Fault-Tolerant Measurement
Reading out a logical qubit reliably requires measuring many physical qubits and reconciling the results against the code, not trusting any single readout.
Logical readout
To measure a logical Z, one measures every physical qubit in the logical Z operator's support in the Z basis and takes the parity of the outcomes. But individual physical measurements are noisy, and a data error present at readout time can flip the parity. A fault-tolerant measurement must be robust to both measurement faults and residual data errors.
Using the stabilizers
The trick is that a transversal Z-basis measurement also reveals the values of all Z stabilizers, because each stabilizer is a product of the same single-qubit Z outcomes. The decoder uses these stabilizer values to correct the raw bit string before extracting the logical parity, exactly as it corrects a syndrome. A few wrong physical readouts are then fixed rather than believed.
- Measure every qubit in the logical operator's support, then take parity.
- The same outcomes give the stabilizer eigenvalues for error correction.
- Decode the classical outcome string, then read off the corrected logical bit.
- Repeated rounds guard against the measurement faults themselves.
Destructive transversal measurement is the simplest fault-tolerant readout and is used at the end of a computation. During a computation, one instead measures logical operators non-destructively, for example by lattice surgery, which measures a joint logical parity of two patches without collapsing them individually.
Measurement fault tolerance closes the loop with preparation and gates: a full fault-tolerant cycle is prepare, compute, and measure, each stage designed so that no single physical fault corrupts the logical result. Getting the measurement stage right is essential because every syndrome-extraction round is itself a measurement subject to the same reliability requirements.