Quantum Learning Path Singapore: Zero to Quantum Circuits

Optional warm-up before the qubit posts: the complex plane, i as a 90° rotation, and why the phase factor eiφ traces a circle.

First principles: what a qubit is, how the Hadamard gate builds superposition, and why tensor products scale the state space.

The geometric bridge from qubit statevectors to gates: where |0⟩, |1⟩, |+⟩, and |−⟩ sit, how X and Z rotate them, and how to verify the result in Qiskit.

A tested workflow for rendering high-resolution Bloch spheres and circuit diagrams directly in Android Termux when full Qiskit will not complete.

Moving beyond single qubits: tensor products, product states vs entangled states, Schmidt decomposition, CNOT as the universal entanglement generator, the four Bell states, Bell basis decoding, and why the single-qubit Bloch vector collapses.

Holevo’s bound, pre-shared entanglement as a communication resource, Alice’s local Pauli encoding (I, Z, X, ZX), Bob’s deterministic Bell basis decoding, and full Qiskit 2.x verification.

The one-qubit QFT turns out to be exactly the Hadamard gate, a small result that anchors the bigger picture.

How the Hadamard sign table generalises to n qubits and powers Grover’s diffusion step.

Why every quantum gate must be reversible, and how ancilla bits turn irreversible logic into unitary logic.

Leftover junk qubits destroy interference; uncomputation cleans them up to protect the speedup.

A short proof that an unknown quantum state cannot be duplicated, and what that impossibility makes possible.

Moving an unknown qubit from one place to another without ever copying it, using entanglement and two classical bits.

The mechanism where the target qubit flips the control’s phase, the trick underneath Deutsch’s, Grover’s, and Shor’s.

The four one-bit Boolean functions, the reversible oracle, and the single query that beats the classical two.

The same algorithm in running Qiskit code: two classical queries against one quantum query.

Scaling to n-qubit Boolean functions: provable exponential query separation, phase kickback, the four canonical oracles, and Qiskit 2.x implementation.

A full three-qubit walkthrough of the oracle and the amplitude amplification that surfaces the marked item.

Putting entanglement into action: an interactive simulator where quantum correlation violates Bell’s inequality, beats the classical 75 percent ceiling, and reaches the Tsirelson bound (85.4%).