Hybrid Quantum-Classical Eigensolver Without Variation or Parametric Gates

TL;DR

This paper introduces a hybrid quantum-classical eigensolver that avoids variational and parametric gates, using effective Hamiltonian projection and classical diagonalization, suitable for near-term quantum devices.

Contribution

It presents a novel method for eigenenergy computation that combines quantum measurements with classical diagonalization without requiring variational circuits.

Findings

Accurately computed ground and excited states of molecules.

Demonstrated hardware implementation on IBM quantum devices.

Results agree well with exact solutions.

Abstract

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground sate and excited states of BeH$_2$ and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H$_2$ molecule.