Orthogonality catastrophe on quantum devices

I recently read Walter Kohn's Nobel Lecture on density functional theory. It's an accessible introduction to a method that is hugely important for materials science. Sec. IIC makes some remarks on the orthogonality catastrophe, arguing that many-body wave functions are not meaningful for more than ~1000 particles because the exponential growth of the Hilbert space makes any approximation to a desired state have an exponentially-vanishing overlap with that state.

Quantum computational chemistry is promoted as one of the most promising potential applications of quantum computers, offering an exponential speed-up compared to classical algorithms. But there is a big caveat hidden behind these claims: Algorithms exhibiting rigorous speed-ups such as quantum phase estimation require as an input an approximation to the ground state wavefunction. The overlap with the ground state determines the success probability of the algorithm. Thus, computing the ground state energy of a large many body system will require an exponentially good approximation to the corresponding wavefunction, potentially killing the quantum speed-up.

Some experts in quantum chemistry considered this issue in an arXiv preprint a few years ago: Postponing the orthogonality catastrophe: efficient state preparation for electronic structure simulations on quantum devices. There the authors estimated that efficiently-computable approximations such as Hartee-Fock wavefunctions may provide a sufficiently good overlap for moderate system sizes of up to 40 electrons that are already beyond the reach of classical computations. But it seems quantum computers won't be a magic bullet for larger systems involving hundreds of electrons; it will still be necessary to use physical insight to decompose large systems into smaller tractable subsystems. 

 

It is curious that this study has only received 18 citations to date and was not published in a journal - there must be a story behind that...