Quantum Recursion and Second Quantisation
نویسنده
چکیده
This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical example is recursive quantum walks, which are obtained by slightly modifying the construction of the ordinary quantum walks. The operational and denotational semantics of quantum recursions are defined by employing the second quantisation method, and they are proved to be equivalent.
منابع مشابه
Quantum curves for the enumeration of ribbon graphs and hypermaps
The topological recursion of Eynard and Orantin governs a variety of problems in enumerative geometry and mathematical physics. The recursion uses the data of a spectral curve to define an infinite family of multidifferentials. It has been conjectured that, under certain conditions, the spectral curve possesses a non-commutative quantisation whose associated differential operator annihilates th...
متن کاملDeformation Quantisation of Constrained Systems
We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear σ-model. Some new light is also shed on the Dirac bracket. Furthermore, it is shown how classical constraints not in involution with the classical Hamiltonian...
متن کاملTime-Dependent Real-Space Renormalization Group Method
In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...
متن کاملQHJ, WKB and exact quantisation
We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.
متن کاملar X iv : m at h / 04 11 06 6 v 1 [ m at h . D G ] 3 N ov 2 00 4 QUANTISATION OF LIE - POISSON MANIFOLDS
In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and C∗-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid which deals with a big enough class of functions to include the above mentioned example. As an ...
متن کامل