Quantum Computing

The short list of real speedups, and the much longer list of problems it leaves untouched.

Magnitude and phase, and why squaring a magnitude is where probability comes from.

A state is a column of numbers, a gate is a matrix, and that is the whole toolkit.

Write superposition down as two numbers instead of describing it in words.

Why |0⟩ and |+⟩ look identical in one basis and completely different in another.

Build a circuit from X, H, Z and T, and match Statevector output against your hand-written table.

Four amplitudes instead of two, and why n qubits take 2^n numbers to write down.

CNOT, Bell states, and the argument for why none of this sends a message.

Deutsch-Jozsa and Bernstein-Vazirani with the cancelling amplitudes written out by hand.

Amplitude amplification, a quadratic speedup, and the databases it does not actually search.

Period finding, why RSA falls in principle, and the million-qubit price tag on doing it.

Set up IBM Quantum Platform and plan around 10 minutes of QPU time per 28 days.

Use a preset pass manager to turn your circuit into the one the hardware will really run.

Submit PUBs through SamplerV2 and EstimatorV2 and read a result object without guessing.

Build an Aer noise model from a fake backend and reproduce hardware behavior on your laptop.

Put an uncertainty on every bar and tell a real signal from a pretty chart.

Tell the three error-handling families apart and state what each one costs you.

Simulate a repetition code in Stim and count the physical qubits one logical qubit costs.

Track one claim from announcement to classical counter-result on the Quantum Advantage Tracker.

Name what breaks, what does not, and why ML-KEM is already shipping in production TLS.