Generation of accessible sets in the dynamical modelling of quantum network systems

TL;DR

This paper develops an analytic method for generating accessible sets in quantum network systems with qubits, simplifying state space modeling and aiding in the analysis of system dynamics for quantum networks.

Contribution

It introduces a novel analytic approach to generate accessible sets for quantum networks with time-independent Hamiltonians, improving modeling efficiency.

Findings

Analytic formulas for accessible set generation

Guidance on ordering elements in the state vector

Application to a 1D-chain quantum system

Abstract

In this paper, we consider the dynamical modeling of a class of quantum network systems consisting of qubits. Qubit probes are employed to measure a set of selected nodes of the quantum network systems. For a variety of applications, a state space model is a useful way to model the system dynamics. To construct a state space model for a quantum network system, the major task is to find an accessible set containing all of the operators coupled to the measurement operators. This paper focuses on the generation of a proper accessible set for a given system and measurement scheme. We provide analytic results on simplifying the process of generating accessible sets for systems with a time-independent Hamiltonian. Since the order of elements in the accessible set determines the form of state space matrices, guidance is provided to effectively arrange the ordering of elements in the state vector. Defining a system state according to the accessible set, one can develop a state space model with a special pattern inherited from the system structure. As a demonstration, we specifically consider a typical 1D-chain system with several common measurements, and employ the proposed method to determine its accessible set.