Subspace Selected Variational Quantum Configuration Interaction with a Partial Walsh Series

Abstract

Estimating the ground-state energy of a quantum system is one of the most promising applications for quantum algorithms. Here we propose a variational quantum eigensolver (VQE) \emph{Ansatz} for finding ground state configuration interaction (CI) wavefunctions. We map CI for fermions to a quantum circuit using a subspace superposition, then apply diagonal Walsh operators to encode the wavefunction. The algorithm can be used to solve both full CI and selected CI wavefunctions, resuling in exact and near-exact solutions for electronic ground states. Both the subspace selection and wavefunction \emph{Ansatz} can be applied to any Hamiltonian that can be written in a qubit basis. The algorithm bypasses costly classical matrix diagonalizations, which is advantageous for large-scale applications. We demonstrate results for several molecules using quantum simulators and hardware.

Figures (3)

• Figure 1: Circuit diagram for the preparation of $|\Psi\rangle$, where H is the Hadamard gate and $|a_W\rangle$ is the ancilla qubit for the Walsh Ansatz. The subspace selection step is performed either with the Dicke or quantum walk state preparation algorithm.
• Figure 2: Dissociation of (a) H$_2$ using the subspace selected Walsh approach on IBMQ's Torino processor (blue circles), Torino noisy simulator (green triangles) each with 1024 shots, and the FCI solution (line) and (b) linear H$_6$ with a statevector simulator (teal squares), CCSD(T) (orange triangles), and FCI (black line). The red dashed line denotes 1.6 mHa error, which is chemical accuracy.
• Figure 3: Dissociation of H$_2$ in 6-31G basis with a statevector simulator (teal squares), noiseless Aer simulator (purple diamonds), using an oversampled Walsh basis. The red dashed line denotes 1.6 mHa error, which is chemical accuracy.