Chemistry

The chemistry problem this library is prepared to talk about is the electronic ground-state energy of a molecule, or a small spin model standing in for one. It is not a survey of materials, drug discovery, or catalysis.

Aspuru-Guzik, Dutoi, Love, and Head-Gordon proposed computing molecular energies by quantum phase estimation: prepare an approximate ground state, simulate the Hamiltonian, and read the phase. The precision bound, and the eigenstate it assumes, are on that page. The simulation those controlled powers require is Hamiltonian simulation: product formulas, a truncated Taylor series, or qubitization, each with the access model written on that page. The coherence required by phase estimation is the constraint VQE was built to relax. Peruzzo, McClean, and coauthors replace the long evolution with a parameterized circuit and a classical optimizer, and they demonstrate the loop on HeH+ in a photonic experiment.

The theory paper to read next is McClean, Romero, Babbush, and Aspuru-Guzik (2016). The Hamiltonian is a sum of Pauli terms. Estimating the energy to a stated precision takes a number of state preparations that depends on those terms and on their variances. Unitary coupled cluster is their structured ansatz. A hardware-efficient ansatz is the alternative when the gate set is chosen to fit a device. Kandala and coauthors run that second style on a superconducting processor for LiH, BeH2, and a four-qubit Heisenberg model. Those molecules are the scale of the published demonstration this library will stand behind.

McClean, Boixo, Smelyanskiy, Babbush, and Neven (2018) show why a random layered ansatz is a poor default as the qubit count grows: gradients of a wide class of such circuits are exponentially small, so estimating a gradient to fixed precision takes exponentially many samples. Any chemistry roadmap that treats "deeper hardware-efficient layers" as the scaling plan has to answer that paper.

Classical quantum chemistry is the baseline the quantum experiments are measured against, even when this page does not re-derive coupled cluster or density-functional theory. A variational upper bound is only as useful as the gap to the best classical number on the same Hamiltonian. This stub exists to keep that comparison attached to the VQE page and to the papers, not to grow into a review.