A quantum circuit is a qubit's journey through a sequence of gates before measurement. This simulator lets you build that sequence from a six-gate palette, then step through it one gate at a time to see exactly how the Bloch vector and measurement probabilities change at every stage.
• A click-to-add palette of six gates: H, X, Y, Z, S and T. • A live circuit diagram showing the built sequence, with highlighting for gates already executed. • Step-forward and step-backward controls, plus an instant run-all option. • A live Bloch-vector view synced to the current step. • Live P(0)/P(1) probability bars for the current step, plus the specific gate just applied.
• Build H, X, H and step through it — notice the intermediate |1>-after-X step before the final Hadamard brings it back to an equal superposition with a flipped phase. • Build H, S, H versus H, Z, H and compare the final probability bars — S gives a partial rotation, Z gives a full flip. • Build a long sequence such as H, X, Z, H, X and step through it slowly, predicting each intermediate Bloch position before advancing.
Quantum gates are matrices applied in sequence, and matrix multiplication does not commute in general — the same gates in a different order can produce a completely different final state. Watching each intermediate step, rather than only the final answer, is the fastest way to build real intuition for how a circuit's behavior emerges gate by gate, the same way the Bell-State-Preparation and Quantum Teleportation labs build up their circuits.
It is a sequence of quantum gates applied to one or more qubits, read left to right, ending in a measurement. Each gate transforms the qubit's state, and the final measurement converts the accumulated quantum state into a classical 0 or 1 result.
S and T are phase gates that rotate the Bloch vector by 90 degrees and 45 degrees respectively around the Z axis, without changing measurement probabilities on their own — smaller, finer versions of the full 180-degree Z gate, useful for building up arbitrary phase rotations.
Quantum gates are matrices, and matrix multiplication is generally not commutative — applying H then Z gives a different final state than applying Z then H. Stepping through the circuit gate by gate in this simulator makes that order-dependence directly visible on the Bloch sphere.
Because S performs a smaller (90-degree) phase rotation than Z's full 180 degrees, sandwiching S between two Hadamards produces an intermediate measurement probability rather than the fully flipped probability that H, Z, H produces — try both sequences to see the difference in the resulting bars.