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arxiv: 2404.02280 · v3 · submitted 2024-04-02 · 🪐 quant-ph

Recognition: 1 theorem link

Demonstration of logical qubits and repeated error correction with better-than-physical error rates

A. Paetznick (1) , M. P. da Silva (1) , C. Ryan-Anderson (2) , J. M. Bello-Rivas (1) , J. P. Campora III (2) , A. Chernoguzov (2) , J. M. Dreiling (2) , C. Foltz (2)
show 25 more authors
F. Frachon (1) J. P. Gaebler (2) T. M. Gatterman (2) L. Grans-Samuelsson (1) D. Gresh (2) D. Hayes (2) N. Hewitt (2) C. Holliman (2) C. V. Horst (2) J. Johansen (2) D. Lucchetti (2) Y. Matsuoka (2) M. Mills (2) S. A. Moses (2) B. Neyenhuis (2) A. Paz (1) J. Pino (2) P. Siegfried (2) A. Sundaram (1) D. Tom (1) S. J. Wernli (1) M. Zanner (1) R. P. Stutz (2) K. M. Svore (1) ((1) Microsoft Azure Quantum (2) Quantinuum)
Authors on Pith no claims yet

Pith reviewed 2026-05-16 23:10 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum error correctionlogical qubitsfault tolerancetrapped-ion processorerror suppressionQCCD
0
0 comments X

The pith

Trapped-ion processor shows logical error rates below physical levels via fault-tolerant encoding.

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

This paper reports experiments on a trapped-ion QCCD processor that use fault-tolerant encoding and error correction to make logical qubit error rates lower than those of physical qubits. Logical qubits in the [[7,1,3]] code reach error rates 9.8 to 500 times lower than physical, while a [[12,2,4]] code based on Knill's scheme reaches 4.7 to 800 times lower depending on post-selection. The work further shows repeated error correction cycles on the [[12,2,4]] code where the logical error rate per cycle, despite involving over 100 physical CNOTs, approaches the rate of just two physical CNOTs.

Core claim

Logical qubits encoded in the [[7,1,3]] code and a [[12,2,4]] code exhibit error rates 9.8 to 800 times lower than physical qubits, with repeated error correction on the latter code yielding per-cycle logical error rates that approach the baseline of two physical CNOT operations.

What carries the argument

Fault-tolerant encoding and repeated error correction on the [[7,1,3]] Steane code and Knill's [[12,2,4]] code implemented on a trapped-ion QCCD processor.

If this is right

  • Logical qubits can outperform physical qubits in error performance under fault-tolerant operation.
  • Repeated error correction cycles remain beneficial even when each cycle uses over 100 physical gates.
  • Error rates per logical cycle can approach those of minimal physical two-qubit gates.
  • These capabilities mark a transition toward reliable quantum computing at larger scales.

Where Pith is reading between the lines

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

  • Sustained suppression at this level could support computations with millions of logical operations if overheads remain manageable.
  • The post-selection dependence suggests that hybrid strategies combining correction with selective discarding may be useful in early fault-tolerant systems.
  • Similar encoding schemes could be tested on other hardware to check whether the error-rate crossover is platform-independent.

Load-bearing premise

The comparison between logical and physical error rates assumes that post-selection and circuit implementations do not introduce unaccounted biases or that the physical error baselines accurately represent the relevant operations without systematic offsets.

What would settle it

An experiment that measures logical error rates exceeding the physical baseline when using identical operations but without post-selection would show the claimed suppression does not hold.

read the original abstract

The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels inversely proportional to the size of the computation. As a step towards this ambitious goal, we present experiments on a trapped-ion QCCD processor where, through the use of fault-tolerant encoding and error correction, we are able to suppress logical error rates to levels below the physical error rates. In particular, we entangled logical qubits encoded in the [[7,1,3]] code with error rates 9.8 times to 500 times lower than at the physical level, and entangled logical qubits encoded in a [[12,2,4]] code based on Knill's C4/C6 scheme with error rates 4.7 times to 800 times lower than at the physical level, depending on the judicious use of post-selection. Moreover, we demonstrate repeated error correction with the [[12,2,4]] code, with logical error rates below physical circuit baselines corresponding to repeated CNOTs, and show evidence that the error rate per error correction cycle, which consists of over 100 physical CNOTs, approaches the error rate of two physical CNOTs. These results signify a transition from noisy intermediate scale quantum computing to reliable quantum computing, and demonstrate advanced capabilities toward large-scale fault-tolerant quantum computing.

