Nadarasa · references · Quantinuum Helios 2026
The logical-qubit frontier, in nine papers
Reference set anchoring the 2026 Helios result. Each paper is mapped into the four Nadarasa frontiers — rule (M) soundness under noise, G1 QFT-readout, tomographic equivalence, and the PQP frontier — so the identities we verify in _cache_2q_noise/ sit inside the current empirical envelope.
Headline · arXiv:2602.22211 · Feb 2026
arXiv ↗Computing with many encoded logical qubits beyond break-even
Dasu, DeCross et al.
48–94 simultaneous logical qubits on 98-qubit Helios via iceberg [[k+2,k,2]] + concatenated [[(k₁+2)(k₂+2), k₁k₂, 4]] beat their unencoded counterparts across FT and pFT benchmarks.
- 98 physical qubits (Helios)
- 48–94 logical qubits active
- d=2 (iceberg) → d=4 (concatenated)
- beyond break-even on GHZ + 3D XY pFT
Code-family timeline · logical qubits per demonstration
Two years of Quantinuum scaling: 1 logical qubit ([[7,1,3]] color, 2022) → 12 logical qubits (tesseract d=4, 2024) → 94 logical qubits (concatenated iceberg d=4, 2026), each above physical break-even.
A different road · doi:10.1038/s41586-026-10709-y · Nature 655 · Jul 2026
Nature ↗Universal gates from braiding and fusing anyons on quantum hardware
Lo, Lyons, … Verresen, Iqbal (Nature 655)
54-qubit ground state of the S₃ quantum double on Quantinuum H2; braiding + anyon-fusion measurement yields a universal topological gate set, demonstrated by topologically preparing a magic state.
- H2 · 54 physical qubits · 3×3 lattice
- Ground-state fidelity 0.977(6)–0.986(4)
- Magic state fidelity 0.930(8)–0.978(2)
- First universal topological gate set on hardware
Off-axis to the timeline above: logical information lives in the global fusion space of non-Abelian S₃ anyons, not in a stabilizer code, so it doesn't map onto the "logical qubits per code distance" scale. Fusion rules a × ā = a + … are the same string-diagram combinatorics that Ch. 8 spider fusion abstracts in our methodology citations — the same algebra, one road ideal, one road on 54 physical qubits.
Generative Quantum AI · arXiv:2607.22468 · Jul 2026
arXiv ↗Learning to Prepare Molecular Ground States with Transformer Models
Koziell-Pipe, Brewer, Guhit, Farag, Panchagnula, Laude, Finger, Gaggioli, Szulakowska, Backhouse, Papalitsas, Mustakis, Soini, Muñoz Ramo, Clark, Kyoseva, Rinaldi
ADAPT-GQE: train transformers on ADAPT-VQE reference circuits, then use RL to generate compact ground-state preparation circuits for drug-scale molecules; demonstrated on imipramine and executed on Quantinuum Helios-1.
- Helios-1 · AI-generated chemistry circuits
- Imipramine (tricyclic antidepressant) target
- Order-of-magnitude faster than ADAPT-VQE
- RL refines circuits past training-data accuracy
ADAPT-GQE sits at the synthesis layer: where the rewriter shrinks circuits by syntax, this pipeline learns to generate them from data. The two routes can compose — a generated subcircuit can be canonicalised by the same rule-(M) / rule-(N) machinery that proves identities on Selene. See the deep-dive at /nadarasa/g15.
Non-Clifford break-even · arXiv:2506.14688
Breaking even with magic: a high-fidelity logical non-Clifford gate
[[6,2,2]] magic-state prep + logical CH gate: 2.3×10⁻⁴ infidelity beats the 10⁻³ physical CH; projected 6×10⁻¹⁰ at d=4.
- · 8 physical qubits (H1-1)
- · logical CH infidelity ≤ 2.3×10⁻⁴
- · physical CH ≈ 10⁻³
- · projected d=4: 6×10⁻¹⁰ at p=10⁻³
Memory lifetime multiplier · arXiv:2503.22107
Order-of-magnitude extension of qubit lifetimes with a DFS-QEC code
Concatenated decoherence-free subspace + outer QEC extends logical memory lifetime by >10× vs. bare physical qubits on Quantinuum H1.
- · Quantinuum H1
- · >10× memory lifetime multiplier
- · DFS inner + QEC outer
Hardware context — Helios and H1-1
Certified randomness · arXiv:2511.03686
Certified randomness amplification by dynamically probing remote random states
Real-time 64-qubit / 276-2Q-gate random circuits on 98-qubit Helios reach F=0.586 with a 30 ms classical spoofing window — device-independent certified randomness.
- · Helios, 98 qubits
- · 64Q · 276 2Q gates · F = 0.586
- · 30 ms spoofing window
- · ≈ 0.9 s coherence maintained
Unconditional info separation · arXiv:2509.07255
Demonstrating an unconditional separation between quantum and classical information
12 qubits on H1-1 (2Q fidelity 99.941%) solve a task provably requiring 62–382 classical bits — unconditional, no complexity-theoretic assumptions.
