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CHAPTER 24

# Reading the experimental frontier in 2026

Learning goals. Classify current claims, connect experiments to the theory already learned, and identify what evidence would strengthen or weaken a conclusion.

## 24.1 A dated scientific snapshot

Research cutoff: 5 September 2026. This chapter collects selected primary evidence relevant to an introductory course. It is not a league table or a census of every announcement. The purpose is to connect mathematical and engineering concepts to inspectable results while keeping the limits of each claim visible.

The references distinguish a journal article from its earlier preprint and online date from issue year. Where full text was inaccessible, the scope below is restricted to the accessible primary abstract or official record. The source notes identify those cases. No figure or experimental dataset in this chapter is a fabricated measurement.

## 24.2 Error suppression and logical operations

Experiment: a below-threshold surface-code memory. Google Quantum AI’s Willow study was published online on 9 December 2024 and appeared in Nature 638 (2025). It reported distance-dependent logical suppression and a distance-seven memory beyond its physical-memory comparison. The publisher lists an author correction dated 28 April 2026; it fixes repetition-code axis and legend labels in Figure 3a, and the updated article and correction were consulted [47, 48]. Chapter 18 discusses the reported per-cycle metric. Scaling a memory establishes an important component, while universal operations and sustained large computations add further requirements.

Experiment: neutral-atom logical architecture. Bluvstein et al.’s article appeared online on 10 November 2025 and in Nature 649 (2026). Its accessible primary abstract describes repeated surface-code characterization, logical entangling operations, teleportation-based logic, and mid-circuit reuse in reconfigurable arrays [49]. The evidence supports demonstrated architectural components under the reported circuits. It does not establish unlimited-depth operation or practical advantage for arbitrary applications.

Experiment with correction and detection. Paetznick et al., published 10 June 2026, reported logical error improvements ranging from 11-fold to 800-fold relative to several physical circuit baselines on a trapped-ion QCCD device. The work combines correction, detection, and postselection [50]. The accessible journal abstract was used here. The improvement factors must therefore be interpreted with the different baselines and acceptance conditions; they are not a universal multiplier applicable to every algorithm.

These studies demonstrate why the distinction among encoding, detection, correction, memory, and logical gates matters. A single word such as “logical” cannot carry the whole experimental specification.

## 24.3 Hardware scale and benchmark scope

Experiment: a 98-qubit trapped-ion processor. The Helios article was published online on 17 June 2026 [59]. Its reported all-to-all architecture is a physical platform result. This book uses the primary publication record and preprint as a platform reference, rather than treating the qubit count as evidence for a particular large algorithm’s runtime.

Experiment: modular photonics. Aghaee Rad and collaborators’ 2025 work investigates a modular photonic architecture and networking [60]. The important lesson is system composition: sources, optical components, detection, switching, and loss must work together. An architecture experiment is different from a complete useful fault-tolerant application.

Experiment: networked processing. Main et al.’s 2025 optical-link study connects trapped-ion modules and demonstrates distributed operations [66]. Teleportation and feed-forward become concrete engineering tools. A successful laboratory link does not by itself provide a scalable wide-area quantum network.

Experiment and classical comparison: many-body interference. Google’s October 2025 Nature paper studies interference in quantum dynamics and associated classical simulation difficulty, often discussed under the “Quantum Echoes” name [63]. Such a result must be read with its observable, circuit family, accuracy, and comparison algorithm. The paper’s benchmark claim does not imply that every quantum circuit is difficult to simulate or that every application now has an advantage.

## 24.4 Conditional resource estimates

Preprint / theory: revised RSA resources. Gidney’s 21 May 2025 preprint analyzes a different space–time tradeoff for RSA-2048 factoring [52]. Its hardware assumptions include a square-grid architecture, specified gate error, code-cycle time, and classical response time. Chapter 20 compares its scope with the peer-reviewed 2021 estimate. These are architecture analyses, not observed cryptographic attacks.

Preprint / theory: reconfigurable-atom resources. Cain et al.’s 30 March 2026 preprint explores high-rate coding and reconfigurable atomic architectures [53]. Its abstract describes cryptographically relevant instances at approximately ten-thousand-qubit scales; a 26,000-qubit scenario is associated with a few-day P-256 discrete-log estimate, whereas RSA-2048 is one to two orders of magnitude slower under its assumptions. The workloads and tradeoffs must remain attached to the numbers.

This distinction is especially important when a title’s smallest qubit count is repeated without its runtime or target cryptosystem. An improved theoretical estimate can change planning priorities while still requiring substantial unbuilt engineering.

## 24.5 Disputed interpretations and company announcements

Microsoft-associated hybrid-device parity measurements have prompted scientific debate about what the diagnostic evidence establishes [61, 62]. This text describes the measurement work and the existence of a technical challenge to its interpretation. It does not adjudicate a disputed topological-computation claim by treating a press release as a proof.

A company roadmap states an intended future capability. It is useful evidence about that company’s goals, not evidence that the capability exists or will arrive on schedule. This book deliberately gives no forecast date for a general cryptographically relevant or commercially useful fault-tolerant machine. Such a date is not established by the sources considered.

## 24.6 What would count as stronger evidence?

For error correction, seek replicated distance scaling, clearly defined logical operations, acceptance and discard statistics, stable long runs, realistic noise, and an integrated decoder. For an algorithm, seek a task matched to the input-output problem, total resource accounting, controlled accuracy, and comparison against strong classical methods. For hardware, seek representative simultaneous-operation results and scaling behavior, rather than only the best isolated component.

Negative results also matter. A classical method reproducing a claimed difficult observable can narrow an advantage claim. A decoder floor can invalidate a favorable large-distance extrapolation. A failed optimization can expose a state-preparation bottleneck. Scientific progress includes refining the conditions under which a claim holds.

A beginner is ready to read frontier papers when they can ask: What state was prepared? What operation was implemented? What was measured? What was conditioned on? Which errors were modeled? Which costs were counted? Which conclusion follows directly, and which is an extrapolation?

## 24.7 Exercises

24.1. Classify “a paper estimates an algorithm needs 20,000 qubits under specified noise” as experiment, theorem, estimate, or roadmap.

Show solution / guidance

It is an estimate or theoretical analysis. It may contain mathematical theorems, but the physical requirement remains conditional on the architecture and model.

24.2. A logical demonstration reports 99.99% conditional accuracy while accepting 5% of attempts. Find accepted-correct probability per attempt.

Show solution / guidance

0.9999×0.05=0.049995 0.9999\times0.05=0.049995, or 4.9995%. This does not make the experiment unimportant, but it changes its throughput interpretation.

24.3. Why retain both online and issue dates?

Show solution / guidance

They distinguish when a result became available from the bibliographic year assigned to its issue. A 2026 issue can contain work publicly available in 2025.

24.4. A benchmark’s classical runtime was later reduced greatly. Does the original experiment disappear?

Show solution / guidance

No. Its measurements remain evidence, but the comparative advantage claim may need revision. Experimental validity and superiority over a moving baseline are separate questions.

24.5. What is missing from “our processor has the most logical qubits”?

Show solution / guidance

The definition of logical, code and distance, supported operations, error and acceptance metrics, stability, physical overhead, timing, and the task being compared.

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