Implementing Jastrow-Gutzwiller operators on a quantum computer using the cascaded variational quantum eigensolver algorithm

Demonstration of the Effectiveness of the Cascaded Variational Quantum Eigensolver Using the Jastrow Ansatz for Molecular Calculations

“…The goal is to compute the energy expectation value of a Hamiltonian Ĥ . Given the measurement results of the quantum state , an analytical equation for E (θ) can be derived that is efficiently computable on a classical computer. , The efficiency of the calculation is due to D̂ (θ) being diagonal. As long as D̂ (θ) contains only operators that are diagonal in the initial basis of the quantum computer, the energy expectation value E (θ) can be calculated from sample distributions measured in the same number of bases required to calculate .…”

“…We can address both the issue of short relaxation times and resource scarcity using the cascaded variational quantum eigensolver (CVQE). Unlike VQE, CVQE does not require circuit executions to be repeated throughout the parameter optimization process. , Instead, measurement samples obtained from the quantum computer are processed on a classical computer according to a variational ansatz. A natural choice of ansatz for CVQE is the Jastrow ansatz. ,− The Jastrow ansatz has been used in VQE-type algorithms in the past.…”

“…Unlike VQE, CVQE does not require circuit executions to be repeated throughout the parameter optimization process. , Instead, measurement samples obtained from the quantum computer are processed on a classical computer according to a variational ansatz. A natural choice of ansatz for CVQE is the Jastrow ansatz. ,− The Jastrow ansatz has been used in VQE-type algorithms in the past. However, because the Jastrow operator is nonunitary, special care needs to be taken when employing the ansatz for QC.…”

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

“…96,101−108 Of particular interest to this paper are those VQE computations that report the effectiveness of d i ff e r e n t e r r o r m i t i g a t i o n schemes, 56,59,60,63,64,69,73,75,79,82,83,85,88,93,94,103,105 or that are p e r f o r m e d o n I B M d e v ices. 41,54,55,[58][59][60]62,65,67,69,73,74,76,78,79,82,85,[87][88][89]92,93,95,[97][98][99][100][101][102][103][104][105]107 Since our computations will utilize IBM devices and performance is device-specific, …”

“…In the literature, the closest reference points are VQE computations, as hardware results on PQE have not yet been reported. Some papers have reported VQE ground-state energies or properties. ,,− Other studies have used VQE as an ingredient of methods to compute excited-state energies and properties, ,,,,,,,,− linear response properties, , molecular dynamics, and vibrational eigenstates, , while yet more studies have used VQE as an active space solver for a dynamical correlation or embedding method. ,− Of particular interest to this paper are those VQE computations that report the effectiveness of different error mitigation schemes, ,,,,,,,,,,,,,,,, or that are performed on IBM devices. ,,,− ,,…”