Source-verifiedLevel 4

Randomized Benchmarking

Randomized Benchmarking (RB) measures average gate fidelity by running ever-longer random gate sequences that should return the qubit to |0⟩ and fitting the exponential decay of the survival probability.

What it means

Randomized Benchmarking (RB) is the standard procedure for grading how well a quantum processor executes gates.The recipe: ① generate a random sequence of gates; ② a classical computer computes the net effect of the sequence and appends the inverse gate that undoes everything, so a perfect device would always return to |0⟩; ③ compile the sequence with the current calibration and run it on the QPU; ④ measure the 'survival probability' — how often the device really returns to |0⟩ — over hundreds of repetitions; ⑤ repeat for progressively longer sequences.Longer sequences accumulate more error, so the survival probability decays exponentially with sequence length, following P(m) = A·p^m + B.The decay rate yields the average gate fidelity (e.g., 99.92%), while A and B absorb state-preparation-and-measurement (SPAM) errors — a key strength, because it separates gate quality from readout quality.RB averages over random sequences; to grade one specific gate such as CNOT, Interleaved RB inserts that gate between the random ones and compares decay rates.

Everyday analogy

Give the machine ever-longer strings of random dance moves, each string ending with the exact 'undo everything' move. A perfect dancer always returns to the starting position (|0⟩); count how often the machine really does. Longer strings accumulate more error, so the survival probability decays exponentially — and that decay rate IS the average gate error.
The word benchmark comes from a surveyor's 'bench mark' — a mark chiseled into stone that served as a fixed reference height for all other measurements. RB chisels a fixed reference into the quantum stack: a number against which every device and every day can be compared.

Common misconceptions

  • RB is the heaviest job in the stack — a single RB run stress-tests the transpiler (ever-longer circuits), the compiler, the pulse scheduler, client-server transport, the job scheduler, the control electronics AND the QPU all at once, which is why it takes so long.
  • The RB number is an average over random sequences — it does NOT give the fidelity of one specific gate. For that you need Interleaved RB, which inserts the target gate between the random gates and compares decay rates.

Key takeaways

  • Procedure: ① random gate sequence → ② classical computer appends the inverse ('undo') gate → ③ run on the QPU with the current calibration → ④ measure survival probability over hundreds of repeats → ⑤ repeat for growing sequence lengths.
  • Survival probability decays exponentially with sequence length; the decay rate yields the average gate fidelity (e.g., 99.92%).
  • The fit P(m) = A·p^m + B absorbs state-preparation-and-measurement (SPAM) errors into A and B, isolating gate error from readout error.
  • Standard RB gives an average over the gate set; Interleaved RB measures the fidelity of a specific gate.

Check your understanding

In Randomized Benchmarking, what does the classical computer append to each random gate sequence before it runs on the QPU?

  1. A.A measurement in the X basis
  2. B.The inverse gate that undoes the entire sequence
  3. C.An extra random gate
  4. D.A calibration pulse
Show the answer

Answer: B. The inverse gate that undoes the entire sequence

Why: The appended inverse gate means perfect hardware would always return the qubit to |0⟩ — so any failure to return measures the accumulated gate error, independent of which random gates were chosen.

In the RB fit P(m) = A·p^m + B, what is the role of the constants A and B?

  1. A.They set the average gate fidelity
  2. B.They absorb state-preparation-and-measurement (SPAM) errors
  3. C.They count the number of qubits
  4. D.They fix the sequence length
Show the answer

Answer: B. They absorb state-preparation-and-measurement (SPAM) errors

Why: SPAM errors shift and scale the curve but do not change the decay parameter p — that is why RB isolates gate error from preparation and readout error.

Builds on

Gate Fidelity

Primary source: Magesan, Gambetta & Emerson, Phys. Rev. Lett. 106, 180504 (2011), doi:10.1103/PhysRevLett.106.180504

RB protocol and exponential decay model per Magesan 2011; P(m)=A p^m + B with SPAM absorption is the standard form.

Learn it hands-on

This concept is part of a 46-level curriculum with an interactive simulator and Lumen, a tutor whose answers are verified before you see them. Levels 1–5 are free.

Start freeSee the curriculum