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Physics Letters A

Variational results for the Rabi Hamiltonian

R. F. Bishop, NEIL J. DAVIDSON, R. M. Quick, DAVID M. VAN DER WALT

Published Apr 1, 1999• 12 citations
Publisher
DOI
10.1016/s0375-9601(99)00074-2

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In the study of solving the ground state of quantum systems by variational principle, variational quantum algorithm is widely adopted to solve the ground state. As one kind of quantum classical hybrid algorithm, variational quantum eigensolver plays an important role. In this paper, we calculate ground state of quantum Rabi model in the ultra-strong coupling regime by invoking the variational quantum eigensolver in the open-source quantum computing simulator Qiskit. In the 3-qubit computing basis, we use the standard binary encoding method to encode the operators and quantum states in the quantum Rabi model, and measure the minimum average value (ground state energy) on the quantum circuit constructed by the Hamiltonian variational ansatz. Finally, comparing the calculation results of the variational quantum eigensolver with the exact values obtained by classical numerical simulations, we discuss the dependence of computational accuracy of the variational quantum eigensolver on the consumption of the number of the qubits and the coupling strength in quantum Rabi model.
The generalized rotating-wave approximation (GRWA) method is extended to the two-qubit quantum Rabi model. In the first-order approximation (one photon exchange), the Hamiltonian matrix in photon number space is simplified by introducing two variational parameters. However, the Hamiltonian matrix is not a diagonalizable matrix yet. Furthermore, by presenting a constraint condition on coupling strength and atomic transition frequency, the Hamiltonian matrix is simplified and an effective solvable Hamiltonian with block diagonal form is obtained. In the even and odd parity space, the energy spectra and eigenstates of the two-qubit quantum Rabi model are achieved analytically. Most of the energy spectra, especially the lower energy levels, agree well with the numerical exact results in ultra-strong coupling region, and the ground state wave function can gives a fairly accurate result of mean photon number.