Quantum Circuit Builder

Build a 2-qubit circuit one gate at a time. The simulator tracks the full statevector — four complex amplitudes for the basis states $\lvert 00\rangle$, $\lvert 01\rangle$, $\lvert 10\rangle$ and $\lvert 11\rangle$ — and shows the measurement probabilities live.

The circuit starts pre-loaded with the classic Bell-state recipe ($H$ on q0, then CNOT q0→q1). Press Clear to start from $\lvert 00\rangle$.

Qubit q0

Qubit q1

Two-qubit

Circuit: H(q0) · CNOT(q0→q1)

Basis	Amplitude	P
|00⟩	0.71	50.0%
|01⟩	0.00	0.0%
|10⟩	0.00	0.0%
|11⟩	0.71	50.0%

|00⟩ — 50.0%

|01⟩ — 0.0%

|10⟩ — 0.0%

|11⟩ — 50.0%

Experiments

1. Bell state — H(q0) · CNOT(q0→q1) gives $(\lvert 00\rangle + \lvert 11\rangle)/\sqrt{2}$: two qubits, perfectly correlated, 50/50 between $\lvert 00\rangle$ and $\lvert 11\rangle$. This is entanglement.
2. All four Bell states — try adding an $X$ or $Z$ on q0 before the CNOT.
3. Superposition without entanglement — H(q0) · H(q1) spreads probability evenly over all four outcomes, but the qubits are still independent.
4. GHZ-style correlation — chain H(q0) · CNOT(q0→q1) and inspect how the amplitudes concentrate.

From two qubits to many

This simulator stops at two qubits to stay fast and clear, but the idea scales: $n$ qubits need $2^n$ complex amplitudes — which is exactly why simulating large quantum systems on classical computers is so hard, and why real quantum hardware is interesting.

Ready to run circuits on a real simulator? Head to the Hands-on Labs and build them in Qiskit.