Quantum Computing by Hand: Qubit Amplitudes, Gates as Small Matrices, Measurement Probabilities, Entanglement & a Two-Qubit Search

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn the two amplitudes of eight one-qubit states into measurement probabilities, see that the sign disappears when you square, measure the length of two raw pairs and normalise them into valid states.
• Apply the X, Z and Hadamard gates to a qubit state with SUMPRODUCT (one matrix row times the state), read the new amplitudes and see how the Hadamard gate changes the odds of measuring 0.
• Build the probability table of a measured qubit, turn it into cumulative lower bounds, simulate 20 shots from a fixed column of random numbers with MATCH and compare the observed counts with the expected ones.
• Label the four basis states of two qubits in binary, build their amplitudes as products of the single-qubit amplitudes, square them into probabilities and check that they add up to 1.
• Apply a Hadamard and then a CNOT to |00⟩ with 4 × 4 matrix rows, get the Bell state, and use COUNTIFS on shot logs to show that entangled qubits always agree while a product state agrees only half the time.
• Follow one qubit through two short circuits, split the |1⟩ amplitude into its two contributions to see them cancel, and show that a single Z between two Hadamards turns a certain 0 into a certain 1.
• Run one round of a quantum search over four items: the oracle flips the sign of the marked item, the diffusion step reflects every amplitude about the mean, and the marked item ends up with probability 1.
• Read the final state of a four-gate circuit, turn it into probabilities, chart the observed shots, and calculate how many amplitudes and how much memory a classical simulator needs as the number of qubits grows.