Generalized unitary coupled cluster excitations for multireference molecular states optimized by the variational quantum eigensolver

Abstract

The variational quantum eigensolver (VQE) algorithm, designed to calculate the energy of molecular ground states on near‐term quantum computers, requires specification of symmetries that describe the system, for example, spin state and number of electrons. This opens the possibility of using VQE to obtain excited states as the lowest‐energy solutions of a given set of symmetries. In this paper, the performances of various unitary coupled cluster (UCC) ansätze applied to VQE calculations on excited states are investigated using quantum circuits designed to represent single reference and multireference wavefunctions to calculate energy curves with respect to variations in the molecular geometry. These ansätze include standard Unitary Coupled Cluster Singles and Doubles (UCCSD), as well as modified versions of Unitary Coupled Cluster Generalized Singles and Doubles (UCCGSD) and k‐UpCCGSD, which are engineered to tackle excited states without undesired spin symmetry crossover to lower states during VQE optimization. These studies are carried out on a range of systems, including H2, H3, H4, NH, OH+, CH2, and , covering examples of spin singlet, doublet, and triplet molecular ground states with single and multireference excited states. In most cases, our calculations are in excellent agreement with results from full‐configuration interaction calculations on classical machines, thus showing that the VQE algorithm is capable of calculating the lowest excited state at a certain symmetry, including multireference closed‐ and open‐shell states, by setting appropriate restrictions on the excitations considered in the cluster operator and appropriate constraints in the qubit register encoding the starting mean field state.

A quantum computing view on unitary coupled cluster theory

“…been applied in ref. 117 and 118. While the former rather focuses on benefits of the therein proposed non-orthogonal VQE, ref.…”

“…While the former rather focuses on benefits of the therein proposed non-orthogonal VQE, ref. 118 applies the k -UpCCGSD for a thorough study of computing excited and ionised states. Their results are promising and findings about the performance of the k -UpCCGSD parametrisation itself are in alignment with what is described above.…”

A Quantum Computing View on Unitary Coupled Cluster Theory

“…been applied in Refs. [98,99]. While the former rather focuses on benefits of the therein proposed non-orthogonal VQE, Ref.…”

“…While the former rather focuses on benefits of the therein proposed non-orthogonal VQE, Ref. [99] applies the k-UpCCGSD for a thorough study of computing excited and ionised states. Their results are promising and findings about the performance of the k-UpCCGSD parametrisation itself are in alignment with what is described above.…”

Variational Quantum Eigensolver with Reduced Circuit Complexity

“…The variational quantum eigensolver (VQE) is one of the leading hybrid quantum-classical algorithms developed specifically to simulate molecular systems in their ground [11][12][13][14] and ultimately excited states [15][16][17][18][19][20]. In a typical VQE setup, a variational parameterized ansatz is used to represent the trial wave function prepared with a quantum circuit and the expectation value of the qubit Hamiltonian is measured.…”