Robust determination of molecular spectra on a quantum processor

TL;DR

This paper demonstrates a hybrid quantum-classical approach using VQE and Quantum Subspace Expansion to accurately determine the full energy spectrum of H2, mitigating errors and optimizing quantum resource use.

Contribution

It introduces a novel Quantum Subspace Expansion method to enhance VQE, enabling accurate spectral calculations and error mitigation on quantum processors.

Findings

Successfully calculated the H2 energy spectrum with near chemical accuracy.

Demonstrated error mitigation capabilities of the Quantum Subspace Expansion.

Showed potential for scaling quantum algorithms without complex error correction.

Abstract

Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results in the efficient calculation of Hamiltonian ground states--an important eigenvalue problem in the physical sciences that is often classically intractable. In these protocols, a Hamiltonian is parsed and evaluated term-wise with a shallow quantum circuit, and the resulting energy minimized using classical resources. This reduces the number of consecutive logical operations that must be performed on the quantum hardware before the onset of decoherence. We demonstrate a complete implementation of the Variational Quantum Eigensolver (VQE), augmented with a novel Quantum Subspace Expansion, to calculate the complete energy spectrum of the H2 molecule with near chemical accuracy. The QSE also enables the mitigation of incoherent errors, potentially allowing the implementation of larger-scale algorithms without complex quantum error correction techniques.