Randomized Benchmarking

qc/noise qc/qiskit

A technique for measuring a specific gate’s error rate directly on hardware, isolated from state-preparation and measurement error. Run a long random sequence of gates from the Clifford group, choosing the sequence so it composes to the identity — ideally you always measure back $|0{⟩}^{\otimes n}$, and any deviation is accumulated gate error.

Reference vs. interleaved

• Reference RB — random Clifford sequences alone, gives a baseline decay rate $r_{\text{reference}}$.
• Interleaved RB — the same random sequences, but with the gate under test inserted between every random Clifford, giving $r_{\text{interleaved}}$.

The error per Clifford (EPC) for the gate under test is extracted from the difference:

$\text{EPC}=\left(1-\frac{r_{\text{interleaved}}}{r_{\text{reference}}}\right)\times \frac{D-1}{D}$

where $D=2^n$ for $n$ qubits. Key insight: comparing interleaved to reference cancels out the other Clifford gates’ contribution to decay, isolating the error attributable specifically to the interleaved gate.

In Qiskit

from qiskit_experiments.library import InterleavedRB
from qiskit.circuit.library import CXGate
 
exp = InterleavedRB(
    interleaved_element=CXGate(),
    qubits=(0, 1),
    lengths=[1, 10, 30, 50, 100],
    num_samples=10,
    backend=backend,
)
result = exp.run().block_for_results()

Related

• Universal Gate Sets and the Clifford Group — why Clifford sequences specifically
• Coherent vs Incoherent Gate Errors
• Backend Properties

Self-Check

• Why does a randomized benchmarking sequence get built to compose to the identity?
• What does comparing interleaved RB to reference RB let you isolate that either alone wouldn’t?
• Why are Clifford gates specifically the right building block for this technique?