Quantum Computing for Developers
From zero to a correct working mental model: qubits, amplitudes, measurement, gates, entanglement — every claim runnable, no physics degree required.
A quantum computer is a special helper chip, not a faster everyday computer. It only pays off when a proven quantum method fits the shape of the problem. And each run gives back just a few ordinary bits. It never hands you its full inner state.
A bit holds one value you can read: 0 or 1. A qubit carries two amplitudes, one for each outcome. An amplitude is a number that says how strongly the qubit leans toward that outcome. Measuring a qubit gives back a single bit. The chance of each result is its amplitude's size, squared.
An amplitude is a number attached to an outcome. It can be negative, or even complex. Square its size and you get the outcome's chance. For a real state, all the chances add up to exactly 1. Squaring wipes out the sign, which is called phase. But later gates can still use it.
One shot gives back one ordinary bit, picked at random using the state's chances. Real counts wobble around the perfect chances. The typical wobble shrinks like 1/√N, where N is the number of shots. Measuring also changes the qubit: afterwards it sits in the state you just saw.
The Bloch sphere draws one qubit as a point on a globe. How far north or south the point sits sets the 0/1 chances. How far around it sits records the relative phase. Gates turn the globe. The picture is exact for one qubit. It does not work for entangled groups of qubits.
X swaps the amplitudes of |0⟩ and |1⟩. Z flips the sign of the |1⟩ amplitude. Y does both, with factors of i. Z changes the phase, which the current histogram can't see. But later gates can turn that hidden change into chances you can see.
The Hadamard gate adds and subtracts the two amplitudes, then divides each by √2. It turns |0⟩ into an even superposition, and applying it twice undoes it. A phase placed between two H gates decides the final result. So H works as a phase detector, not a randomiser.
Phase gates (Z, S, T and RZ) turn the direction of the |1⟩ amplitude. On their own, they don't change the readout chances. But put an H before and after, and that hidden turn becomes a histogram change you can see — even a certain one. Rotation gates take an angle in radians and change the chances directly. RY(θ) on |0⟩ gives cos²(θ/2) zeros. So the chance follows half the angle, not the angle itself.
n qubits are described by one amplitude for each joint outcome. That is 2ⁿ amplitudes in total, not n separate pairs. QPU137 shows bit strings with q0 as the rightmost bit. Some joint states split into separate one-qubit states. Entangled ones cannot.
CX (also called CNOT) flips its target qubit only in the parts of the joint state where the control qubit is 1. It works part by part, with no measurement and no if-statement at run time. The order [control, target] is part of the program. Swap it and you run a different circuit.
H then CX turns |00⟩ into the Bell state (|00⟩+|11⟩)/√2. Each bit on its own is a fair coin. Yet the two bits agree on every shot. Simple arithmetic shows that no pair of separate qubit descriptions can make this state. The link lives in the joint state, and it can't be used to send a message.
Interference means amplitudes are added first, and only then squared into chances. So parts with the same sign build each other up, and parts with opposite signs cancel. In H–Z–H, the two parts heading to outcome 0 are +0.5 and −0.5. They cancel exactly. So a change in phase alone becomes a sure result of 1.
A circuit is a program. It is an ordered list of steps. Each step names a gate, the qubits it acts on, and any settings. The diagram is just a drawing of that list. Gate count and depth measure different costs. And the order of the qubits in a step matters: swap one [control, target] pair and the output changes.
The final project is one complete experiment. Write a number prediction for the Bell circuit. Run 1,000 shots. Check the counts against the expected random wobble. Change one gate and predict again. Then record the circuit, shot count, seed, counts and explanation, so someone else can repeat both the result and your reasoning.