Quantum subspace expansion algorithm for Green's functions

Understand

We present an algorithm to compute Green's functions on quantum computers for interacting electron systems, which is a challenging task on conventional computers.

• It uses a continued fraction representation based on the Lanczos method, where the wave functions are expanded as linear combination of basis states within a quantum subspace.
• While on conventional computers the cost of the computation grows exponentially with system size, limiting the method to small systems, by representing the basis states on a quantum computer one may overcome this exponential scaling barrier.
• We propose a two-level multigrid Trotter time evolution for an efficient preparation of the basis states in a quantum circuit, which takes advantage of the robustness of the subspace expansion against Trotter errors.