View article

Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using N Gaussian orbitals, leading to Hamiltonians with O (N 4) second-quantized terms. We avoid this overhead and extend methods to condensed phase materials by utilizing a dual form of the plane wave basis which diagonalizes the potential operator, leading to a Hamiltonian representation with O (N 2) second-quantized terms. Using this representation, we can implement single Trotter steps of the Hamiltonians with linear gate depth on a planar lattice. Properties of the basis allow us to deploy Trotter-and Taylor-series-based simulations with respective circuit depths of O (N 7/2) and O (N 8/3) for fixed charge densities. Variational algorithms also require significantly fewer measurements in this basis, ameliorating …