Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm

TLDR

Quantum processors with limited qubits and finite lifetimes require efficient management, and hybrid algorithms that combine classical resources have shown promise for efficiently computing Hamiltonian ground states, a key eigenvalue problem often intractable classically. The study implements a Variational Quantum Eigensolver augmented with a novel Quantum Subspace Expansion to compute the full energy spectrum of H₂ with near chemical accuracy. The authors use a shallow quantum circuit to evaluate Hamiltonian terms and minimize the resulting energy classically, implementing VQE with a Quantum Subspace Expansion to obtain the spectrum. The approach reduces the required consecutive logical operations before decoherence and the Quantum Subspace Expansion mitigates incoherent errors, enabling larger‑scale 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.