Unlocking Quantum Computing

What Is a Quantum Circuit?

A quantum circuit is the quantum equivalent of a classical program. It's a sequence of operations (gates) applied to qubits, followed by measurement.

Unlike classical programs that manipulate bits deterministically, quantum circuits manipulate probability amplitudes to produce probabilistic outputs.

Circuit Anatomy

Wires (Qubits)

Horizontal lines represent qubits. Time flows left to right. Each wire starts in state |0⟩ by default.

Gates

Boxes and symbols on the wires represent operations. Gates are reversible (you can always undo them).

Measurement

The meter symbol at the end collapses the quantum state to classical bits (0 or 1). This is how we extract results.

Try It: Build Your Own Circuit

Drag gates from the palette onto the qubit wires to build a circuit. Watch how the output state changes as you add gates.

Circuit Builder

Qubits:

GATES

Single Qubit

Hadam.

HHadamard

Creates superposition - puts qubit in both |0⟩ and |1⟩ simultaneously

|0⟩ → |0⟩+|1⟩ (50/50)

Pauli-X

XPauli-X

Quantum NOT gate - flips the qubit state

|0⟩ → |1⟩, |1⟩ → |0⟩

Pauli-Y

YPauli-Y

Combines bit flip and phase flip

|0⟩ → i|1⟩, |1⟩ → -i|0⟩

Pauli-Z

ZPauli-Z

Phase flip - adds negative phase to |1⟩ (invisible until measured through H)

|0⟩ → |0⟩, |1⟩ → -|1⟩

S Gate

SS Gate

Quarter turn around Z-axis (90° phase)

|1⟩ → i|1⟩

T Gate

TT Gate

Eighth turn around Z-axis (45° phase) - key for universal quantum computing

|1⟩ → e^(iπ/4)|1⟩

Two Qubit

⊕

C-NOT

⊕CNOT

Controlled-NOT: flips target qubit only if control qubit is |1⟩

|10⟩ → |11⟩, |00⟩ → |00⟩

SWAP

×SWAP

Exchanges the states of two qubits

|01⟩ → |10⟩

Drag gates onto the circuit wires

Step Start / —

Speed:

Space Play/Pause← → StepR Reset

OUTPUT STATE

Definite state |00⟩

State

Phase

Probability

Angle

Amplitude

|00⟩

Phase: 0°

100.0%

0°

1.00

Normal (0° phase)

Phase shifted

0° = right90° = up180° = left

Drag gates onto wiresClick gate + Delete to removeCNOT/SWAP connect to next qubit

Beyond the Basics: More Gates

The Circuit Builder above covers the fundamentals. Real quantum frameworks like Qiskit offer many more gates:

Gate	Name	What It Does
Rx(θ)	X-Rotation	Rotates qubit around X-axis by any angle θ. Generalizes the X gate.
Ry(θ)	Y-Rotation	Rotates around Y-axis. Creates superposition with controllable amplitudes.
Rz(θ)	Z-Rotation	Rotates around Z-axis by any angle. Generalizes Z, S, and T gates.
CZ	Controlled-Z	Applies Z to target when control is \|1⟩. Symmetric — both qubits act as control.
CCX	Toffoli	3-qubit gate. Flips target only when BOTH controls are \|1⟩. Universal for classical computing.
S†, T†	Inverse Gates	Reverse the S and T gates. S† = -90° phase, T† = -45° phase.
U(θ,φ,λ)	Universal Gate	Any single-qubit operation with 3 parameters. All other single-qubit gates are special cases.
iSWAP	iSWAP	Swaps qubits and adds phase. Native to some superconducting hardware.

The gates in the Circuit Builder (H, X, Y, Z, S, T, CNOT, SWAP) form a universal gate set — you can build any quantum algorithm with them.

Multiple Shots Simulation

Watch how running many shots reveals the true probability distribution!

|0⟩

→ 50/50 expected

Shot 0 / 100

|0⟩ (0%)

|1⟩ (0%)

💡 More shots = more accurate probability estimate. Real quantum computers use 1000+ shots!

The Simulation Workflow

1
Build , Define qubits and gates using Qiskit
2
Transpile , Convert to executable form for the backend
3
Run , Execute on the simulator (many shots)
4
Analyze , Count outcomes to estimate probabilities

Key Insight: Multiple Shots

Because quantum measurement is probabilistic, we run the same circuit many times (e.g., 1,000 "shots") and count the results. This gives us a histogram of outcomes that approximates the true probability distribution.

Quantum Circuits