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The adiabatic theorem in this heuristic context tells essentially that quantum jumps are preferably avoided, and the system tries to conserve the state and the quantum numbers. [9] The quantum mechanical concept of adiabatic is related to adiabatic invariant, it is often used in the old quantum theory and has no direct relation with heat exchange.
Adiabatic quantum computing has been shown to be polynomially equivalent to conventional quantum computing in the circuit model. [6] The time complexity for an adiabatic algorithm is the time taken to complete the adiabatic evolution which is dependent on the gap in the energy eigenvalues (spectral gap) of the Hamiltonian.
In quantum theory, the word adiabatic can mean something perhaps near isentropic, or perhaps near quasi-static, but the usage of the word is very different between the two disciplines. On the one hand, in quantum theory, if a perturbative element of compressive work is done almost infinitely slowly (that is to say quasi-statically), it is said ...
The old quantum theory was formulated by equating the quantum number of a system with its classical adiabatic invariant. This determined the form of the Bohr–Sommerfeld quantization rule: the quantum number is the area in phase space of the classical orbit.
In quantum field theory, the Gell-Mann and Low theorem is a mathematical statement that allows one to ... G. Nenciu and G. Rasche proved it using the adiabatic ...
In quantum mechanics, the Berry phase arises in a cyclic adiabatic evolution. The quantum adiabatic theorem applies to a system whose Hamiltonian H ( R ) {\displaystyle H(\mathbf {R} )} depends on a (vector) parameter R {\displaystyle \mathbf {R} } that varies with time t {\displaystyle t} .
All of these models of computation—quantum circuits, [41] one-way quantum computation, [42] adiabatic quantum computation, [43] and topological quantum computation [44] —have been shown to be equivalent to the quantum Turing machine; given a perfect implementation of one such quantum computer, it can simulate all the others with no more ...
This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules. [4] Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In ...