VQE

What will a quantum computer's first real job be? Probably chemistry, not code-breaking. VQE, the Variational Quantum Eigensolver, is the algorithm built for today's noisy machines.

What this Short covers:

1. Drug and battery design need a molecule's lowest energy, and exact answers get impossibly expensive as molecules grow.
2. VQE splits the work: the quantum chip prepares a guess and measures its energy.
3. A normal computer tunes the parameters ("turns the dials") and the loop repeats, lower and lower.
4. Analogy: walking downhill in fog. Each step you only check whether you went lower, so you can get stuck.
5. VQE first ran in 2014 on a tiny molecule (HeH+). It runs on today's quantum hardware, but no proven advantage over classical chemistry yet.

Fine print: "lowest-energy shape" = VQE returns the energy at a given shape; the shape is found by scanning shapes for the lowest energy (the 2014 experiment did exactly this for HeH+, the helium hydride ion, on a photonic chip). "Code-breaking" isn't happening today: the best 2025 estimate for breaking RSA-2048 is about 1 million noisy qubits running for about a week. 2014 = first VQE run, not the first quantum chemistry ever (H2 was done with phase estimation in 2010). "No proven win yet" = no demonstrated advantage over classical chemistry methods, not "VQE doesn't work". The fog line is an analogy for local search: it can get stuck.

1. Peruzzo et al., "A variational eigenvalue solver on a photonic quantum processor", Nat. Commun. 5, 4213 (2014)arxiv.org
2. Kandala et al., "Hardware-efficient variational quantum eigensolver for small molecules", Nature 549, 242 (2017)arxiv.org
3. Tilly et al., "The Variational Quantum Eigensolver: a review", Physics Reports (2022)arxiv.org
4. Lee et al., "Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry", Nat. Commun. 14, 1952 (2023)arxiv.org
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