Abstract
Bayesian phase difference estimation (BPDE) is a controlled-time evolution-free quantum algorithm that is capable of computing the energy difference between two electronic states directly, without inspecting the total energies of individual states.
Highlights
University Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan † Electronic supplementary information (ESI) available: Definitions of quantum gates, computational conditions for quantum chemical calculations, quantum circuits for the state preparations and controlled-Excit operations, numerical quantum circuit simulations for the Bayesian phase difference estimation (BPDE) and Bayesian phase estimation (BPE) algorithms, and Trotter decomposition error analysis
As we demonstrated in the preceding paper, direct calculations of vertical ionisation energies are possible by using the BxB algorithm.[45]
We examined the Bayesian phase difference estimation (BPDE) algorithm, which is a general quantum algorithm capable of computing the difference of two eigenphases of unitary operators, in several cases of direct calculations of energy gaps including vertical ionisation energies, singlet– triplet energy gaps, and vertical excitation energies
Summary
Design novel compounds and materials with valuable functionalities. quantum computers allow us to calculate full-CI energy in polynomial time, by utilising a quantum phase estimation (QPE) algorithm.[10]. The direct calculation of energy gaps between two electronic states on quantum computers is one of the plausible and promising solutions.[44,45,46,47] Note that several approaches to calculate excitation energies have been proposed in VQE, such as subspace expansion,[48] subspace search VQE,[49] using orthogonality of wave functions,[50] and so on. We proposed a quantum algorithm ‘‘Bayesian exchange coupling parameter calculator with broken-symmetry wave functions (BxB)’’,45 that is capable of directly computing the energy difference between two electronic states belonging to different spin quantum numbers.
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