Efficient Simulation of Quantum Chemistry Problems in an Enlarged Basis Set - Maxine Luo; J. Ignacio Cirac (PRX Quantum)
We propose a quantum algorithm to simulate the dynamics in quantum chemistry problems. It is based on adding fresh qubits at each Trotter step, which enables a simpler implementation of the dynamics in the extended system. After each step, the extra qubits are recycled, so that the whole process accurately approximates the correct unitary evolution. A key ingredient of the approach is an isometry that maps a simple diagonal Hamiltonian in the extended system to the original one, and we give a procedure to compute this isometry. We estimate the error at each time step, as well as the number of gates, which scales as O(N^{2}), where N is the number of orbitals. We illustrate our results with three examples: the hydrogen chain, small molecules, and the FeMoco (Fe_{7}MoS_{9}C) molecule. In the hydrogen chain and the hydrogen molecule, we observe that the error scales in the same way as the Trotter error. For FeMoco, we estimate the number of gates in a fault-tolerant setup.