Superposition and Measurement

An $n$-qubit pure state contains $2^n$ complex amplitudes:

$$|\psi ⟩=\sum _{k=0}^{2^n-1}{c}_k|k⟩,\sum _{k=0}^{2^n-1}|c_k{|}^2=1.$$

The probability of measuring basis state $k$ is $|c_k{|}^2$. An amplitude itself is not a probability: its complex phase affects interference.

Superposition

Superposition(register, state) stores the original register and the current state vector. For three qubits, entries 0 and 1 contain the real and imaginary parts of the amplitude of 000; entries 2 and 3 contain the amplitude of 001; and so on through 111.

Use a state reader for meaningful output. Superposition.toHumanString prints the raw float vector.

import scotty.quantum._
import scotty.quantum.gate.StandardGate._
import scotty.simulator.QuantumSimulator

implicit val simulator: QuantumContext = QuantumSimulator()
val state = simulator.run(Circuit(H(0)))
println(StateProbabilityReader(state).toHumanString)

Superposition.applyGate mutates the vector and requires an implicit QuantumContext. combine computes a tensor product; when constructing larger states directly, ensure the associated register matches the combined vector.

Collapsed state

Collapsed(register, index) represents a sampled classical result. toBinary returns a fixed-width basis string. For example, index 6 in a three-qubit register is "110".

val measured = simulator.runAndMeasure(Circuit(X(1), X(2)))
assert(measured.toBinary == "110")
val bits: BitRegister = measured.toBitRegister

BitRegister contains Zero and One values. Binary strings are the clearest way to inspect a multi-qubit measurement; see the label and ordering caveat.

Measurement behavior

runAndMeasure executes the circuit and samples the whole register. A circuit containing any Measure operation also returns Collapsed from run.

In this simulator, measurements happen after all gates, regardless of where the Measure operation appears. The entire register collapses, even when only one qubit is named in Measure. This does not implement general intermediate measurements, partial collapse, or classical feed-forward.

Read Operations for examples.