A parity measurement determines whether the combined bit values of a multiqubit computational-basis state have even or odd parity. It extracts correlation information rather than separate information about each qubit. section 4.6.1
Implement a parity measurement with an auxiliary qubit:
- Allocate an auxiliary qubit in |0⟩. section 4.6.1
- Apply one CNOT per input qubit, using each input qubit as control and the auxiliary qubit as target. section 4.6.1
- Measure the auxiliary qubit to read the parity bit. section 4.6.1
Table 4.2 The steps of performing a parity measurement on a two-qubit state
| The input state | \(0.8 |00\rangle + 0.6 |11\rangle\) | \(0.8 |01\rangle + 0.6 |10\rangle\) |
|---|---|---|
| Parity of the input state | 0 | 1 |
| Allocate auxiliary qubit (last bit) | \(0.8 |00\rangle|0\rangle + 0.6 |11\rangle|0\rangle\) | \(0.8 |01\rangle|0\rangle + 0.6 |10\rangle|0\rangle\) |
| Apply CNOT (first qubit as control) | \(0.8 |00\rangle|0\rangle + 0.6 |11\rangle|1\rangle\) | \(0.8 |01\rangle|0\rangle + 0.6 |10\rangle|1\rangle\) |
| Apply CNOT (second qubit as control) | \(0.8 |00\rangle|0\rangle + 0.6 |11\rangle|0\rangle\) | \(0.8 |01\rangle|1\rangle + 0.6 |10\rangle|1\rangle\) |
| State of the auxiliary qubit | \(|0\rangle\) | \(|1\rangle\) |
Trace the auxiliary qubit through two even- and odd-parity superpositions, including each CNOT and the final auxiliary state. section 4.6.1
