Multiple qubits
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.
Why care? Real programs use many qubits. And the way qubits combine is where both the power and the cost of quantum computing come from.
One qubit needs two amplitudes. (An amplitude is a number you square to get a chance.) Two qubits need one amplitude for each joint outcome, and there are four of those: 00, 01, 10 and 11. Each labelled outcome is called a basis state. The full list of amplitudes is called the state vector.
Three qubits have 8 basis states. n qubits have 2ⁿ. The list doubles with every qubit you add. Think of a row of light switches. Two switches can be set 4 ways. Three switches can be set 8 ways. (Unlike switches, the qubits carry an amplitude for every one of those settings.)
The measurement rule stays the same. The chance of reading a bit string is the squared size of its amplitude. And the squares must add up to 1.
Worked example. Say the amplitudes are 0.6 on 00, 0 on 01, 0 on 10, and 0.8 on 11. The squares are 0.36, 0, 0 and 0.64. Check it: 0.36 + 0.64 = 1. So 36% of shots read 00, and 64% read 11. The strings 01 and 10 never appear.
- Which bit is which qubit?
- H on q0 only: which bit moves?INTERACTIVE
- When are two qubits just two separate qubits?
- A product state in the histogramINTERACTIVE
- Which states can't be split into separate qubits?
- Worked exampleINTERACTIVE
- Does a bigger qubit count mean a better machine?
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