Carbon-capture chemistry on a quantum machine

Why classical DAC chemistry runs out of road

Direct air capture is, at heart, a materials problem. The active site of a sorbent — whether an amine-functionalised silica, a metal-organic framework (MOF), or a covalent organic framework — has to bind CO₂ at 420 ppm partial pressure, release it under a manageable temperature or pressure swing, survive humidity, and not degrade over thousands of cycles. The binding energy window is narrow: too weak and you do not capture; too strong and the regeneration energy eats your entire carbon budget.

To design a new sorbent in silico you need to know, accurately, the electronic structure of the binding pocket and the CO₂–framework interaction. Classical density functional theory (DFT) is the workhorse, but DFT functionals systematically under- or over-bind depending on the choice of exchange-correlation term, and they handle dispersion and strong correlation poorly. Coupled-cluster methods like CCSD(T) — the so-called "gold standard" — scale as roughly O(N⁷), which limits practical use to ~30-50 heavy atoms. A real MOF unit cell with an open metal site, a CO₂ guest, and a water co-adsorbate sits well past that ceiling.

This is the gap quantum carbon capture work is trying to close. Not because quantum machines will replace DFT for screening millions of candidate frameworks — they will not, in any near-term horizon — but because they can give you a reference-grade electronic-structure answer for the small, hard, strongly-correlated active-site cluster that DFT gets wrong.

The active-site embedding problem

The pragmatic architecture for DAC chemistry quantum workloads on a 100-qubit superconducting transmon machine is embedding. You take the full periodic MOF, treat the bulk with DFT or a tight-binding method, carve out an active region — typically the open metal centre, its first coordination sphere, the bound CO₂, and any nearby water — and hand that fragment to the quantum processor as a second-quantised Hamiltonian.

That fragment is still expensive. A Cu-paddlewheel site with a bound CO₂ in a minimal active space might require 20-30 spatial orbitals, which after Jordan-Wigner or Bravyi-Kitaev encoding maps to 40-60 logical qubits. On a 100-physical-qubit transmon device with no logical encoding yet, you are running variational quantum eigensolver (VQE) or its derivatives directly on physical qubits, which means you are bound by coherence and two-qubit gate fidelity — not just qubit count.

The honest engineering position: at 100 physical qubits with current transmon T₁/T₂ times in the 100-300 µs range and CZ gate errors around the 10^-3 level, you are doing reference calculations on small active spaces — perhaps 8-14 spatial orbitals — and using them to recalibrate classical multireference methods (CASSCF, NEVPT2, DMRG) for the larger problem. This is useful. It is not a replacement for classical chemistry; it is a calibration probe for it.

Algorithms that actually fit the hardware

The textbook quantum chemistry algorithm is quantum phase estimation (QPE), which gives you eigenvalues to arbitrary precision but demands deep circuits and fault tolerance we do not yet have. For a NISQ-era superconducting machine, the realistic algorithm stack is:

• VQE with hardware-efficient ansätze — shallow parameterised circuits matched to the heavy-hex connectivity, optimised classically. The known weakness is barren plateaus; we mitigate with layer-wise training and physically-motivated initialisations such as UCCSD-inspired ansätze truncated to fit the coupling map.
• ADAPT-VQE — grows the ansatz operator-by-operator from an operator pool, which gives more compact circuits at the cost of more measurement rounds.
• Quantum subspace expansion and quantum equation-of-motion — for excited states and response properties relevant to spectroscopic verification of binding modes.
• Sample-based quantum diagonalisation (SQD) and quantum-selected configuration interaction — recent approaches that use the quantum device to sample important determinants and finish the eigenvalue problem classically. These tolerate noise better than vanilla VQE.

All of these are addressable from the standard SDK ecosystem — Qiskit, PennyLane, Cirq — compiled to OpenQASM 3 and submitted through a queue. Ireland Quantum 100 will expose those interfaces directly; we are not building a parallel software stack.

Error mitigation and the noise budget

Before surface-code error correction is on the table — and at 100 physical qubits it is not — every chemistry result on the machine depends on error mitigation. The relevant techniques are zero-noise extrapolation (ZNE), probabilistic error cancellation (PEC), readout-error mitigation via calibration matrices, and dynamical decoupling on idle qubits. PEC in particular is expensive: sampling overhead grows exponentially with circuit volume, so you trade wall-clock time for accuracy.

For a CO₂-binding energy you typically want chemical accuracy — about 1 kcal/mol, or roughly 1.6 mHartree. That is a stringent target on a noisy device. The pragmatic answer for the first eighteen months of operation is relative energies: differences between bound and unbound states, or between two candidate frameworks, where systematic errors cancel. Absolute reference-grade numbers come later, with logical qubits.

What this means for MOF and amine sorbent design

Concretely, the MOF quantum workload we expect to run first looks like this. Take a known DAC-relevant framework family — open-metal-site MOFs in the M-MOF-74 series, diamine-appended variants, or amine-grafted mesoporous silicas. Build a cluster model of the binding site. Run a high-level classical multireference calculation. Run the same active space on the quantum device using ADAPT-VQE or SQD. Compare. Use the discrepancy to validate or correct the classical method, then deploy that corrected classical method across a screening library of thousands of candidate structures.

The same loop applies to amine chemistry — the kinetics of carbamate versus bicarbonate formation, the role of water, the degradation pathways through urea formation and oxidative breakdown. These are all small-molecule problems with strong correlation in transition states, and they are exactly the regime where a quantum reference calcul