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 presents experimental results from a trapped-ion QCCD processor demonstrating fault-tolerant logical qubits using the [[7,1,3]] code and [[12,2,4]] code based on Knill's C4/C6 scheme. It reports suppression of logical error rates below physical error rates for entangling operations, with factors ranging from 9.8x to 500x for the former and 4.7x to 800x for the latter depending on post-selection. The work also shows repeated error correction with the [[12,2,4]] code, achieving logical error rates below physical baselines for repeated CNOTs, and evidence that the per-cycle logical error rate approaches that of two physical CNOTs despite over 100 physical operations per cycle.

Significance. If validated, these results mark an important advance in experimental quantum error correction by achieving better-than-physical error rates on encoded qubits and demonstrating repeated correction cycles. This provides empirical support for the transition to fault-tolerant quantum computing on current hardware platforms, particularly highlighting the potential of trapped-ion systems for scalable error-corrected operations.

major comments (2)
  1. [Error-rate extraction and C4/C6 implementation details] The comparison of logical error rates (with post-selection discarding detected-error runs) to physical baselines for repeated CNOTs lacks explicit demonstration that the physical error model applies an identical post-selection filter. Without this, the reported suppression factors (4.7–800×) and the per-cycle error approaching two CNOTs may not be directly comparable, as unfiltered physical errors could include detectable components not accounted for equivalently.
  2. [Repeated error correction results] The claim that the error rate per error correction cycle approaches the error rate of two physical CNOTs requires a detailed breakdown of the physical baseline circuit, including state preparation, measurement, and transport overheads in the QCCD architecture, to confirm equivalence with the logical implementation.
minor comments (2)
  1. [Abstract] The ranges of suppression factors in the abstract are presented without specifying the exact conditions, number of trials, or statistical uncertainties for each endpoint.
  2. [Methods] Clarify the precise definition of 'physical circuit baselines' for repeated CNOTs, including whether they match the full set of operations and error sources present in the logical circuits.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and have revised the manuscript to incorporate additional clarifications and details as requested.

read point-by-point responses

  1. Referee: The comparison of logical error rates (with post-selection discarding detected-error runs) to physical baselines for repeated CNOTs lacks explicit demonstration that the physical error model applies an identical post-selection filter. Without this, the reported suppression factors (4.7–800×) and the per-cycle error approaching two CNOTs may not be directly comparable, as unfiltered physical errors could include detectable components not accounted for equivalently.

    Authors: We agree that an explicit demonstration of identical post-selection is necessary for rigorous comparison. The physical baseline error rates were in fact computed using the same error model and post-selection filter (discarding runs with detected errors) as the logical case. To address this concern, the revised manuscript now includes an expanded Methods section with a step-by-step description of the shared post-selection procedure and a new supplementary figure that directly compares physical error rates with and without the filter. This confirms that the reported suppression factors remain valid under equivalent filtering. revision: yes

  2. Referee: The claim that the error rate per error correction cycle approaches the error rate of two physical CNOTs requires a detailed breakdown of the physical baseline circuit, including state preparation, measurement, and transport overheads in the QCCD architecture, to confirm equivalence with the logical implementation.

    Authors: We thank the referee for this suggestion. The physical baseline was constructed to include equivalent overheads for state preparation, measurement, and ion transport in the QCCD architecture, matching the logical circuit's resource count. The revised manuscript now provides a detailed breakdown in the main text (Section on repeated error correction) together with a supplementary table enumerating all physical operations per cycle, including preparation gates, measurements, CNOTs, and transport steps. This breakdown substantiates that the per-cycle logical error rate approaches the cost of two physical CNOTs after accounting for these overheads. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental measurements with explicit post-selection accounting

full rationale

This is an experimental demonstration paper reporting measured logical error rates from fault-tolerant circuits on a trapped-ion QCCD processor. The claims rest on direct comparisons of observed error rates (with and without post-selection) against physical circuit baselines, not on any derivation, equation, or prediction that reduces to its own inputs by construction. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations appear in the reported results. The post-selection filter is explicitly described and applied to logical data; physical baselines are reported separately without equivalent filtering, but this is a methodological choice open to scrutiny rather than a circular reduction. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard quantum error correction theory and the assumption that the physical device behaves according to established models for the tested codes.

axioms (1)
  • domain assumption Standard quantum error correction theory applies to the hardware
    The paper assumes the [[7,1,3]] and [[12,2,4]] codes function as predicted by theory on the trapped-ion processor without unmodeled noise sources dominating.

pith-pipeline@v0.9.0 · 5814 in / 1262 out tokens · 40690 ms · 2026-05-16T23:10:21.391413+00:00 · methodology

discussion (0)

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