Contract Machine

On the next crossing, Tala's left hand found the rail weld with Osei's mark before she looked down. Sable filled the clear floor until Iona opened the algorithm-rack door and station structure closed around them.

The contract machine stood immediately inside: an ordinary equipment rack with optical ports and one status lamp. Beneath recent paint, Tala could still read the inventory from its first life as a survey locker: anchors, oxygen, drilling charges.

A newer inscription had been cut deeply enough to survive its next use.

Uf |x,y> = |x, y xor f(x)>

For fixed Boolean function f, the map preserved input x and XORed f(x) into target y. The plate described no implementation cost, internal construction, or useful purpose.

"This cabinet is the oracle?" Mara asked. The noun had promised her more architecture.

Its status lamp supplied the only available reply.

ORACLE READY
calls remaining: 1

Sable's first charter crews had called their thermal-fracture forecaster an oracle. It displayed a risk color and concealed the mapping, assumptions, and geology. When a forecast failed, the vendor explained that Sable's captured-rock strata fell outside the service boundary. The camp display had carried no such warning, and the vendor's charter ended before the repairs did.

The cooperative later required every callable promise to fit on a plate that could outlast vendor and enclosure. Quantum engineers retained the inherited word oracle after placing its complete map where prophecy could not hide inside it.

An oracle supplied a callable input-output map and no explanation of its internals. Any computational difficulty remained real; someone had to implement it behind the interface.

Iona selected one allowed one-bit function behind an opaque screen. Sana sealed its implementation digest before collecting predictions. The choice remained hidden from the crew and fixed in the record.

The experiment required their ignorance. The evidence required known parentage.

The promise divided the allowed functions into two classes. A constant function returned one shared value for both inputs; a balanced function returned one of each value. One classical query could receive zero or one from either class, so classical classification required both inputs.

The quantum procedure permitted one oracle call. Tala's transit practice had been to accumulate queries until inconsistency exposed itself. Here she had to arrange one interaction so the relation between two function values survived while the values themselves did not.

"We receive one question."

"The station pays for one call," Iona said.

Physical cost made the restriction immediately credible to Mara.

They prepared the target qubit in |1> and applied H.

H|1> = (|0> - |1>) / sqrt(2)

The resulting state, written |->, responded to X by acquiring a global sign.

X|-> = -|->

An unconditional flip changed only global phase on the target. Conditioning that flip on input made the sign differ across input alternatives. The target's local state returned unchanged while the joint amplitudes carried f(x) in phase.

|x>|->  ->  (-1)^f(x) |x>|->

The effect was called phase kickback, though nothing propagated backward. Old diagrams had encouraged that mistake with backward arrows. Iona struck out the arrows and preserved the marked pages so their error could remain visible.

Control-dependent phase now belonged to the corresponding input amplitude.

An equal input superposition exposed amplitude components for both promised values. Under a constant function, those components received matching signs.

(+,+) or (-,-)

The final Hadamard mapped either shared-sign pattern to measured input 0. Patterns (+,+) and (-,-) differed by global phase, which this measurement could not distinguish.

quantum class DeutschConstant {
  state long result = 0;
  qreg q = new qreg(2);

  unitary void oracle() {
  }

  entry void main() {
    prepare(q, 2);
    H(q[0]);
    H(q[1]);
    oracle();
    H(q[0]);
    result = measure(q[0]);
    assert(result == 0);
  }
}

With prepare(q, 2), low-order input q[0] began at zero and target q[1] at one. An empty oracle represented constant zero. A constant-one implementation would apply X to the target and differ only by the unobservable global sign in this procedure.

A balanced function assigned opposite signs to the input amplitude components.

(+,-) or (-,+)

The last Hadamard converted either opposing-sign pattern into input outcome 1.

quantum class DeutschBalanced {
  state long result = 0;
  qreg q = new qreg(2);

  unitary void oracle() {
    CNOT(q[0], q[1]);
  }

  entry void main() {
    prepare(q, 2);
    H(q[0]);
    H(q[1]);
    oracle();
    H(q[0]);
    result = measure(q[0]);
    assert(result == 1);
  }
}

CNOT supplied the identity oracle because it flipped the target when q[0] was one. A negation oracle would create the other relative-sign pattern and retain the same balanced classification.

Iona concealed which case occupied the rack. Mara ignored the source, listened to the controls, and misclassified one run.

"The left relay has a balanced sound," Mara said.

"The left relay operates refrigeration."

Cooling hardware had revealed less about the oracle than Mara's ear requested.

The ideal executions classified both promised cases without sampling uncertainty.

DeutschConstant  result = 0
DeutschBalanced  result = 1

One oracle call answered whether the two function values agreed. The circuit neither read both values in parallel nor recovered the hidden table. It encoded their equality relation in phase, then used interference to preserve the classification while discarding the individual values.

Sable gained no operational advantage from the tiny classification. Its value lay in a complete four-row world whose amplitudes could be followed by hand. The station kept it as Catenary kept hand pumps beside automated water walls: a small mechanism exposed the law hidden by larger machinery.

Sana preserved separate identities for the promise, callable map, hidden implementation, calling circuit, and result. Collapsing them under algorithm would obstruct later questions about which part had failed.

A delayed Catenary message arrived while Sana completed the chain. Neris Venn had signed it as director of traffic continuity. The charged front was accelerating within its forecast range.

Traffic control advanced the beacon-retuning deadline.

The request named the physical sample, the intended application, and the chain between them. An attached traffic plan showed the cost of failure. Catenary could keep the old beacon profile through the charged front by widening every approach interval. Ore and passengers would arrive. Air catalysts and garden trace metals would wait in outer orbits.

The Second Navigation had taught Catenary that a common standard would fail if distant observations arrived as anonymous authority. Six years earlier Venn had trusted a green transit display that hid fourteen cars. Tala could not tell whether the new care came from that failure or some later policy. The care was here. She read Venn's signature three times and found that correction could travel without apology.

Sable could neither shorten light travel nor extend Catenary's traffic margins. Its crew could finish within the remaining window and make every link required for honest acceptance.

After both classifications passed, the rack released another module. It contained four basis states and one phase-marked value, allowing complete inspection of amplitude amplification.

The abandoned camp names on its channels opened into Search.