Circuit Sandbox | QuantumNotes

Section 01

Circuit Builder

Gate palette — drag a gate onto the circuit below

Section 02

Results

Theory — exact probabilities (Born rule)

Measure — simulate wavefunction collapse

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Section 03

Preset Circuits

Single qubit

Two qubits

Three qubits

Section 04

How to Use the Circuit Editor

The circuit editor is powered by Q.js, a free open-source quantum circuit simulator by Stewart Smith. Each horizontal wire is one qubit starting in |0⟩. Each column is one moment (a clock tick). Below is everything you need to build and analyze any circuit.

Place a single gate. Drag any gate from the Gate Palette (the blue strip above the circuit) and drop it onto any cell. Each cell is a register (row) × moment (column) combination. The circuit re-evaluates automatically after every change.

Palette: [ H ] [ X ] [ Y ] [ Z ] [ S ] [ T ] [ * ] [ M ] … r1 ──── [ H ] ────────────────────── r2 ────────────────────────────────── m1 m2 m3 m4

To remove a gate, drag it off the circuit board into empty space outside the grid and release — it disappears with a brief animation.

Create a CNOT (controlled-X) gate. A CNOT links two qubits: a control (filled dot) and a target (⊕). In Q.js you build it by first placing the two components and then joining them:

Drag the ● Identity cursor (* in the palette) onto the control qubit at the desired moment.
Drag an X gate onto the target qubit at the same moment.
Click the ● cursor cell to select it, then Shift-click the X cell to add it to the selection.
Click the C button in the circuit's own toolbar (the dark bar above the wire labels). The two operations merge into a single CNOT gate connected by a vertical line.

Step A — place * on r1,m2 and X on r2,m2: r1 ─── [ H ] ─── [ * ] ─── r2 ───────────── [ X ] ─── Step B — select both → click C: r1 ─── [ H ] ─── [ ● ] ─── ← control dot │ r2 ───────────── [ ⊕ ] ─── ← target (X gate)

Try it now: this is the Bell state circuit. H on r1 at m1, then CNOT (control r1, target r2) at m2. Click ▶ Evaluate — you get 50% |00⟩ and 50% |11⟩, a maximally entangled state. Then click ⚄ ×100 and watch the measured histogram converge to the theory bars.

Create a SWAP gate. Place the ● Identity cursor (*) on both wires at the same moment. Select both cells, then click the S button in the toolbar. The two cursors become a SWAP gate (shown as ✕ on each wire with a connecting line).

Place * on both wires at the same moment → select both → click S: r1 ─── [ * ] ─── → r1 ─── [ ✕ ] ─── r2 ─── [ * ] ─── │ r2 ─── [ ✕ ] ───

Select, move and delete.

Move a gate: drag it to a new cell — it snaps to the grid.
Select a column: click the moment number at the top of the circuit.
Select a row: click the register number on the left.
Select all: click the ↘ icon in the top-left corner of the circuit.
Undo / Redo: use the ⟲ / ⟳ buttons in the circuit toolbar.
Delete a gate: drag it outside the circuit board area and drop.

The circuit toolbar also has a 🔓 lock toggle. When locked, no gates can be moved or added — handy when you want to measure without accidentally editing the circuit.

Reading the Theory panel. After clicking ▶ Evaluate (or after any gate change), the Theory panel shows:

Probability bars — the exact Born-rule probability |α|² for each basis state.
Amplitude table — the full complex amplitude re + im·j for each state. The probability is |re|² + |im|².
Bloch sphere — for single-qubit circuits, the state vector on the Bloch sphere.

The Theory panel shows the quantum state before any measurement — a superposition of all outcomes simultaneously. No single run of the circuit produces all these numbers at once; they describe the distribution of outcomes over many runs.

Reading the Measure panel. Each click on ⚄ ×1 simulates a single wavefunction collapse — a random draw weighted by the Born probabilities. ⚄ ×100 and ×1000 accumulate many shots rapidly. The histogram shows two bars per state:

Outlined bar (theory) — what quantum mechanics predicts.
Solid bar (measured) — what your simulated shots have produced.

As you add more shots, the solid bars converge onto the outlined ones — this is the law of large numbers applied to quantum probability. A "≈ converging ✓" note appears once they match within 5%.

Quantum randomness is fundamental, not due to ignorance. Even with a perfect circuit and perfect detector, the outcome of a single measurement on a superposed qubit is genuinely unpredictable. The Born rule only tells you the probability distribution.