A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

Abstract

We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H 6 , H 8 , and BeH 2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

Near-optimal ground state preparation

“…However the exact complexity of this algorithm is not clear because it relies on a proper choice of ansatz and needs to solve a non-convex optimization problem. Other such algorithms include quantum imaginary-time evolution, quantum Lanczos [37], and quantum filter diagonalization [40,44]. Their complexities are either quasi-polynomial or unknown.…”

A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers

“…Our strategies to compile gradients can be done entirely in the fermionic representation making it independent of the used qubit mapping. The developed techniques combined with Tequilas automatic differentiation framework provide a testbed for quantum chemistry on quantum computers where new ideas, like low-depth approaches based on pair-natural orbitals 55 or Krylov subspaces, 74,75 can be prototyped and demonstrated in a blackboard fashion. Our implementation provides an easy to use, automatically differentiable framework for unitary-coupled cluster, that leverages state of the art high performance simulators 58,59 and is ready for emerging quantum computers.…”

Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems

“…Our method also uses the optimal filtering polynomial, which solves a minimax problem as recorded in Lemma 2. There are several other hybrid quantum-classical algorithms to compute ground state energy and to prepare the ground state [47,55], whose computational complexities are not yet analyzed and therefore we do not make comparisons here.…”