quirqs and quantum computing

The most speculative page in this section, labeled open in the claim ledger. It starts with a procurement problem any quantum cloud buyer has today, and ends in shot-count mathematics. The structural fit is real; the applications are proposals, not results.

The story, in business language

A materials team wants ground-state energies for a candidate battery molecule, validated to chemical accuracy, because a wrong energy sends a quarter of lab work down a dead end. They buy quantum compute the only way it is sold: per shot and per QPU-second, across devices whose error rates, mitigation stacks, and shot requirements differ wildly. Three vendors quote three prices in three incomparable units, and none of the quotes mentions the only thing the buyer wants: a validated number.

Quantum computing has the token problem, exactly. Shots are quantum's tokens: an input meter that rises when the device is noisy, changes meaning across hardware, and cannot distinguish a calibration sweep from a customer outcome. The quirq construction transfers whole: the buyer budgets the validated estimate (say B = $600, what the answer is worth against lab time saved), the definition of done is a statistical acceptance test, and devices compete on cost per quirq: dollars spent per dollar of validated answer delivered.

The same job on three devices, quantified

One unit of work: estimate ground-state energy to within δ = 1.6 mHa at 95% confidence, beating the classical baseline. Illustrative numbers:

Read the last column and the procurement problem dissolves. Devices A and B deliver the answer at a loss (c_q > 1: the validated answer costs more than it is worth); device C delivers it at 53 cents on the dollar. Shot price told the buyer nothing (A had the cheapest shots); cost per quirq ranks devices by delivered value, which is the only ranking a buyer needs.

The criterion this creates: economic quantum advantage on a unit type is not a speedup claim, it is

c_q(quantum)  <  min( 1,  c_q(classical) )

cheaper than the outcome is worth, and cheaper than the classical route. The crossover frontier draws itself on the ledger, per unit type, per quarter, and nobody has to argue about supremacy benchmarks in a press release.

The math, as you scroll deeper

From precision to cost. For an observable with sample standard deviation σ, a confidence half-width δ needs roughly

N ≈ (1.96 σ / δ)²    shots

so unit cost scales as C ≈ N·p_shot + overhead, and cost per quirq on an atomic unit becomes

c_q(δ) ≈ (1.96 σ)² · p_shot / (δ² · B(δ))

The 1/δ² term is why precision is expensive; B(δ), the owner's value of precision, is why it is sometimes worth it. The owner's optimal precision is where marginal value equals marginal cost, dB/dδ = dC/dδ: a decision the budget makes explicit and shot pricing hides. Error mitigation and better devices enter as σ and p_shot; the whole hardware roadmap compresses into the trajectory of c_q(δ) per unit type.

Routing as a bandit. With classical and quantum backends both metered, the dispatcher's problem is route each unit to argmin over backends b of E[c_q | b, unit type], learned online from the ledger: a multi-armed bandit whose regret is measured in dollars of overpaid outcomes. The ledger is both the training data and the scoreboard, and the empirical crossover frontier (which unit types have flipped to quantum, and when) falls out of the routing history: the field's biggest open question answered by bookkeeping.

Intent as data. Each unit contributes a triple (G, B, execution record): a formal, weighted, machine-checkable statement of what a human wanted, what it was worth, and what verifiably satisfied it. Aggregated, that is a labeled corpus of scientific intent: which observables, at which precisions, at which values, which is precisely the demand signal quantum hardware roadmaps currently guess at.

The verification parallel, held as analogy. Verifying a quantum device's claim with a weaker classical verifier is a deep open problem, and its trust geometry is the quirq's: never accept the worker's self-report, extract evidence the verifier can check. The protocols differ entirely (interactive proofs there, state comparison here); the shared discipline is that the party doing the work never keeps the score. Each field's techniques deserve the other's attention, and that sentence is an invitation, not a result.

Status

Tier: open, all of it. No quantum experiment has run under quirq accounting. The harness extends naturally (statistical checks exist; a quantum backend is one more metered executor), and the first real ledger would turn the table above from illustration into measurement. If you work on quantum benchmarking or verification: suraj@xo.builders.

That closes the frontier cases. Back to the ground: how to integrate this today.