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Ab initio electronic excited state calculations are necessary for thequantitative study of photochemical reactions, but their accurate computationon classical computers is plagued by prohibitive scaling. The VariationalQuantum Deflation (VQD) is an extension of the Variational Quantum Eigensolver(VQE) for calculating electronic excited state energies, and has the potentialto address some of these scaling challenges using quantum computers. However,quantum computers available in the near term can only support a limited numberof circuit operations, so reducing the quantum computational cost in VQDmethods is critical to their realisation. In this work, we investigate the useof adaptive quantum circuit growth (ADAPT-VQE) in excited state VQDcalculations, a strategy that has been successful previously in reducing theresource for ground state energy VQE calculations. We also invoke spinrestrictions to separate the recovery of eigenstates with different spinsymmetry to reduce the number of calculations and accumulation of errors. Wecreated a quantum eigensolver emulation package - Quantum Eigensolver Buildingon Achievements of Both quantum computing and quantum chemistry (QEBAB) - fortesting the proposed adaptive procedure against two VQD methods that usefixed-length quantum circuits. For a lithium hydride test case we found thatthe spin-restricted adaptive growth variant of VQD uses the most compactcircuits by far, consistently recovers adequate electron correlation energy fordifferent nuclear geometries and eigenstates while isolating the singlet andtriplet manifold. This work is a further step towards developing techniqueswhich improve the efficiency of hybrid quantum algorithms for excited statequantum chemistry, opening up the possibility of exploiting real quantumcomputers for electronic excited state calculations sooner than previouslyanticipated.

physical chemistry chemical physics/pccp. physical chemistry chemical physics

Molecular Excited State Calculations with Adaptive Wavefunctions on a  Quantum Eigensolver Emulation: Reducing Circuit Depth and Separating Spin  States