Abstract
Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.
Highlights
Since the discovery of a polynomial quantum algorithm for factorization,[1] other quantum algorithms that provide exponential speedup over their classical counterparts have been found
A multi-reference configuration interaction (MRCI)—truncated CI—calculation based on an a multiconfigurational self-consistent field (MCSCF) wave function can sometimes provide results within chemical accuracy, but with much less computational work than full configuration interaction (FCI) due to the smaller Hilbert space associated with the calculation
Using an MCSCF wave function as the initial guess can deal with the strong interaction between states straightforwardly
Summary
Since the discovery of a polynomial quantum algorithm for factorization,[1] other quantum algorithms that provide exponential speedup over their classical counterparts have been found. We show that by improving the quality of the trial wave function, the proposed algorithm yields substantially higher success probabilities than by employing the 5388 | Phys. The use of a MCSCF wave function simultaneously reduces the amount of quantum computing resources needed and extends the range of reliable quantum computations to excited states and treacherous regions of the potential energy surface. We introduce a more compact mapping technique for molecules by employing symmetry properties. This approach reduces the computational resources for representing the wave function on a quantum computer and avoids the state crossing-problem.
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