Abstract
Quantum computers have an enormous impact on quantum chemical calculations. Approaches to calculate the energies of atoms and molecules on quantum computers by utilizing quantum phase estimation (QPE) and the variational quantum eigensolver (VQE) have been well documented, and dozens of methodological improvements to decrease computational costs and to mitigate errors have been reported until recently. However, the possible methodological implementation of observables on quantum computers such as calculating the spin quantum numbers of arbitrary wave functions, which is a crucial issue in quantum chemistry, has been discussed less. Here, we propose a quantum circuit to simulate the time evolution of wave functions under an S2 operator, exp(-iS2t)|Ψ, and integrate it into the QPE circuit enabling us to determine the spin quantum number of the arbitrary wave functions. We demonstrate that the spin quantum numbers of up to three spins can be determined by only one qubit measurement in QPE.
Highlights
Quantum computers have an enormous impact on quantum chemical calculations
The results of quantum circuit simulations of the time evolution exp(ÀiS2t)|Ci for the two- and three-spin systems starting from |Ci = |abi and |aabi are depicted in Fig. 2 and 3, respectively, and several simulations starting from other initial
We have developed a quantum circuit for the time evolution of wave functions under the S2 operator, and we use it to determine the spin quantum number of wave functions by means of quantum phase estimation (QPE), illustrating that the quantum circuit approach underlain by quantum algorithms affords extreme efficiency in evaluating observables, which is a seemingly intractable problem
Summary
Designs, elucidation of catalytic mechanisms of enzymes, and so on. The ideas to use computers built of quantum mechanical elements to simulate quantum mechanics were proposed by Feynman in the early 1980s.29 An approach to calculate full-CI energy was proposed by Aspuru-Guzik and coworkers in 20052 by using quantum phase estimation (QPE).[30]. An approach to calculate full-CI energy was proposed by Aspuru-Guzik and coworkers in 20052 by using quantum phase estimation (QPE).[30] In the QPE-based full-CI calculations, the time evolutions of the wave function |Ci using a Hamiltonian are simulated and an energy eigenvalue E is extracted as a phase f, as given in eqn (1), using inverse quantum Fourier transformation.[31] exp(ÀiHt)|Ci = exp(ÀiEt)|Ci = exp(Ài2pf)|Ci (1). The determination of spin quantum numbers is an important task, especially for the study of open shell systems. Molecules and materials having open shell electronic structures play an important role in chemistry and related fields: molecules undergoing covalent bond cleavages, molecular magnets and molecular spin devices, transition metal complexes in active centers of enzymes, etc., and the study of open shell electronic structures is crucial in current chemistry and condensed matter physics. We propose a quantum circuit that allows us to efficiently simulate the time evolution of wave functions under the S2 operator to calculate the S2 eigenvalues of arbitrary wave functions by using QPE
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