Quickly extracting fidelity decay rates in random circuit benchmarking experiments

arXiv:2610.11540 · quant-ph · Submitted 2026-10-08 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quickly extracting fidelity decay rates in random circuit benchmarking experiments".

Mira: The gist: The trace filter function, introduced as a one-parameter family of estimators,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So to summarize this paper, they are focusing on how to fix that finite-depth mixing bias in randomized benchmarking for structured circuits. The main claim is that by using classical post-processing with a family of estimators, specifically the trace filter function, we can suppress those transient modes causing biased short-depth fidelity estimates.

Mira: They argue this is necessary because waiting for those transients to decay in deeper circuits pushes the signal below the noise floor, which has been a persistent obstacle in linear cross-entropy benchmarking.

Lev: Essentially, they're redesigning the estimators themselves rather than changing the circuit ensemble or normalizing by an ideal reference signal to handle this finite-depth mixing bias.

Kai: The paper introduces a one-parameter family of filter functions that interpolate between the standard LinXEB post-processing and this new trace filter function. They rigorously argue that under time-stationary Markovian gate-dependent noise and practical local symmetry assumptions, the associated RB experiment has a mixing length of zero for this technique.

Mira: The key finding there is that for perfect gates, the expected RB signal becomes dependent only on sequence length and independent of m, which means we can extract fidelities from much shorter circuits.

Lev: They prove that the subdominant decays are perfectly suppressed with this trace filter function, even in the absence of noise when gates are implemented perfectly.

Kai: The paper also discusses how this method allows us to tune a parameter alpha to trade off variance for mixing length, which is a practical consideration for experimental setups.

Mira: So what they're claiming is that this approach gives us an interpretable fidelity decay at short depth, with theoretical guarantees comparable to standard RB, but with an increased variance cost.

Lev: The implication here is that we can use these techniques to characterize relevant structured circuit ensembles and short-depth regimes that conventional estimators simply couldn't handle before.

Conclusion: Kai: So looking at the title, "Quickly extracting fidelity decay rates in random circuit benchmarking experiments," it really captures the essence of what they did: finding a faster way to get those important fidelity estimates.

Mira: The authors, Köhne, Efthymiou, Majsak, Wilkens, Evert, Patterson, Helsen and Heinrich and Roth are tackling the technical challenge of finite-depth mixing bias head-on with a specific mathematical tool.

Lev: What this means in simple terms is that if you're running experiments on quantum hardware today and you only have limited depth or time to run circuits, this paper offers a method to get a more reliable fidelity characterization than what standard methods provide.

Kai: It moves the problem from waiting for deep circuits to fix the signal to using classical post-processing to clean up the data from shorter runs.

Mira: They've shown that by tuning this filter function, we can make short circuit fidelities more reliable, even if it means we have to live with a higher variance in our estimates.

Lev: So for someone listening who is just trying to understand why this paper matters, it's about extending the practical reach of randomized benchmarking fidelity characterization to regimes that were previously too noisy or too shallow for standard techniques.

CWI & QuSoft, Amsterdam · Quantum Research Center, Technology Innovation Institute, Abu Dhabi · Institute for Theoretical Physics, University of Cologne, Cologne, Germany · Johannes Kepler Universität Linz, Austria · Rigetti Computing

quant-ph

Submitted: 2026-10-08

Updated: 2026-10-08

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 83/100

The gist: The gist: The trace filter function, introduced as a one-parameter family of estimators, overcomes finite-depth mixing bias in randomized benchmarking by suppressing transient modes and exposing

Key concepts

Randomized Benchmarking (RB)
RB is a technique used to estimate the average fidelity of quantum gates by running random sequences of gates on a system. When applied to structured circuits, it helps characterize how errors accumulate over time, but it can be biased at short circuit depths due to mixing issues.
Transient Modes
These are temporary, non-decaying components in the RB signal that appear when the circuit depth is insufficient for complete ensemble mixing. Waiting for these modes to disappear in deeper circuits often results in a signal too weak to measure reliably above the noise floor.
Trace Filter Function
This new post-processing technique is part of a family of estimators designed to suppress transient modes. By using this filter, the method exposes an interpretable fidelity decay even at short circuit depths, providing reliable characterization where conventional methods fail.

Terminology

Summary

The gist: The trace filter function, introduced as a one-parameter family of estimators, overcomes finite-depth mixing bias in randomized benchmarking by suppressing transient modes and exposing interpretable fidelity decay at short circuit depths, extending reliable characterization to regimes inaccessible to conventional estimators

The Problem Addressed

Randomized benchmarking (RB) with structured circuits is experimentally scalable but yields biased short-depth fidelity estimates due to incomplete ensemble mixing introducing transient modes Waiting for these transients to decay in deeper circuits can push the signal below the noise floor This issue is a well-established obstacle, e.g., in linear cross-entropy benchmarking (LinXEB) Neglecting these components biases single-exponential estimates of the decay rate

The Proposed Solution

The authors introduce a one-parameter family of estimators that interpolate between the standard LinXEB-type post-processing and a new technique called the trace filter function Under practical assumptions, the trace filter function provably suppresses transient modes, exposing an interpretable fidelity decay at short depth, with theoretical guarantees comparable to standard RB The method is defined by a filter function family fα interpolating between the standard LinXEB-type estimator and a new estimator, called the trace filter function

Key Theoretical Findings

**)&Proposition 3. Assume the RB experiment admits a time-stationary, Markovian gate-set description with perfect state-preparation (0⟩⟨0, ϕ, E˜i) on the support of ν. Let M˜ = PxEx)(E˜x and T: X 7→R ω†(g)Xϕ(g)dν(g). Further assume that [T m(M˜), ω(Cl⊗n1)] = 0, then E[f3] = 2n + 1/4n Tr[P T m(M˜)] If ϕ(g) = ω(g), i.e., gates are perfectly implemented, and ν is right-invariant under Cl×n1, T m[M˜] commutes with local Clifford channels for all m and operators M˜. Here, the first circuit layer implements (at least) a perfect local Clifford twirl For perfect gates the expected RB signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T(M˜)] independent of m The underlying assumption that the noise does not break the local Clifford symmetry of ν-twirls is rather weak and often justifiable in practice The trace filter function α = 3 has a mixing length indistinguishable from zero, numerically validating the analytical statements in the previous section For perfect gates the expected RB signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal exhibits a mixing phase dependent on sequence length m even in the absence of noise Thus, for the trace filter function, the subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n Tr[P T m(M˜)] independent of m The subdominant decays are perfectly suppressed The expected f3 signal becomes E[f3(x, g)] = 2n+1/4n

Improvements for AI systems

  1. Improved fidelity characterization for structured circuits by utilizing trace filter functions to suppress transient modes, allowing reliable fidelity estimation at short circuit depths (e.g., the trace filter function provably suppresses transient modes, exposing an interpretable fidelity decay at short depth). This enables the system to reliably characterize performance in regimes inaccessible to conventional estimators, such as those below 10 layers for 12 qubits.

  2. Development of a tunable parameter family of estimators that allows for a trade-off between variance and mixing length, controlled by the parameter α (where the parameter α allows us to trade off variance for mixing length). This enables the system to select an optimal estimator based on noise rates and architecture to minimize uncertainty in the extracted decay rate.

  3. Creation of efficient, scalable classical post-processing algorithms for evaluating filter functions, including a practically scalable stabilizer-based implementation for Clifford circuits (as mentioned in Section D). This ensures that the fidelity estimation process remains computationally tractable even when dealing with complex circuit ensembles.

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