Orbital optimized unitary coupled cluster theory for quantum computer

Abstract

We propose an orbital optimized method for unitary coupled cluster theory (OO-UCC) within the variational quantum eigensolver (VQE) framework for quantum computers. OO-UCC variationally determines the coupled cluster amplitudes and also molecular orbital coefficients. Owing to its fully variational nature, first-order properties are readily available. This feature allows the optimization of molecular structures in VQE without solving any additional equations. Furthermore, the method requires smaller active space and shallower quantum circuits than UCC to achieve the same accuracy. We present numerical examples of OO-UCC using quantum simulators, which include the geometry optimization of water and ammonia molecules using analytical first derivatives of the VQE.

A state-averaged orbital-optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states

“…However, a quantum computer only improves the solution of a chemistry problem within the active space; it targets E CASCI 0 (or E CASSCF 0 when orbital-optimization is considered), and not the true ground state energy E 0 . Designing relevant active spaces is key to finding useful applications of quantum devices within the field of chemistry, and is an active field of research [26,29,47,[97][98][99][100][101][102][103][104][105].…”

“…two-states example will be considered in the following to illustrate the different steps of the method. SA-OO-VQE can however be straightforwardly generalized to any number of states, as well as to the particular case of a single state (thus leading to 'state-specific'-OO-VQE [26,29]).…”

“…While computing the ground state of a molecule gives information about the equilibrium geometries and transition states (essential to determine the energy barrier of a chemical reaction), several chemical reactions also depend on excited states (see for instance reference [21] and references therein). To date, most variational quantum algorithms have been specifically designed to prepare ground states [1,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] while excited state calculations have received less attention until only recently [23,[38][39][40][41][42][43][44][45][46][47][48][49]. It should be noted that some excited states can also be obtained as the lowest energy solutions of a given set of symmetries [50][51][52][53][54][55].…”

Towards Accurate Description of Chemical Reaction Energetics by Using Variational Quantum Eigensolver: A Case Study of the C2v Quasi-Reaction Pathway of Beryllium Insertion to H2 Molecule

“…So far, a wide variety of theoretical developments have been made in VQE. For example, development of new ansatzes, [16][17][18][19][20][21][22][23][24] qubit reductions by utilizing natural orbitals, 25,26 extension of ansatzes for larger systems, [27][28][29][30] introduction of error mitigation techniques, [31][32][33] spatial and spin symmetry adaptations, [34][35][36][37] reduction of the number of qubit measurements, [38][39][40][41] applications for electronic excited states, [42][43][44][45] and so on. Proof-of-principle demonstrations on quantum devices were also reported.…”

Spin-projection for quantum computation: A low-depth approach to strong correlation

“…It is worth noting that the orbital basis is still that of RHF, whereas UHF is expressed by a linear combination of excited determinants from | RHF -the Thouless theorem [41]. We can extend this scheme to any other VQE Ansatz including UCC without loss of generality [42][43][44][45]. For UCCSD, however,T 1 andK play similar roles and are considered largely redundant.…”