Concept 5 of 7 · Where this scales

Scaling roadmap

Today’s quantum computers can do toy chemistry; the real fusion-wall problem needs hardware that doesn’t exist yet — but is on a credible roadmap. The same code in this repo bridges both eras.

Quantum-hardware scaling, with this repo’s milestones marked on it. Each point’s colour and its (circuit) / (early-FT) / (logical) tag flag which qubit unit it uses — those units are not interchangeable (see the note below). The dashed line is a projected trajectory, not measured data.

About the y-axis

Read this before drawing comparisons. The “qubits” number means different things at different points on the chart. NISQ-era markers (Bell, H₂, WH⁻ 6q, CAS(10,10) — tagged (circuit)) are circuit qubits: raw qubits on the chip with no error correction. The FT-era marker (W₈ vacancy + H — tagged (logical)) is logical qubits: error-corrected abstractions, each backed by hundreds-to-thousands of physical qubits. The “multi-W cluster” milestone sits in the transition and is tagged (early-FT) to reflect that ambiguity.

These are not the same unit of resource, and the chart cannot be read as “200 logical = 33× 6 circuit” — the physical-qubit footprints differ by orders of magnitude. The chart’s value is showing milestone order and timing, not a literal resource scaling. See the README’s qubit-terminology note for the precise definitions.

What it actually means

In quantum computing there’s a critical distinction between physical qubits and logical qubits.

A physical qubit is the actual transmon (or trapped ion, or whatever) sitting on the chip. They’re noisy — every gate has ~0.1–1% error, errors compound, and a deep circuit becomes useless.
A logical qubit is what you get when you combine many physical qubits with error-correcting codes. A logical qubit is essentially error-free for as long as the underlying physical qubits maintain coherence.

Today’s biggest IBM Quantum machines (Heron r2 — ibm_marrakesh, ibm_kingston, ibm_fez) have 156 physical qubits. Zero logical qubits. Everything currently running is “NISQ” — Noisy Intermediate-Scale Quantum — which is the polite term for “we’re getting useful circuits to work despite the noise, but only just.”

The transition from NISQ to fault tolerance is the next decade’s story. Roughly:

Era	Hardware	What chemistry can do
NISQ now → ~2027	~150 noisy physical qubits	Toy molecules with active spaces ≤ ~10 circuit qubits. Single-point energies on QPU. Full VQE optimization on simulator.
Early FT ~2027–2029	Thousands of physical qubits → tens of logical	Mid-sized molecules, ~20-qubit active spaces. Trotterized UCCSD becomes practical.
Fault-tolerant 2029+	Millions of physical → hundreds of logical	The problems that motivate the field: transition metal catalysis, nitrogenase, fusion materials. Quantum Phase Estimation becomes the standard.

Two things to internalize from this table:

The interesting chemistry sits in the 2029+ row. That’s the row where quantum methods are expected to beat classical ones on problems of actual scientific value. The NISQ row is necessary infrastructure development, not production results.
The order-of-magnitude jumps come from error correction, not from adding more physical qubits. Going from 156 to 1560 physical qubits would still be NISQ. The fault-tolerant transition unlocks 100× more usable compute even if total qubit count grows modestly.

Why it matters for our problem

This repo lives at the lowest milestone on the diagram. WH⁻ at 6 qubits. That’s deliberate.

Here’s the part most readers miss: the same code in 03_wh_binding.ipynb extends through every milestone on the chart. What changes is parameters, not architecture:

What you change	NISQ · today	Early-FT (2027+)	FT-target (2029+)
Geometry	W + H (diatomic)	W₂H₂, small clusters	W₈ + vacancy + H
Basis	`LANL2DZ` / `STO-3G`	`def2-SVPD`	`def2-TZVPD-J`
Active space	`CAS(4, 4)` → 6q	`CAS(10, 10)` → ~16q	`CAS(20, 20)` → ~30+q
Ansatz	`EfficientSU2(reps=4)`	UCCSD-trotterized	QPE (Quantum Phase Estimation)
Backend	Aer sim + single-shot QPU	NISQ QPU + error mitigation	Fault-tolerant QPU
Result	Demonstration	Useful approximation	Chemical accuracy

This is what “scales when hardware catches up” actually means in practice. Not “rewrite everything” — just substitute different objects into the same Qiskit pipeline.

The investment you make today in understanding this workflow pays off across the entire roadmap. Whoever picks up your repo in 2029 with access to fault-tolerant hardware can swap out the ansatz line and the backend line, scale the active space, and be doing real fusion-wall chemistry.

Where to go next

Concept 6 walks through the train-on-simulator, validate-on-QPU pattern that’s standard for the entire NISQ era. If you want to see why the qubit numbers in the tables above are what they are, back up to Active spaces.