Efficient simulation of quantum chemistry problems in an enlarged basis set

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 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.