Excited state calculations using variational quantum eigensolver with spin-restricted ansätze and automatically-adjusted constraints

Abstract

The ground and excited state calculations at key geometries, such as the Frank–Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC does not require the pre-determination of constraint weights and has the potential to describe smooth potential energy surfaces. To validate this strategy, we performed the excited state calculations at the FC and CI geometries of ethylene and phenol blue at the complete active space self-consistent field (CASSCF) level of theory, and found that the energy errors were at most 2 kcal mol−1 even on the ibm_kawasaki device.

Complete Active Space Methods for NISQ Devices: The Importance of Canonical Orbital Optimization for Accuracy and Noise Resilience

“…The idea of a hybrid orbital optimization routine has been explored first by Takeshita et al, and a fully hybrid quantum-classical CASSCF has been reported by Tilly et al where the 1 and 2 body RDMs were sampled independently to mitigate their error and noncanonical orbitals were used. Other quantum multi-configurational SCF implementations have been also reported in the literature. ,− Nevertheless, to our knowledge, no comparison has been made with the results coming from an orbital-optimized wave function in the quantum measurement after VQE. We have implemented a CASSCF routine (Figure ) that evaluates the 1 and 2 body RDMs as auxiliary operators to the Hamiltonian and uses canonical CASSCF orbitals (and thus in particular natural orbitals within the active space) by default.…”

Applications of noisy quantum computing and quantum error mitigation to “adamantaneland”: a benchmarking study for quantum chemistry

“…Notable recent progress includes the development of new variational ansa ¨tze, [34][35][36] adaptations of spatial and spin symmetries, 37 optimizing qubit measurement efficiency, [38][39][40][41] techniques for reducing qubit resources, 42,43 error mitigation strategies, 44,45 and development of quantum simulators. 46 Researchers are actively leveraging these algorithmic advancements to assess the potential of VQE in studying molecular systems, including applications related to electronic ground states, [47][48][49] excited states, [50][51][52] and vibrations. [53][54][55] Most VQE applications in chemistry, including proof-ofprinciple demonstrations or benchmarking studies, have focussed on determining absolute energies and potential energy curves resulting from bond dissociation or spatial deformations.…”

“…Notable recent progress includes the development of new variational ansätze, 34–36 adaptations of spatial and spin symmetries, 37 optimizing qubit measurement efficiency, 38–41 techniques for reducing qubit resources, 42,43 error mitigation strategies, 44,45 and development of quantum simulators. 46 Researchers are actively leveraging these algorithmic advancements to assess the potential of VQE in studying molecular systems, including applications related to electronic ground states, 47–49 excited states, 50–52 and vibrations. 53–55…”

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. ,,,− ,,…”