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2024

2024

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“…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): $$\begin{array}{cc}\hfill |\mathrm{\Psi}\u27e9& ={e}^{}\hfill \end{array}$$ …”

confidence: 99%

“…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): $$\begin{array}{cc}\hfill |\mathrm{\Psi}\u27e9& ={e}^{}\hfill \end{array}$$ …”

confidence: 99%