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We present a stable and systematically improvable quantum Monte Carlo (QMC)approach to calculating excited-state energies, which we implement using ourfast randomized iteration method for the full configuration interaction problem(FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, ourapproach, which is an asymmetric variant of subspace iteration, avoids the useof dot products of random vectors and instead relies upon trial vectors tomaintain orthogonality and estimate eigenvalues. By leveraging recent advances,we apply our method to calculate ground- and excited-state energies of stronglycorrelated molecular systems in large active spaces, including the carbon dimerwith 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metalcomplex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority ofthese test cases, our approach yields total excited-state energies that agreewith those from state-of-the-art methods -- including heat-bath CI, the densitymatrix renormalization group approach, and FCIQMC -- to within sub-milliHartreeaccuracy. In all cases, estimated excitation energies agree to within about 0.1eV.

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification