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Variational Quantum Eigensolver (VQE) provides a lucrative platform todetermine molecular energetics in near-term quantum devices. While the VQE istraditionally tailored to determine the ground state wavefunction with theunderlying Rayleigh-Ritz principle, the access to specific symmetry-adaptedexcited states remains elusive. This often requires high depth circuit oradditional ancilla qubits along with prior knowledge of the ground statewavefunction. We propose a unified VQE framework that treats the ground andexcited states in the same footings. With the knowledge of the irreduciblerepresentations of the spinorbitals, we construct a multi-determinantalreference that is adapted to a given spatial symmetry where additionally, thedeterminants are entangled through appropriate Clebsch-Gordan coefficients toensure the desired spin-multiplicity. We introduce the notion of totallysymmetric, spin-scalar unitary which maintains the purity of the reference ateach step of the optimization. The state-selectivity safeguards the methodagainst any variational collapse while leading to any targeted low-lyingeigenroot of arbitrary symmetry. The direct access to the excited statesshields our approach from the cumulative error that plagues excited statecalculations in a quantum computer and with few parameter count, it is expectedto be realized in near-term quantum devices.

Ground or Excited State: a State-Specific Variational Quantum Eigensolver for Them All