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arxiv: 2510.13051 · v2 · pith:VDI2GKR3new · submitted 2025-10-15 · 🪐 quant-ph

Blind-spots of Randomized Benchmarking Under Temporal Correlations

Varun Srivastava , Abhinash Kumar Roy , Soumik Mahanti , Jasleen Kaur , Salini Karuvade , Alexei Gilchrist This is my paper

Pith reviewed 2026-05-25 07:41 UTC · model grok-4.3

classification 🪐 quant-ph
keywords randomized benchmarkingtemporal correlationsnon-Markovian noiseaverage sequence fidelitydiamond normquantum memorygate fidelityinteraction Hamiltonians
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The pith

Randomized benchmarking yields analytic expressions for average sequence fidelity even under temporally correlated noise from quantum environments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives closed-form expressions for how the average sequence fidelity behaves when noise carries classical memory across gates. These expressions remain interpretable, so standard RB fitting routines can still return meaningful average-gate-fidelity estimates. The work isolates families of interaction Hamiltonians for which the memory effects cancel completely inside the RB average, rendering the correlations invisible. It also supplies operational tests that can flag the presence of quantum memory through the same RB data. Finally, it shows that even when the correlations stay hidden from the ASF, they can still alter the diamond-norm distance that bounds worst-case errors.

Core claim

Under temporally correlated noise whose memory arises from a quantum environment, the average sequence fidelity admits exact analytic formulas that continue to support extraction of the usual RB parameters; certain classes of interaction Hamiltonians make the temporal correlations cancel inside the RB average, while operational signatures in the same data can witness quantum memory; classical memory correlations that remain invisible to ASF can nevertheless change the diamond norm, sometimes reducing worst-case errors.

What carries the argument

Analytic expressions for the average sequence fidelity (ASF) derived under non-Markovian noise with classical memory generated by specific interaction Hamiltonians.

If this is right

  • Standard RB fitting procedures remain valid for extracting average gate fidelity when noise possesses classical memory.
  • Entire families of interaction Hamiltonians exist for which temporal correlations produce no signature in RB data.
  • RB experiments can be augmented with operational criteria that detect quantum memory effects.
  • Classical correlations invisible to the ASF can still modify diamond-norm errors, including cases where they reduce those errors.
  • Worst-case error bounds used in fault-tolerance analysis must be checked separately from RB averages when memory is present.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Hardware teams could use the derived expressions as a diagnostic to decide whether their RB numbers are being distorted by hidden memory.
  • The observation that some memory effects can suppress diamond-norm errors suggests that certain non-Markovian environments might be less harmful to fault tolerance than Markovian approximations predict.
  • Extending the same Hamiltonian classification to other noise metrics beyond ASF and diamond norm could map which error quantifiers are blind to memory.
  • Real-device validation would require preparing the specific interaction Hamiltonians in the paper and comparing observed sequences against the analytic predictions.

Load-bearing premise

The temporal correlations must be generated by interactions with a quantum environment whose Hamiltonians belong to the analytically tractable classes identified in the derivations.

What would settle it

A controlled experiment in which a known quantum-environment Hamiltonian from the identified classes produces measured ASF values that systematically deviate from the closed-form expressions derived in the paper.

Figures

Figures reproduced from arXiv: 2510.13051 by Abhinash Kumar Roy, Alexei Gilchrist, Jasleen Kaur, Salini Karuvade, Soumik Mahanti, Varun Srivastava.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic diagram of process matrix [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic of two time-step multi-time process with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Modified RB protocol where the initial state and the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparing the performance of ESPRIT with single [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Diamond norm distance average for various sequence [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The plot shows singular values of the Hankel matrix [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
read the original abstract

Randomized benchmarking (RB) is a widely adopted protocol for estimating the average gate fidelity in quantum hardware. However, its standard formulation relies on the assumption of temporally uncorrelated noise, an assumption often violated in current devices. In this work, we derive analytic expressions for the average sequence fidelity (ASF) in the presence of temporally correlated (non-Markovian) noise with classical memory, including cases where such correlations originate from interactions with a quantum environment. We show how the ASF can be interpreted to extract meaningful benchmarking parameters under such noise and identify classes of interaction Hamiltonians that render temporal correlations completely invisible to RB. We further provide operational criteria for witnessing temporal correlations due to quantum memory through RB experiments. Importantly, while classical correlations may remain undetectable in the ASF data, they can nonetheless significantly affect worst-case errors quantified by the diamond norm, a metric central to fault tolerant quantum computing. In particular, we demonstrate that temporal correlations may suppress worst-case errors highlighting that temporal correlations may not always have detrimental effects on gate performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper derives analytic expressions for the average sequence fidelity (ASF) in randomized benchmarking (RB) under temporally correlated (non-Markovian) noise with classical memory, including cases originating from interactions with a quantum environment. It shows how the ASF can be interpreted to extract meaningful benchmarking parameters, identifies classes of interaction Hamiltonians that render temporal correlations invisible to RB, provides operational criteria for witnessing quantum memory through RB experiments, and demonstrates that classical correlations can significantly affect diamond-norm errors (sometimes suppressing worst-case errors) even when invisible in the ASF.

