Error Rates in Quantum Hardware
Error rates quantify how often operations go wrong; their size relative to the fault-tolerance threshold decides whether error correction can work.
Counting errors
An error rate is the probability that a given operation, single-qubit gate, two-qubit gate, measurement, or idle period, produces the wrong result. It is the complement of fidelity: an error rate of 0.001 corresponds to 99.9 percent fidelity. Because a computation chains many operations, the relevant question is how errors accumulate and whether they can be corrected.
Types of error
- Coherent errors: systematic over- or under-rotations, in principle calibratable away
- Incoherent errors: random decoherence, the hard floor set by T1 and T2
- Leakage: population leaving the computational subspace, hard to correct with standard codes
- Correlated errors: crosstalk and cosmic-ray events that hit many qubits at once
Typical magnitudes
In leading devices, single-qubit gate errors are around 0.0001 to 0.001, two-qubit gate errors around 0.001 to 0.01, and readout errors around 0.005 to 0.05. Idle errors depend on how gate time compares with coherence time. These numbers vary widely across qubits on the same chip and drift over hours, so they are reported as distributions and re-measured often.
The threshold theorem
The threshold theorem states that if the physical error rate per operation is below a code-dependent threshold, quantum error correction can suppress logical errors to any desired level by adding more physical qubits. For the surface code that threshold is often quoted near 1 percent. Getting comfortably below it, especially for two-qubit gates and correlated errors, is the gate that separates NISQ from fault-tolerant computing.
Correlated and leakage errors are especially dangerous because error-correcting codes assume mostly independent, in-subspace errors, so hardware teams work to suppress those specifically, not just to lower the average rate.