Graph-theoretic quantum system modelling for information/computation processing circuits

Abstract

This paper introduces graph-theoretic quantum system modelling (GTQSM), which is facilitated by considering the fundamental unit of quantum computation and information, viz. a quantum bit or qubit as a basic building block. Unit directional vectors ‘ket 0’ and ‘ket 1’ constitute two distinct fundamental quantum across variable orthonormal basis vectors (for the Hilbert space) specifying the direction of propagation, as it were, of information (or computation data) while complementary fundamental quantum through (flow rate) variables specify probability parameters (or amplitudes) as surrogates for scalar quantum information measure (von Neumann entropy). Applications of GTQSM are presented for quantum information/computation processing circuits ranging from a simple qubit and superposition or product of two qubits through controlled NOT and Hadamard gate operations to a substantive case of 3-port, 5-stage circuit for quantum teleportation. An illustrative circuit for teleporting a qubit is modelled as a complex ‘system of systems’ resulting in four probable transfer function models. It has the potential of extending the applications of GTQSM further to systems at the higher end of complexity scale too. The key contribution of this paper lies in generalization or extension of the graph-theoretic system modelling framework, hitherto used for classical (mostly deterministic) systems, to quantum random systems. Further extension of the graph-theoretic system modelling framework to quantum field modelling is the subject of future work.

Keywords:

• quantum system models
• quantum information processing
• quantum computing
• graph-theoretic modelling