The variational quantum eigensolver for chemistry: promise and limits

Short answer: The variational quantum eigensolver (VQE) is a hybrid method that uses a quantum computer and a classical optimizer to estimate the lowest energy of a molecule or other system. Reviews call it one of the most promising near-term applications. Benchmarks say the picture is mixed: one study found that all tested variants can hardly reach chemical accuracy at stretched bond lengths, and another found noisy hardware misestimates energies. This is research, and no quantum advantage is claimed here.

What VQE is

A review hosted by University College London says VQE was first developed by Peruzzo and colleagues in 2014. It uses the variational principle to compute the ground state energy of a Hamiltonian, a problem central to quantum chemistry and condensed matter physics. The review says conventional methods are constrained in accuracy by the exponential growth of the electronic wavefunction for many-electron systems, and that VQE may be used to model these wavefunctions in polynomial time. It adds that variational algorithms have been shown to present some degree of resilience to noise in quantum hardware.

What a 2022 benchmark found

An arXiv study benchmarked more than ten kinds of VQE ansatz, on systems of up to 30 qubits, comparing energy accuracy, runtime until convergence, and number of parameters. The authors say the ADAPT ansatz can give more accurate energy for small systems, below 14 qubits, but costs much more in computational resources. For larger molecules, they say UCCSD0 performs better. They also say all the tested ansatzes can hardly reach chemical accuracy at stretched bond lengths.

A hardware study on a small molecule

A study in the Journal of Chemical Theory and Computation ran VQE for the BeH2 molecule, comparing two ansatz types in noiseless and noisy simulation, and on a real IBM quantum computer. The authors report that one ansatz was reliable in ideal conditions, while the other was more robust to hardware noise. They also report that current devices optimized circuit parameters well despite misestimating the energies, and that energies evaluated by a simulator were a better guide to solution quality than the energies estimated on the quantum hardware. These are the authors' reports on one small molecule.

Why this matters

Together, the sources show why VQE is described as promising but unfinished. The UCL review also notes that finding a path through the literature has become overwhelming, with many methods promising to improve different parts of the algorithm. None of the sources claims that VQE has beaten the best classical methods on a chemistry problem of practical value.

What this does not tell you

This article summarises three research papers. It describes no product and makes no claim about commercial use. Results depend on the molecule, ansatz, noise and hardware used in each study.

FAQ

What is VQE?

A hybrid quantum-classical algorithm that uses the variational principle to compute the ground state energy of a Hamiltonian.

Why is it of interest for chemistry?

Conventional methods are limited by the exponentially growing electronic wavefunction, and a review says VQE may model these wavefunctions in polynomial time.

How accurate is it?

A 2022 benchmark says all tested ansatzes can hardly reach chemical accuracy at stretched bond lengths.

What happens on real hardware?

A study on BeH2 says devices optimized parameters effectively despite misestimating the simulated energies.

Has VQE shown a quantum advantage?

None of the sources used here claim that.