- · H1-1 · 12 qubits
- · 2Q fidelity 99.941(7)%
- · classical lower bound: 62–382 bits
- · unconditional advantage
Full references · 11 papers
| Ref | Title | Mapping | Result |
|---|---|---|---|
| arXiv:2602.22211 Feb 2026 | Computing with many encoded logical qubits beyond break-even Dasu, DeCross et al. | rule-MG1PQP | 48–94 simultaneous logical qubits on 98-qubit Helios via iceberg [[k+2,k,2]] + concatenated [[(k₁+2)(k₂+2), k₁k₂, 4]] beat their unencoded counterparts across FT and pFT benchmarks. |
| arXiv:2503.22107 Mar 2025 | Order-of-magnitude extension of qubit lifetimes with a DFS-QEC code Dasu et al. | rule-M | Concatenated decoherence-free subspace + outer QEC extends logical memory lifetime by >10× vs. bare physical qubits on Quantinuum H1. |
| arXiv:2506.14688 Jun 2025 | Breaking even with magic: a high-fidelity logical non-Clifford gate Dasu et al. | tomographyPQP | [[6,2,2]] magic-state prep + logical CH gate: 2.3×10⁻⁴ infidelity beats the 10⁻³ physical CH; projected 6×10⁻¹⁰ at d=4. |
| arXiv:2507.10519 Jul 2025 | A Classification of Transversal Clifford Gates for Qubit Stabilizer Codes Dasu & Burton | rule-MPQP | Diagonal transversal Clifford group of any ℓ-block stabilizer code lies in exactly one of six matrix-group families, completing the Rains classification. |
| arXiv:2511.03686 Nov 2025 | Certified randomness amplification by dynamically probing remote random states Liu, Niroula, DeCross et al. | G1PQP | Real-time 64-qubit / 276-2Q-gate random circuits on 98-qubit Helios reach F=0.586 with a 30 ms classical spoofing window — device-independent certified randomness. |
| arXiv:2509.07255 Sep 2025 | Demonstrating an unconditional separation between quantum and classical information Kretschmer, Grewal, DeCross et al. | tomographyPQP | 12 qubits on H1-1 (2Q fidelity 99.941%) solve a task provably requiring 62–382 classical bits — unconditional, no complexity-theoretic assumptions. |
| arXiv:2409.04628 Sep 2024 | Quantum computation and error correction with a tesseract code Reichardt et al. | rule-MPQP | [[16,4,4]] tesseract subsystem color code on trapped ions prepares 12-logical-qubit graph states with ~10× error reduction across 5 QEC rounds. |
| arXiv:2208.01863 Aug 2022 | Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code Ryan-Anderson et al. | rule-MG1 | First FT logical CNOTs on [[5,1,3]] and [[7,1,3]] with logical SPAM 99.94–99.96% beating physical SPAM 99.68–99.70% — the origin of the flagging + pieceable-FT gadget library. |
| doi:10.1038/s41586-026-10709-y Jul 2026 | Universal gates from braiding and fusing anyons on quantum hardware Lo, Lyons, … Verresen, Iqbal (Nature 655) | Topological QCH2 hardwareMagic state prep | 54-qubit ground state of the S₃ quantum double on Quantinuum H2; braiding + anyon-fusion measurement yields a universal topological gate set, demonstrated by topologically preparing a magic state. |
| arXiv:2607.22468 Jul 2026 | Learning to Prepare Molecular Ground States with Transformer Models Koziell-Pipe, Brewer, Guhit, Farag, Panchagnula, Laude, Finger, Gaggioli, Szulakowska, Backhouse, Papalitsas, Mustakis, Soini, Muñoz Ramo, Clark, Kyoseva, Rinaldi | Generative QCH2 hardwarePQP | ADAPT-GQE: train transformers on ADAPT-VQE reference circuits, then use RL to generate compact ground-state preparation circuits for drug-scale molecules; demonstrated on imipramine and executed on Quantinuum Helios-1. |
| arXiv:2607.24937 Jul 2026 | Resolving Structure in Prethermal Floquet Dynamics with Precision Quantum Computation Leviatan, Watad, Perry, Broers, Mullath, Alberton, Arad, Atia, Bairey, Barkan, Ben Dov, Berkovitch, van den Berg, Cohen, Golan, Gurwich, Haber, Katzir, Kenneth, Levi, Lifshitz, Lukovsky, Melcer, Meyer, Muratov, Panahi, Schul, Shnaider, Shutman, Seif, Shirakawa, Sinay, Su, Tepanyan, Trebitch, Zubida, Aharonov, Gharibyan, Kandala, Yunoki, Lindner | PQPH2 hardwareError mitigation | Floquet mixed-field Ising magnet on a heavy-hex lattice. QESEM (PEC + ZNE) on IBM Heron r3 reaches percent-level precision at up to 74 qubits; subharmonic prethermal oscillations corroborated on Quantinuum H2 and Helios. |
Cross-links: rule (M) noise sweep → /nadarasa/proofs/noise-2q · promoted conjectures → /nadarasa/proofs/conjectures-2q-selene · G1 QFT-readout → /nadarasa/g1.