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arxiv: 2606.31428 · v1 · pith:33KEUI4Enew · submitted 2026-06-30 · 🪐 quant-ph · cs.IT· math.IT

The limits of erasure-based postselection for quantum error mitigation

Sam J. Griffiths , Jamie Friel , Brian Vlastakis This is my paper

Pith reviewed 2026-07-01 05:25 UTC · model grok-4.3

classification 🪐 quant-ph cs.ITmath.IT
keywords postselectionerasure mitigationdual-rail qubitsquantum error mitigationNISQ devicesquantum Fourier transformerasure noise
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The pith

Postselection on dual-rail qubits fully mitigates erasure noise for check error rates under 3 percent and exceeds single-rail performance at kiloquop scales.

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

This paper examines postselection as a method to mitigate errors in quantum circuits using dual-rail transmon qubits that detect erasures. By discarding any circuit runs where an erasure is flagged, the technique removes the impact of erasure errors when the checks themselves err less than 3 percent of the time. Simulations of the quantum Fourier transform show that this postselected dual-rail approach can reach lower effective error rates than a standard single-rail system once the circuit involves thousands of operations. The result suggests postselection offers a practical route to better performance in near-term quantum devices before full error correction is available. A new open-source tool is introduced to model erasure noise and postselection effects.

Core claim

The authors establish that postselection fully mitigates the erasure channel for erasure check error rates less than 3.0%. They further show that a postselected dual-rail system can surpass a fundamental noise floor at the kiloquop scale where a comparable single-rail system cannot. This is demonstrated through numerical simulations that include both erasure noise and gate depolarising noise on the quantum Fourier transform.

What carries the argument

The postselection procedure on dual-rail erasure qubits, which discards shots detecting erased qubits, combined with the numerical framework for circuit-level erasure noise.

Load-bearing premise

The numerical noise model and postselection procedure accurately capture real-device behaviour, including any unmodelled correlations between erasure detection errors and gate depolarisation.

What would settle it

Performing the quantum Fourier transform experiment on dual-rail hardware with varying erasure check error rates and verifying whether the postselected error rate drops to zero below the 3% threshold as predicted by the simulations.

Figures

Figures reproduced from arXiv: 2606.31428 by Brian Vlastakis, Jamie Friel, Sam J. Griffiths.

Figure 1
Figure 1. Figure 1: Illustrations of the two equivalent erasure noise models implemented in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Cost of postselection for QFT with 5000 target shots. The trends show erasure noise with ideal checks (green), erasure noise with check noise (orange), and erasure noise with check noise and gate depolarising noise (blue). Note how false pos￾itives dominate to strictly increase the rejection rate over ideal checks. Error bars for rejection rate show the 95% confidence interval, calculated via the Clopper-P… view at source ↗
Figure 3
Figure 3. Figure 3: Mean and minimum circuit fidelity for QFT with 5000 target shots, with and without postselection, for pe = 0.005 and q = 0.010. The T1 → ∞ reference is equivalent to a standalone de￾polarising model (i.e. pe = q = 0). Error bars for mean fidelity (here and hereinafter) show the 95% confidence interval, calculated via Student’s t dis￾tribution of the standard error of the mean (SEM). 8 [PITH_FULL_IMAGE:fig… view at source ↗
Figure 4
Figure 4. Figure 4: Gain in mean circuit fidelity for QFT achieved with postselection. For the absolute fi￾delity gain ∆F (top), the curves are fitted via non￾linear least-squares regression on the difference be￾tween two reverse logistic (i.e. sigmoid) functions, as in Figure 3c (with error bars propagated accord￾ingly), with their approximated maxima shown. The relative gain (bottom) shows the quotient rather than the diffe… view at source ↗
Figure 5
Figure 5. Figure 5: Mean circuit fidelity for QFT with 10,000 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mean circuit fidelity for QFT with sa = 1000 target shots for both single-rail and postse￾lected dual-rail qubits, assuming pe = 0.008 and q = 0.005. The dashed horizontal line marks a 1/ √ 1000 ≈ 3% fidelity benchmark [22] [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

In both classical and quantum error correction, heralded erasures are known to be easier to tolerate than unheralded general stochastic errors. Whilst an established benefit of loss-dominant quantum architectures such as photonic qubits, this fact has received renewed interest, with a pivot towards reconstructing other architectures to be erasure-dominant, such as dual-rail transmons. This work investigates exploiting these 'erasure qubits' in the near term by using postselection as a technique for error mitigation, wherein circuit shots detecting any erased qubits are discarded from the computational ensemble and repeated. Firstly, we outline a numerical framework for representing circuit-level erasure noise and present 'erado', an open-source library capable of simulating erasure noise and postselection. Secondly, we investigate the effects of both erasure noise and noise in the erasure checks themselves on the quantum Fourier transform (QFT), in the additional presence of gate depolarising noise. A worked example is provided of postselection fully mitigating against the erasure channel for erasure check error rates less than 3.0%. We also show how a postselected dual-rail system can surpass a fundamental noise floor at the kiloquop scale where a comparable single-rail system cannot, justifying this approach in the NISQ regime before (and, perhaps, combined with) the practical arrival of QEC.

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

2 major / 2 minor

Summary. The manuscript introduces a numerical framework for circuit-level erasure noise and the open-source 'erado' library for simulating erasure and postselection. Through Monte Carlo simulations of the quantum Fourier transform under combined erasure and depolarizing noise, it shows that postselection can completely mitigate the erasure channel for erasure check error rates below 3%, and that postselected dual-rail qubits can exceed the performance limit of single-rail systems at the kiloquop scale.

Significance. The work offers a practical, simulation-backed strategy for error mitigation in near-term erasure-biased hardware such as dual-rail transmons. The release of reproducible code is a notable strength that allows direct verification of the reported thresholds and scale claims.

major comments (2)
  1. [Abstract] Abstract: the claim that postselection 'fully mitigates' the erasure channel for check error rates less than 3.0% is load-bearing for the central result, yet the abstract provides no explicit statement of the QFT size, circuit depth, or precise fidelity metric used to establish 'full mitigation'; this makes it impossible to judge whether the threshold is robust or specific to the chosen instance.
  2. [Numerical framework] Numerical framework section: the kiloquop-scale claim that a postselected dual-rail system surpasses the single-rail noise floor rests on the Monte-Carlo noise model; the manuscript should quantify the sensitivity of this crossing point to the assumed independence between erasure-check errors and gate depolarisation, as any unmodelled correlation would directly affect the reported advantage.
minor comments (2)
  1. The description of the erado library would benefit from an explicit statement of the default noise-parameter ranges and the exact postselection discard rule implemented in the QFT simulations.
  2. Figure captions should list the precise erasure and depolarising rates together with the number of shots used for each data point to facilitate immediate reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation and constructive comments, which help clarify the presentation of our results. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that postselection 'fully mitigates' the erasure channel for check error rates less than 3.0% is load-bearing for the central result, yet the abstract provides no explicit statement of the QFT size, circuit depth, or precise fidelity metric used to establish 'full mitigation'; this makes it impossible to judge whether the threshold is robust or specific to the chosen instance.

    Authors: We agree that the abstract would benefit from additional context on the specific instance used to demonstrate full mitigation. The main text reports this for a concrete QFT circuit under the stated noise model, with the fidelity metric defined in the numerical framework section. In the revised manuscript we will update the abstract to state the QFT size, circuit depth, and fidelity metric explicitly. revision: yes

  2. Referee: [Numerical framework] Numerical framework section: the kiloquop-scale claim that a postselected dual-rail system surpasses the single-rail noise floor rests on the Monte-Carlo noise model; the manuscript should quantify the sensitivity of this crossing point to the assumed independence between erasure-check errors and gate depolarisation, as any unmodelled correlation would directly affect the reported advantage.

    Authors: The Monte Carlo model treats erasure-check errors and gate depolarisation as independent, consistent with standard circuit-level noise assumptions in the absence of device-specific correlation data. We acknowledge that positive correlations could alter the reported crossing point. We will add an explicit statement of this modeling assumption in the numerical framework section together with a qualitative discussion of how correlations would affect the dual-rail advantage; a full quantitative sensitivity sweep is beyond the scope of the current Monte Carlo study but can be noted as a direction for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper derives its thresholds and performance claims (full mitigation below 3.0% check error; dual-rail surpassing single-rail floor at kiloquop scale) exclusively from direct Monte-Carlo simulations of postselection on a QFT circuit under erasure plus depolarizing noise, implemented in the open-source erado library. No load-bearing analytical step reduces by the paper's own equations to a fitted parameter, self-defined quantity, or self-citation chain; the numerical results are independently reproducible from the stated noise model and procedure without internal redefinition or smuggling of ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The work rests on standard quantum channel models and Monte-Carlo sampling assumptions common to the field.

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