arxiv: 2605.11158 · v1 · submitted 2026-05-11 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Scalable linearized gate set tomography

Ashe Miller, Corey Ostrove, Jordan Hines, Kevin Young, Noah Siekierski, Robin Blume-Kohout, Timothy Proctor

Pith reviewed 2026-05-13 02:35 UTC · model grok-4.3

classification 🪐 quant-ph

keywords linearized gate set tomographyquantum error characterizationsparse error modelsmany-qubit systemscoherent errorscrosstalkgate set tomographyquantum computing

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The pith

Linearized gate set tomography scales error characterization to many-qubit systems by using sparse models and a linear approximation on shallow-circuit data.

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

The paper introduces linearized gate set tomography to characterize errors on many-qubit quantum computers. It combines sparse error models with a linear approximation for efficient fitting of data collected from shallow circuits, keeping the approximation's systematic error small. This approach is tested in simulations of a ten-qubit system that includes both coherent and stochastic errors plus coherent crosstalk. The method proves accurate in these simulations and remains robust even when additional errors outside the assumed model are present. A reader would care because full error characterization has been limited to small systems, and better diagnosis of physical mechanisms is needed to improve larger quantum devices.

Core claim

Linearized gate set tomography enables characterization of many-qubit systems. It relies on sparse error models, a linear approximation to enable efficient data fitting, and data from shallow circuits so that the systematic error in the linear approximation is small. The technique is accurate in simulations of a ten-qubit system with coherent and stochastic errors including coherent crosstalk, and it is robust in the presence of additional errors that are not included within the sparse error model ansatz.

What carries the argument

Linearized gate set tomography, which applies a linear approximation to the gate set tomography fitting problem together with a sparse ansatz for the error model to process shallow-circuit data efficiently.

If this is right

Characterization of coherent, stochastic, and crosstalk errors becomes feasible on systems up to at least ten qubits without assuming only stochastic Pauli errors.
The method stays accurate even when the sparse model omits some physical error sources.
Efficient data fitting from shallow circuits reduces the resources needed compared to full nonlinear tomography.
Physical error mechanisms in many-qubit devices can be diagnosed more directly to guide device improvements.

Where Pith is reading between the lines

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

The same linear-plus-sparse strategy might be adapted to other tomography or benchmarking protocols that currently face scaling limits.
If shallow-circuit data collection remains practical, the approach could be tested on hardware systems beyond ten qubits to check real-world scaling.
Robustness to unmodeled errors suggests the method could serve as a diagnostic tool even when the full error physics is unknown.

Load-bearing premise

The linear approximation introduces only small systematic error when data comes from shallow circuits, and the chosen sparse error model ansatz captures the dominant physical mechanisms even when unmodeled errors are present.

What would settle it

A direct comparison on ten-qubit simulated or experimental data where the error parameters reconstructed by linearized GST deviate substantially from those obtained by a full nonlinear method or from independent fidelity benchmarks on deeper circuits.

Figures

Figures reproduced from arXiv: 2605.11158 by Ashe Miller, Corey Ostrove, Jordan Hines, Kevin Young, Noah Siekierski, Robin Blume-Kohout, Timothy Proctor.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: shows the rank of the design matrix divided by the number of parameters κ, which equals 1 iff D is full rank, as a function of κ. We find that in every randomly-sampled instance the design matrix is full rank for sufficiently many circuits. If a full-rank D can be constructed, then model has no gauge freedom. These results therefore indicate that randomly-sampled models typically have no gauge freedom. In … view at source ↗

read the original abstract

Characterizing errors on many-qubit quantum computers remains a key challenge to understanding and improving the performance of these devices. Current characterization methods either don't scale beyond a few qubits, or make simplifying assumptions (such as assuming stochastic Pauli error) that obscure the underlying physical error mechanisms. In this work, we present a scalable extension to gate set tomography-linearized gate set tomography-that enables characterization of many-qubit systems. Linearized gate set tomography relies on sparse error models, a linear approximation to enable efficient data fitting, and data from shallow circuits-so that the systematic error in the linear approximation is small. We demonstrate the accuracy of our technique using simulations of a ten-qubit system with coherent and stochastic errors, including coherent crosstalk, and we demonstrate that it is robust in presence of additional errors that are not included within the sparse error model ansatz.

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.

Desk Editor's Note private letter to a colleague

Linearized GST scales error characterization to ten qubits in simulation by pairing a linear approximation with sparse models and shallow-circuit data.

read the letter

This paper gives a workable route to gate set tomography on systems larger than a handful of qubits. The key move is linearizing the tomography equations around a reference model, then imposing sparsity on the error parameters so that fitting stays tractable even when the number of qubits grows. Data comes from shallow circuits, which keeps the linearization error small. The authors test the whole pipeline on a ten-qubit simulation that includes both coherent and stochastic errors plus crosstalk, and they check that the fit remains useful when extra unmodeled errors are present.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces linearized gate set tomography (LGST), a scalable extension of gate set tomography for characterizing errors on many-qubit systems. It relies on sparse error models, a linear approximation to the error map for efficient fitting, and data collected from shallow circuits to ensure the approximation error remains small. The central claims are validated through numerical simulations on a 10-qubit system that include coherent and stochastic errors as well as crosstalk, with additional tests showing robustness when the sparse ansatz is incomplete.

Significance. If the linearization and sparsity assumptions hold under realistic conditions, LGST would address a key scalability barrier in quantum error characterization, enabling diagnostics on systems beyond the reach of standard GST. The simulations incorporate physically relevant error types (coherent crosstalk, mixed coherent/stochastic) and explicitly test robustness to unmodeled errors, which strengthens the practical utility of the approach for near-term hardware.

major comments (1)

[Linear Approximation and Fitting Procedure] The linear approximation's systematic error for shallow circuits is load-bearing for the accuracy and robustness claims. The manuscript should include either an analytic bound on the neglected higher-order terms or a direct numerical comparison (e.g., LGST versus full nonlinear GST on the same 10-qubit data) to quantify the approximation error as a function of circuit depth and error strength.

minor comments (1)

Add a brief statement of the computational scaling of the linear least-squares fit (e.g., matrix size versus qubit number) to make the scalability advantage over standard GST explicit.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment and constructive comments on our manuscript introducing linearized gate set tomography. We address the major comment point by point below.

read point-by-point responses

Referee: The linear approximation's systematic error for shallow circuits is load-bearing for the accuracy and robustness claims. The manuscript should include either an analytic bound on the neglected higher-order terms or a direct numerical comparison (e.g., LGST versus full nonlinear GST on the same 10-qubit data) to quantify the approximation error as a function of circuit depth and error strength.

Authors: We agree that explicitly quantifying the systematic error of the linear approximation is important for supporting the accuracy and robustness claims. A direct comparison with full nonlinear GST on the 10-qubit data is not feasible, as full GST does not scale to this size due to exponential growth in parameters and computational cost—this scalability barrier is the central motivation for developing LGST. In the revised manuscript, we will add numerical comparisons between LGST and full GST on smaller systems (2–4 qubits) using the same error models, circuit depths, and error strengths to quantify the approximation error as a function of these parameters. We will also include an analytic bound on the neglected higher-order terms, derived from a perturbative expansion of the error superoperator under the assumption of small error rates consistent with the shallow-circuit regime. These additions will appear in a new subsection of the Methods and an appendix with supporting analysis and figures. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces linearized gate set tomography via sparse error models, a linear approximation to the error map, and shallow-circuit data to keep systematic error small. The central claims of accuracy and robustness are validated through forward simulations of a 10-qubit system containing coherent, stochastic, and crosstalk errors (plus unmodeled errors), rather than by fitting parameters to the same data used to define the model. No self-definitional equations, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract or description. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that a sparse error model plus linear approximation suffices for the dominant errors in shallow circuits. No free parameters or invented entities are explicitly introduced in the abstract.

free parameters (1)

Sparse error model coefficients
Coefficients in the sparse model are fitted to the collected data.

axioms (2)

domain assumption A linear approximation to the error-to-outcome map is accurate for shallow circuits
Invoked to justify efficient fitting while keeping systematic error small.
domain assumption Sparse combinations of Pauli and coherent errors capture the main physical mechanisms
Required for the model to remain tractable and for robustness claims.

pith-pipeline@v0.9.0 · 5450 in / 1361 out tokens · 76474 ms · 2026-05-13T02:35:47.806853+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
Linearized GST relies on sparse error models, a linear approximation to enable efficient data fitting, and data from shallow circuits—so that the systematic error in the linear approximation is small.
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear
We demonstrate the accuracy of our technique using simulations of a ten-qubit system with coherent and stochastic errors, including coherent crosstalk

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