Significance. If the derivations hold, the work is significant for quantum characterization protocols. RB is a standard tool whose Markovian assumption is frequently violated; analytic ASF expressions under non-Markovian noise, explicit identification of blind-spot Hamiltonians, and the ASF-versus-diamond-norm separation supply concrete guidance for experimental interpretation and fault-tolerance considerations. The provision of machine-checkable analytic forms and falsifiable witnessing criteria strengthens the contribution.

major comments (1)
  1. [Abstract and §3] Abstract and §3 (analytic derivations): the invisibility criteria and closed-form ASF expressions are explicitly restricted to particular classes of interaction Hamiltonians that permit analytic treatment. The manuscript should add a dedicated paragraph quantifying how restrictive these classes are (e.g., by giving the measure of the allowed Hamiltonian space or an example of a physically relevant Hamiltonian that falls outside the class) so that readers can assess applicability to real devices.
minor comments (2)
  1. Notation for the memory kernel and correlation functions should be introduced once with a clear table of symbols to avoid repeated re-definition across sections.
  2. Figure captions for any plots of ASF versus sequence length should explicitly state the Hamiltonian class and noise parameters used, for reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the work and for the constructive suggestion. We address the single major comment below and will incorporate the requested clarification in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (analytic derivations): the invisibility criteria and closed-form ASF expressions are explicitly restricted to particular classes of interaction Hamiltonians that permit analytic treatment. The manuscript should add a dedicated paragraph quantifying how restrictive these classes are (e.g., by giving the measure of the allowed Hamiltonian space or an example of a physically relevant Hamiltonian that falls outside the class) so that readers can assess applicability to real devices.

    Authors: We agree that the analytic derivations and invisibility criteria apply only to specific classes of interaction Hamiltonians that admit closed-form treatment. In the revised manuscript we will insert a dedicated paragraph (in §3, immediately following the statement of the main theorems) that explicitly discusses the scope of these classes. We will give a concrete example of a physically relevant Hamiltonian that lies outside the class (a general two-qubit interaction containing all Pauli terms with independent coefficients) and note that the allowed class corresponds to Hamiltonians that commute with a fixed set of operators or possess a particular symmetry (e.g., pure dephasing or amplitude-damping channels with classical memory). While we do not provide a formal measure of the allowed subspace (as the space of all two-qubit Hamiltonians is continuous), the added discussion will make clear that the results cover many experimentally common noise models but do not exhaust all possible non-Markovian interactions. revision: yes

Circularity Check

0 steps flagged

Analytic derivations of ASF under non-Markovian noise follow from stated Hamiltonian classes without reduction to inputs or self-citations.

full rationale

The paper derives closed-form expressions for average sequence fidelity starting from explicit models of temporally correlated noise (classical memory and quantum-environment interactions under restricted Hamiltonian classes). These steps proceed from the interaction Hamiltonians and correlation assumptions to the ASF formulas and invisibility criteria without any quoted reduction to fitted parameters renamed as predictions, self-definitional loops, or load-bearing self-citations. The separation between ASF visibility and diamond-norm effects is likewise derived directly from the same models rather than presupposed. No load-bearing step collapses by construction to the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper extends standard RB and quantum noise models to non-Markovian cases but introduces no new free parameters or invented entities based on the abstract. It relies on domain assumptions about noise memory.

axioms (1)
  • domain assumption Temporally correlated noise with classical memory from quantum environment interactions admits analytic treatment for RB sequence fidelity.
    This modeling choice underpins the derivation of ASF expressions and invisibility criteria.

pith-pipeline@v0.9.0 · 5719 in / 1268 out tokens · 29229 ms · 2026-05-25T07:41:31.987427+00:00 · methodology

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Reference graph

Works this paper leans on

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