefunction will have a defined parity if and only if it is an even or odd function. For example, for ψ(x) = cos(x), P̂ ψ = cos(−x) = cos(x) = ψ; thus ψ is even and P = 1. Similarl ...
... the initial state implying that P̂ 2 = 1. Therefore, the eigenvalues of the parity operation (if such exist) are ±1. A wavefunction will have a defined parity if and only if it is an even or odd function. For example, for ψ(x) = cos(x), P̂ ψ = cos(−x) = cos(x) = ψ; thus ψ is even and P = 1. Similarl ...
Unitary time evolution
... turns out that just the CNOT (or almost any other two-bit gate), together with one-bit gates, can be used to build up any unitary. (We will prove this later in the class!) When we combine standard unitary gates, we call the resulting unitary a quantum circuit. Here’s a simple example that uses three ...
... turns out that just the CNOT (or almost any other two-bit gate), together with one-bit gates, can be used to build up any unitary. (We will prove this later in the class!) When we combine standard unitary gates, we call the resulting unitary a quantum circuit. Here’s a simple example that uses three ...
Science as Representation: Flouting the Criteria
... to the system as a whole (box with cat etc. inside) for which measurement outcome probabilities are certainly different on the two scenarios.7 Let’s admit that von Neumann’s alteration of the quantum theory, with or without Wigner’s addition, implies that the phenomena do derive from the quantum-mec ...
... to the system as a whole (box with cat etc. inside) for which measurement outcome probabilities are certainly different on the two scenarios.7 Let’s admit that von Neumann’s alteration of the quantum theory, with or without Wigner’s addition, implies that the phenomena do derive from the quantum-mec ...
PDF
... communication rests, admits to only two possible states: a classical on-off system must be in either state 0 or state 1, representing a single bit of information. Quantum mechanics is quite different. A two-level quantum system—the reader unfamiliar with basic quantum mechanics should consult the Ap ...
... communication rests, admits to only two possible states: a classical on-off system must be in either state 0 or state 1, representing a single bit of information. Quantum mechanics is quite different. A two-level quantum system—the reader unfamiliar with basic quantum mechanics should consult the Ap ...
Quantum Optics - Assets - Cambridge University Press
... many emerging applications. We therefore emphasize fundamental concepts and illustrate many of the ideas with typical applications. We make every possible attempt to indicate the experimental work if an idea has already been tested. Other applications are left as exercises which contain enough guida ...
... many emerging applications. We therefore emphasize fundamental concepts and illustrate many of the ideas with typical applications. We make every possible attempt to indicate the experimental work if an idea has already been tested. Other applications are left as exercises which contain enough guida ...
Finite Quantum Measure Spaces
... The reason for equation (3) is immediately clear. To understand the importance of (4), consider a situation involving destructive interference. In order for two waves to produce complete destructive interference, thereby “cancelling out” each other, their original amplitudes must have been equal. A ...
... The reason for equation (3) is immediately clear. To understand the importance of (4), consider a situation involving destructive interference. In order for two waves to produce complete destructive interference, thereby “cancelling out” each other, their original amplitudes must have been equal. A ...
Introduction to the general boundary formulation of quantum theory
... Description of free theories in a bounded region of space. [RO] Description of a free Euclidean theory in a bounded region of spacetime [D. Colosi, RO] Description of new types of asymptotic amplitudes, generalizing the S-matrix framework. [D. Colosi, RO] Application of this to de Sitter space. [D. ...
... Description of free theories in a bounded region of space. [RO] Description of a free Euclidean theory in a bounded region of spacetime [D. Colosi, RO] Description of new types of asymptotic amplitudes, generalizing the S-matrix framework. [D. Colosi, RO] Application of this to de Sitter space. [D. ...
The fractional quantum Hall effect in wide quantum wells
... Figure 1: (a) Color plot of the longitudinal resistance of a two-dimensional electron system in an 80 nm quantum well. In the lower density range the second subband (2SB) of the host quantum well is not yet occupied. When it becomes populated at higher densities, we observe an interplay of quantum H ...
... Figure 1: (a) Color plot of the longitudinal resistance of a two-dimensional electron system in an 80 nm quantum well. In the lower density range the second subband (2SB) of the host quantum well is not yet occupied. When it becomes populated at higher densities, we observe an interplay of quantum H ...
Quantum computing
Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. The field of quantum computing was initiated by the work of Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968.As of 2015, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in an effort to develop quantum computers for civilian, business, trade, and national security purposes, such as cryptanalysis.Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm.Given sufficient computational resources, however, a classical computer could be made to simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis.