Further Reading: Quantum Chemistry with VQE

Tagged Tier 1 (confident it exists and recommended) and Tier 2 (real and worth seeking, but verify the current version or URL).

Quantum chemistry is the oldest proposed application of quantum computers and the best documented, so this list is unusually solid — and unusually worth reading critically, because the field's own review literature has become notably more careful in the last few years.

The foundational papers

• Peruzzo, McClean, Shadbolt, Yung, Zhou, Love, Aspuru-Guzik, and O'Brien, "A variational eigenvalue solver on a photonic quantum processor" (2014), Nature Communications 5, 4213. The paper that introduced VQE. Read it for the motivation — the algorithm was designed specifically to fit devices that cannot run phase estimation, which is the constraint §36.8 says still binds. Tier 1.
• Aspuru-Guzik, Dutoi, Love, and Head-Gordon, "Simulated quantum computation of molecular energies" (2005), Science 309, 1704. The phase-estimation route, from before VQE existed. Worth reading after §36.7, because it is the algorithm the arithmetic points back toward. Tier 1.
• McClean, Romero, Babbush, and Aspuru-Guzik, "The theory of variational hybrid quantum-classical algorithms" (2016), New Journal of Physics 18, 023023. The framework paper. Tier 1.

Mappings

• Jordan and Wigner (1928), the original transformation, and Bravyi and Kitaev, "Fermionic quantum computation" (2002), Annals of Physics 298, 210. §36.3's two mappings. Read Bravyi–Kitaev for what it actually claims — the $\mathcal{O}(\log n)$ locality — and notice that it is a claim about weight, not about term count. The chapter measured them giving identical 631-term Hamiltonians. Tier 1.
• Seeley, Richard, and Love, "The Bravyi-Kitaev transformation for quantum computation of electronic structure" (2012), Journal of Chemical Physics 137, 224109. The careful comparison, and the source most often cited for the claim §36.3 tests. Tier 1.
• Work on qubit tapering and $\mathbb{Z}_2$ symmetry reduction. Removes qubits by exploiting particle number and spin symmetries — a real reduction that composes with everything in §36.7's mitigation table. Tier 2.

Active spaces — the part with the least literature and the most consequence

This is the thinnest section of the list, which is itself §36.4's point.

• Any good quantum-chemistry textbook's treatment of CASSCF and active-space selection — Helgaker, Jørgensen, and Olsen, Molecular Electronic-Structure Theory, is the standard reference. Read it for how much judgment is involved. Active-space selection is a craft skill in computational chemistry with decades of accumulated practice, and the quantum computing literature frequently treats it as a preprocessing step. Tier 1.
• Literature on automated active-space selection (entropy-based, natural-orbital-occupation-based). The attempt to make the judgment reproducible. Tier 2 — active, and unsettled.
• Chapter 26 §26.6's seam problem. Case Study 36.1's failure lives in the boundary between two correct pieces of work, and that is a software-engineering finding, not a chemistry one. Tier 1.

The classical baseline you have to beat

Read at least one of these before claiming any quantum chemistry result.

• Bartlett and Musiał, "Coupled-cluster theory in quantum chemistry" (2007), Reviews of Modern Physics 79, 291. CCSD(T), the gold standard §36.6 names. Read it for what "gold standard" means — it is a specific empirical claim about chemical accuracy on main-group chemistry, not a general one, and knowing where it fails is knowing where the quantum case lives. Tier 1.
• Chan and Sharma, "The density matrix renormalization group in quantum chemistry" (2011), Annual Review of Physical Chemistry 62, 465. DMRG, and the structure assumptions that bound it. Tier 1.
• Simons Collaboration benchmark papers on strongly-correlated systems — the multi-method comparisons on models like the Hubbard model and FeMoco. The most useful thing in this list for calibrating claims, because they show many strong classical methods disagreeing with each other on exactly the problems quantum computing proposes to solve. Tier 1.

Resource estimates — the honest ones

• Reiher, Wiebe, Svore, Wecker, and Troyer, "Elucidating reaction mechanisms on quantum computers" (2017), PNAS 114, 7555. The FeMoco resource estimate, and the paper that made quantum chemistry resource estimation a serious subfield. Tier 1.
• Von Burg, Low, Häner, Steiger, Reiher, Roetteler, and Troyer, "Quantum computing enhanced computational catalysis" (2021), Physical Review Research 3, 033055. A much-improved estimate for a related problem. Read the two together — the improvement between them is large, real, and made of exactly the constant factors §36.7's mitigation table is built from. Tier 1.
• Gonthier, Radin, Buda, Doskocil, Abuan, and Romero, "Measurements as a roadblock to near-term practical quantum advantage in chemistry" (2022), Physical Review Research 4, 033154. §36.7's argument, made properly and in detail by people who wanted the answer to come out the other way. If you read one paper from this chapter, read this one. Tier 1.

The critical literature

• Lee, Huggins, Head-Gordon, and Whaley, and related work on whether quantum computers will deliver exponential advantage in quantum chemistry. A careful analysis concluding the evidence for exponential advantage on ground-state chemistry is weaker than commonly assumed. Tier 1.
• Chapter 24 §24.7 and Chapter 21 §21.7. The book's own earlier statements of the shot budget and the baseline problem. Worth re-reading now that they have a molecule attached. Tier 1.

Software

• PennyLane's qml.qchem module — what this chapter's examples use. Tier 1.
• PySCF — the classical quantum-chemistry package most quantum workflows call for integrals, and the tool you would use for the CCSD(T) baseline. Tier 1.
• OpenFermion — Google's library for fermionic mappings and Hamiltonian manipulation. Tier 1.
• Qiskit Nature — IBM's chemistry stack. Tier 2 — it has been restructured more than once; check which version the tutorial you are reading targets.

Backward references

• Chapter 24 — VQE itself, the shot budget, and the three barriers this chapter prices.
• Chapter 21 §21.7 — benchmarking against the method nobody uses.
• Chapter 35 — classical shadows, which appear in §36.7's mitigation table.
• Chapter 22 — the algorithm §36.8 points back toward.

Forward references

• Chapter 37 — the same accounting applied to combinatorial optimization, where the classical baselines are stronger still and far better benchmarked.

Where to go next. If one thing: Gonthier et al. on measurements as a roadblock. It is §36.7's argument done rigorously, by authors at a quantum computing company, and its conclusions are sober in a way that is worth seeing from inside the field.

If two: add the Simons Collaboration benchmark papers. Watching several excellent classical methods disagree with each other on FeMoco-scale problems is the single best calibration available for what "the classical baseline" actually means — and it makes both the difficulty and the opportunity concrete in a way no review article does.

Then Chapter 37, where the baseline problem gets harder, because classical optimization has fifty years of engineering behind it and publishes its benchmarks.