Qubits and measurement

A qubit

A classical bit is 0 or 1. A qubit has a state written α|0⟩ + β|1⟩, where α and β are complex amplitudes with |α|² + |β|² = 1. Measuring it gives 0 with probability |α|² and 1 with probability |β|², and afterwards the qubit is in the state that was read.

Rotations

The gate ry(θ) rotates |0⟩ into cos(θ/2)|0⟩ + sin(θ/2)|1⟩. With θ = π/3 the amplitude of |1⟩ is sin(π/6) = 1/2, so the qubit reads 1 with probability 1/4. With θ = π/2 it reads 0 and 1 equally often, and with θ = π it always reads 1.

Shots

One measurement gives one bit. To see a probability you run the same program many times, each run a shot, and count. With 1,000 shots and a probability of 0.25 you expect about 250 ones; the count typically lands within about 14 of that (the standard deviation, √(1000 × 0.25 × 0.75)).

Your first HiQ program

HiQ Assembly names the program, declares qubits and bits, applies gates one per line and measures with measure q -> m. The lab below is the rotation above: two lines of work. Our run of 1,000 shots read 1 on 24.1% of them, within the expected spread of 25%.