Pointers for Quantum Measurement Theory

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

“…We employ the well‐known Von‐Neumann measurement prescription by constructing the following Hamiltonian [27]: $$$$\begin{eqnarray} H = i A \otimes \mathinner {|{1}\rangle }_P \mathinner {\langle {0}|} - i A^\dag \otimes \mathinner {|{0}\rangle }_P \mathinner {\langle {1}|}, \end{eqnarray}$$$$where $$\otimes$$ denote a tensor product, $$A^\dag$$ is the adjoin of $$A$$, and $$P$$ is the qubit pointer [28, 29]. If we simulate the Hamiltonian $$H$$ in (27) with the initial state $$\mathinner {|{z}\rangle } \mathinner {|{z}\rangle } \mathinner {|{0}\rangle }_P$$ in a quantum computer, the quantum system will evolve in accordance with $$H$$ for a time step $$\epsilon$$ following (19) to reach the following steady‐state $$\mathinner {|{\Psi }\rangle }$$ [21] (see Appendix A.2): …”