Coupling of quantum angular momenta: an insight into analogic/discrete and local/global models of computation

TL;DR

This paper explores a generalized quantum computing framework based on the coupling of quantum angular momenta, integrating discrete and continuous variables, and discusses its potential as a unifying paradigm for digital, analog, and topological quantum computation.

Contribution

It introduces a novel model of quantum computation using SU(2) angular momentum coupling, unifying digital, analog, and topological approaches within a single framework.

Findings

Framework accommodates both discrete and continuous quantum variables.

Models discrete quantum gates as finite state machines.

Potential for a universal paradigm for quantum symbolic computation.

Abstract

In the past few years there has been a tumultuous activity aimed at introducing novel conceptual schemes for quantum computing. The approach proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling theory of SU(2) angular momenta and can be viewed as a generalization to arbitrary values of the spin variables of the usual quantum-circuit model based on `qubits' and Boolean gates. Computational states belong to finite-dimensional Hilbert spaces labelled by both discrete and continuous parameters, and unitary gates may depend on quantum numbers ranging over finite sets of values as well as continuous (angular) variables. Such a framework is an ideal playground to discuss discrete (digital) and analogic computational processes, together with their relationships occuring when a consistent semiclassical limit takes place on discrete quantum gates. When working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum finite states--machines which in turn represent discrete versions of topological quantum computation models. We argue that our model embodies a sort of unifying paradigm for computing inspired by Nature and, even more ambitiously, a universal setting in which suitably encoded quantum symbolic manipulations of combinatorial, topological and algebraic problems might find their `natural' computational reference model.