Short answer: The variational quantum eigensolver (VQE) uses a parametrized quantum circuit and a classical optimizer to estimate a molecule's ground-state energy. A 2017 Nature experiment ran it on a quantum processor with a hardware-efficient trial state for molecules up to BeH2, and a 2022 preprint studied how noise degrades it for the hydrogen molecule. These are small-scale research demonstrations.
What is VQE?
The 2022 arXiv abstract describes VQE as a hybrid quantum-classical algorithm that calculates the ground state energy of a Hamiltonian using parametrized quantum circuits, with a classical optimizer to find optimal parameter values. The authors call it the most prominent algorithm for chemistry simulations on noisy intermediate-scale devices.
What did the 2017 hardware experiment do?
The 2017 Nature abstract says experimental implementations of electronic-structure problems had been restricted to molecules involving only hydrogen and helium. The authors demonstrate the experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, determining the ground-state energy for molecules of increasing size, up to BeH2. They combine a variational eigensolver with efficiently prepared trial states tailored to the interactions available in their processor, a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. They also apply it to an antiferromagnetic Heisenberg model in an external field, to show flexibility. The remainder of the abstract was cut off in the page text we read, so nothing further is claimed.
What did the 2022 noise study find?
The preprint, which may not have been peer reviewed, asks how far hardware noise can degrade VQE. Using the hydrogen molecule as the example, the authors first compare a set of optimizers and find NFT to be the most suitable one. They then quantify the effect of different noise sources by systematically increasing their strength, varying noise intensity around values common to superconducting devices, and use curve fitting to model the relationship between the energy values obtained and the noise magnitude. Because the amount of noise depends strongly on circuit architecture, they repeat the studies for different ansatzes, including hardware-efficient and chemistry-inspired ones. The abstract reports no numerical results.
What about the 2025 practical study?
A 2025 Journal of Chemical Theory and Computation paper is titled "Ground-State Energy Estimation on Current Quantum Hardware through the Variational Quantum Eigensolver: A Practical Study". Its abstract was not readable in the page text, so nothing is claimed from it beyond the title.
Why does the ansatz choice matter?
The two readable papers both point at the same trade-off. The 2017 authors tailor the trial states to the interactions the processor already has, so circuits stay short. The 2022 authors say the amount of noise in a circuit depends highly on its architecture, which is why they test several ansatzes. Together they suggest that on noisy hardware the circuit design and the optimizer both affect the result, though neither abstract gives a head-to-head ranking, and this post does not invent one.
How to read this
The two readable studies answer different questions: one shows VQE running on hardware for slightly larger molecules, the other shows how noise strength affects accuracy in simulation. Neither claims an advantage over classical chemistry methods in its abstract. This post is based on abstracts, and full texts were not checked. It makes no claim about products.
FAQ
What is a hardware-efficient ansatz?
A trial state built from operations that the processor provides directly, as in the 2017 paper's tailored trial states.
How large a molecule was run in 2017?
Up to BeH2, with up to six qubits and over one hundred Pauli terms.
Which optimizer did the 2022 study favour?
NFT, for the hydrogen molecule case.
Does VQE beat classical methods?
Neither abstract claims that.
All field notes