Quantum Computing · Instrument 03 of 03 · Complex

Circuit Simulator — build a multi-qubit machine

Click a gate, then click the wire to place it. The full 2ⁿ-amplitude statevector recomputes live — entanglement, interference, and phase all visible. Qubit 0 is the top wire and the leftmost bit in each ket.

Qubits

Presets

1-qubit

2-qubit pick a gate, then click a wire · click a placed gate to remove it

Statevector — amplitudes & probabilities

basis	probability	P	amplitude	phase

Reading the panel

Each row is one of the 2ⁿ classical outcomes. The bar is its measurement probability (tallest = the most likely). The amplitude is the underlying complex number; its phase is what interference acts on — two amplitudes pointing opposite ways cancel.

phase color = angle of the amplitude in the complex plane. Real-positive points right (0°); the tick shows the direction.

Things to try

▸ Bell preset → only |00⟩ and |11⟩ survive: the qubits are entangled.
▸ Put H on every qubit → a flat superposition over all states.
▸ Build |+⟩|+⟩ then add a CZ → watch one amplitude flip negative (phase 180°) with no change to the probabilities.
▸ Two T gates stack into an S; four into a Z.