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arxiv: 2504.01936 · v2 · submitted 2025-04-02 · 🪐 quant-ph

Fermionic Averaged Circuit Eigenvalue Sampling

Adrian Chapman , Steven T. Flammia This is my paper

Pith reviewed 2026-05-22 21:32 UTC · model grok-4.3

classification 🪐 quant-ph
keywords fermionic linear opticsaveraged circuit eigenvalue samplingquantum noise characterizationgate-dependent noiseKravchuk transformationsquantum error mitigationFLO circuits
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The pith

FACES protocol simultaneously learns averaged error rates of many fermionic linear optical gates with efficient sampling.

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

The paper introduces the FACES protocol for learning the averaged error rates of multiple fermionic linear optical gates at once from collections of circuits. It does this self-consistently while characterizing gate-dependent noise under assumptions about parameterized gates. A sympathetic reader would care because this could help with noise characterization in quantum systems that have a fermionic description, potentially aiding error mitigation as circuits become universal with added resources. The efficiency of the sampling is shown rigorously using properties of Kravchuk transformations.

Core claim

Fermionic averaged circuit eigenvalue sampling (FACES) is a protocol to simultaneously learn the averaged error rates of many fermionic linear optical (FLO) gates simultaneously and self-consistently from a suitable collection of FLO circuits. It is highly flexible, allowing for the in situ characterization of FLO-averaged gate-dependent noise under natural assumptions on a family of continuously parameterized one- and two-qubit gates. The protocol has an efficient sampling complexity, owing in-part to useful properties of the Kravchuk transformations that feature in our analysis.

What carries the argument

The FACES protocol, which adapts averaged circuit eigenvalue sampling to fermionic linear optical circuits and uses Kravchuk transformations to achieve efficient sampling complexity.

Load-bearing premise

The protocol relies on natural assumptions on a family of continuously parameterized one- and two-qubit gates to enable in situ characterization of FLO-averaged gate-dependent noise.

What would settle it

An experiment or simulation where the number of samples required to achieve a certain accuracy grows super-polynomially with the number of gates or qubits would falsify the efficient sampling claim.

Figures

Figures reproduced from arXiv: 2504.01936 by Adrian Chapman, Steven T. Flammia.

Figure 1
Figure 1. Figure 1: A graphical outline of the FACES protocol. (a) Given a set of noisy gates [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Histogram of relative errors for 2n = 10 fermionic modes with 1000 circuits for each experiment type. See main text for description. by our assumption that both Λi ≥ 1 2 and Λˆ i ≥ 1 4 for all i. Finally, we use this to provide a bound on ∥bˆ − b∥∞ as ∥bˆ − b∥∞ ≤ 4∥δΛ∥∞ (77) = 4∥VδP∥∞ (78) ≤ maxj  4∥δP (j) ∥1  (79) ∥bˆ − b∥∞ ≤ 4ε. (80) From the second to the third line above, we replaced the maximum over… view at source ↗
read the original abstract

Fermionic averaged circuit eigenvalue sampling (FACES) is a protocol to simultaneously learn the averaged error rates of many fermionic linear optical (FLO) gates simultaneously and self-consistently from a suitable collection of FLO circuits. It is highly flexible, allowing for the in situ characterization of FLO-averaged gate-dependent noise under natural assumptions on a family of continuously parameterized one- and two-qubit gates. We rigorously show that our protocol has an efficient sampling complexity, owing in-part to useful properties of the Kravchuk transformations that feature in our analysis. We support our conclusions with numerical results. As FLO circuits become universal with access to certain resource states, we expect our results to inform noise characterization and error mitigation techniques on universal quantum computing architectures which naturally admit a fermionic description.

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 / 0 minor

Summary. The paper introduces Fermionic Averaged Circuit Eigenvalue Sampling (FACES), a protocol for simultaneously and self-consistently learning the averaged error rates of many fermionic linear optical (FLO) gates from collections of FLO circuits. It claims rigorous proof of efficient sampling complexity, leveraging properties of Kravchuk transformations, under natural assumptions on families of continuously parameterized one- and two-qubit gates that enable in situ characterization of FLO-averaged gate-dependent noise; numerical results are provided in support, with expected implications for noise characterization on universal architectures admitting fermionic descriptions.

Significance. If the central claims hold, the work provides a flexible, self-consistent approach to noise learning in FLO circuits that could extend to error mitigation on universal quantum devices. The rigorous efficiency bound via Kravchuk transforms and the numerical validation constitute clear technical strengths.

major comments (1)
  1. [Abstract] Abstract: the efficiency and self-consistency claims rest on unspecified 'natural assumptions' on continuously parameterized 1- and 2-qubit gates that permit in situ FLO-averaged gate-dependent noise characterization; without an explicit list or verification of these assumptions (e.g., continuity, independent variation, closure under FLO averaging), the load-bearing step for the sampling-complexity bound is unanchored.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive suggestion regarding the abstract. We address the major comment below and will incorporate the feedback in a revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the efficiency and self-consistency claims rest on unspecified 'natural assumptions' on continuously parameterized 1- and 2-qubit gates that permit in situ FLO-averaged gate-dependent noise characterization; without an explicit list or verification of these assumptions (e.g., continuity, independent variation, closure under FLO averaging), the load-bearing step for the sampling-complexity bound is unanchored.

    Authors: We agree that the abstract would benefit from greater specificity on the assumptions. These assumptions (continuous parameterization of the gate families, independent variation across gates, and closure under FLO averaging) are formally stated and verified in Section 3 of the manuscript, where they underpin the Kravchuk-transform analysis and the sampling-complexity bound. In the revised manuscript we will expand the abstract to explicitly enumerate the key assumptions and include a direct reference to Section 3 for their definition and verification. revision: yes

Circularity Check

0 steps flagged

No significant circularity; efficiency claim rests on independent Kravchuk transform analysis under stated assumptions.

full rationale

The abstract and description present a protocol whose sampling complexity bound is asserted to follow rigorously from properties of the Kravchuk transformations. No equations or steps are shown that reduce the claimed prediction to a fitted parameter defined by the protocol itself, nor is there load-bearing self-citation of an unverified uniqueness result. The 'natural assumptions' on gate families are listed as prerequisites enabling the in-situ characterization, not derived from the result. This matches the default case of a self-contained derivation with no exhibited circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Ledger extracted from abstract only; full paper may contain additional parameters or assumptions.

axioms (1)
  • domain assumption Natural assumptions on a family of continuously parameterized one- and two-qubit gates
    Invoked to enable in situ characterization of FLO-averaged gate-dependent noise.

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Reference graph

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