Concept 4 of 7 · How we make it fit

Active spaces

Molecules have thousands of orbitals; almost all of them are boring — full or empty all the time. The active space is the handful of orbitals where the interesting chemistry actually happens, and it’s the only part we put on the quantum computer.

What it actually means

A molecule’s electrons sit in molecular orbitals, conceptually like shells in a building. Real molecules have thousands of orbitals in any realistic basis set. But for almost every chemistry question you might ask:

• The deep core orbitals are always fully occupied. The electrons there don’t go anywhere. They affect the energy by a constant amount and you can subtract that off.
• The very high virtual orbitals are always empty. Electrons don’t visit them at any reasonable temperature.

So you carve out a band in the middle — the active space — containing the highest few occupied orbitals and the lowest few empty orbitals. Those are where electrons can actually be promoted, where bond formation and breaking happens, where electron correlation gets interesting. Only the active space goes onto the quantum computer.

The notation CAS(n, m) means Complete Active Space with n electrons distributed among m orbitals. Each spatial orbital is two qubits (one for spin-up, one for spin-down), so CAS(4, 4) is 8 qubits before optimization. Symmetry tricks (the parity mapper with Z₂ tapering) shave that down to 6 qubits — which is what we use for WH⁻.

This isn’t an approximation made up for quantum computers. Classical chemistry has used active spaces for decades — they’re how you make high-accuracy methods like CASSCF and CASPT2 tractable. The quantum adaptation is just: the same active space, encoded into qubits instead of into a classical wavefunction expansion.

Why it matters for our problem

The whole reason WH⁻ fits in 6 qubits is the active space.

• Tungsten has 74 electrons. Even with the LANL2DZ effective core potential (which freezes 60 inner-shell electrons as a fixed background), there are still 14 valence electrons plus hydrogen’s 2 — that’s 16 electrons across dozens of valence orbitals.
• We pick CAS(4, 4) — 4 electrons in 4 orbitals — centred on the W–H bonding region. Those are the orbitals where the W–H σ bond is forming and where electron correlation matters most.
• Everything else (the other 12 valence electrons, all the higher virtuals) is folded into the Hartree-Fock background and treated as a constant.

Scaling up: from 6 qubits to 200+

The fusion-wall problem at scale — tungsten vacancy + embedded hydrogens — needs roughly CAS(20, 20) to capture the multi-centre correlation. In the canonical terminology from the README, that’s ~40 spin-orbital qubits before tapering, ~36 circuit qubits after a Z₂ taper. Even bigger problems (a W₈ vacancy cluster with multiple H sites, the real production target) push into the ~150+ circuit-qubit regime — which is where the error-correction story starts mattering, because at that circuit depth noise compounds faster than NISQ chips can tolerate. The “200+ logical qubits” figure you’ll see quoted elsewhere is the error-corrected count needed to actually run those circuits to chemical accuracy.