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Variational quantum eigensolver (VQE) is a hybrid quantum-classical techniquethat leverages noisy intermediate scale quantum (NISQ) hardware to obtain theminimum eigenvalue of a model Hamiltonian. VQE has so far been used to simulatecondensed matter systems as well as quantum chemistry of small molecules. Inthis work, we employ VQE methods to obtain the ground-state energy ofLiCoO$_2$, a candidate transition metal oxide used for battery cathodes. Wesimulate Li$_2$Co$_2$O$_4$ and Co$_2$O$_4$ gas-phase models, which representthe lithiated and delithiated states during the discharge and the charge of theLi-ion battery, respectively. Computations are performed using a statevectorsimulator with a single reference state for three different trialwavefunctions: unitary coupled-cluster singles and doubles (UCCSD), unitarycoupled-cluster generalized singles and doubles (UCCGSD) and k-unitary paircoupled-cluster generalized singles and doubles (k-UpCCGSD). The resources interms of circuit depth, two-qubit entangling gates and wavefunction parametersare analyzed. We find that the k-UpCCGSD with k=5 produces results similar toUCCSD but at a lower cost. Finally, the performance of VQE methods isbenchmarked against the classical wavefunction-based methods, such ascoupled-cluster singles and doubles (CCSD) and complete active spaceconfiguration interaction (CASCI). Our results show that VQE methodsquantitatively agree with the results obtained from CCSD. However, thecomparison against the CASCI results clearly suggests that advanced trialwavefunctions are likely necessary to capture the multi-referencecharacteristics as well as the correlations emerging from high-level electronicexcitations.

Towards the simulation of transition-metal oxides of the cathode battery materials using VQE methods