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Mid-circuit erasure check ro_erasure

Ancilla- or fluorescence-based test of whether a qubit is still in its code space, flagging decay/leakage as a located erasure without reading the logical state.

Mid-circuit erasure check

ro_erasure · layer 6 Readout · demonstrated · since 2023
Open on the map

Ancilla-based detection of leakage/loss without disturbing the code: 384 ns (transmon), 1.8 µs (cavity), 20 µs (Yb atoms).

Reading marks
crossing technology — fabricated carrier + erasure error structure; natural carrier + ≤ 10 µs readout
Brief →

Key references

[8] Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, “Erasure conversion for fault-tolerant q… · 2022
[334] A. Kubica et al., “Erasure Qubits: Overcoming the T₁ Limit in Superconducting Circuits,” P… · 2023
[399] J. D. Teoh et al., “Dual-rail encoding with superconducting cavities,” Proc. Natl. Acad. S… · 2023
[141] S. Ma et al., “High-fidelity gates with mid-circuit erasure conversion in a metastable neu… · 2023
[143] P. Scholl, A. L. Shaw, R. B.-S. Tsai, R. Finkelstein, J. Choi, and M. Endres, “Erasure con… · 2023

Design space — attributes

(a) carrier affinity
intermediate / carrier-agnostic
(b) time · entangling
—
(c) readout
ancilla erasure check · 398 ns · non-destructive · mid-circuit
(d) mobility
—
(e) control
microwave @ room temperature
(f) error structure
erasure-convertible
(g) manufacturing
—

Evaluation space — dated attributes

transmon dual-rail check → 384 ns; FP/FN ≈ separation error 0.8% (SNR 11.6)
defines: clock (cycle time) · 2026-04 · source
cavity dual-rail check → 1.8 µs, FP 0.51% / FN 3.7%
defines: clock (cycle time) · 2025-01 · source
Yb erasure detection → 20 µs (1Q) / 420 µs (2Q)
defines: clock (cycle time) · 2023-05 · source

Standard records

reset / initialisation time → not published · typical
Transmon dual-rail check: 'The SRO intrinsically resets on a timescale set by its linewidth kappa (tens to hundreds of ns)' · 2026-04 · source [D] ⓘ
reset error → not published · typical
No reset error quoted; the budget is given as separation, dephasing and residual error per check · 2026-04 · source [D] ⓘ
SPAM error → 8.00e-3 · typical
Transmon dual-rail erasure check: 384 ns pulse, separation error eps_sep = 0.8% at SNR 11.6(5); FP/FN limited by the same 0.8% · 2026-04 · source [D] ⓘ
QND fidelity / survival → 1 · best
Symmetric readout resonator: induced dephasing 8(3)e-5 per erasure check; total residual error 6.0(2)e-4 per check · 2026-04 · source [D] ⓘ

Actors & goals — annotations

Dual-rail erasure qubits — D-Wave/QCI, AWS, SUSTech · G3 G4
Rydberg tweezer array — alkaline-earth(-like) (Yb/Sr), erasure-native (alternate) — Atom Computing/Microsoft, Princeton, Caltech, planqc, Yaqumo · G1 G3 G7

Edges

needs: Dual-rail (erasure) encoding°, Metastable ('omg') erasure encoding°
needed by: Dual-rail (erasure) encoding°, Erasure-adapted codes
° one of several that would do · the usual route, not a strict need

Used by 11 machines (10 primary · 1 alternate)

↗ its register card · paper / product / press: links that name the machine (attribution checked on 20 Sep 2026)

Pictures

Every picture carries the story of what it shows and its credit line.

Fig. 3 — Figure 3: Converting decay errors into erasures. a, The dynamics of the qubit relaxation are measured by idling the qubit at a fixed Φext for a
A seven-panel figure of pulse-sequence drawings and measured data: populations of the lowest three energy levels over time, transition rates versus external flux, and a grid of repeated erasure-check outcomes. It is Figure 3 of "Converting qubit relaxation into erasures with a single fluxonium" by Chenlu Liu, Yulong Li and co-authors (arXiv). It illustrates mid-circuit erasure checks: the caption notes that direct decay between levels 2 and 0 is suppressed by orders of magnitude, which lets relaxation be caught as a detected erasure; compare selected (blue) and unselected (green) data. “Fig. 3 — Figure 3: Converting decay errors into erasures. a, The dynamics of the qubit relaxation are measured by idling the qubit at a fixed Φext for…” by Chenlu Liu et al., arxiv.org/abs/2601.11086, CC BY 4.0 (creativecommons.org/licenses/by/4.0/)
Fig. 5 — Figure 5: Mid-Circuit Quantum Erasure Detection. (a) Our composite erasure detection scheme comprises a tweezer depth increase, an error detection i…
Four-panel figure, cartoon and data plots, not a photograph: a sketch of a molecule held in an optical tweezer with the erasure-detection timing (deeper trap, detection image, Raman π pulse), Ramsey fringe offset and amplitude versus repeated detections, and population-loss measurements. From the arXiv paper "Demonstration of Erasure Conversion in a Molecular Tweezer Array" by Connor M. Holland, Lawrence W. Cheuk and co-authors. It shows a mid-circuit check that turns certain errors into flagged erasures; the plots track how much each repeated check disturbs the stored qubit. “Fig. 5 — Figure 5: Mid-Circuit Quantum Erasure Detection. (a) Our composite erasure detection scheme comprises a tweezer depth increase, an error detection image, and a…” by Connor M. Holland, Yukai Lu, Samuel J. Li, Callum L. Welsh, Lawrence W. Cheuk, arxiv.org/abs/2406.02391, CC BY 4.0 (creativecommons.org/licenses/by/4.0/)
Fig. 1 — Fig. 1: Overview of a fault-tolerant neutral atom quantum computer using erasure conversion.a Schematic of a neutral atom quantum computer, with a p…
Four-panel concept figure of a neutral-atom computer using erasure conversion. (a) A microscope objective above a plane of atoms; (b) ytterbium-171 levels: the qubit sits in the metastable 3P0 (F = 1/2) level, gates excite it to a Rydberg state, and most decays from there end in the ground state or, after ionization, in Yb+, where camera fluorescence flags them as erasures; (c) a surface-code patch with X and Z checks; (d) a syndrome circuit with erasure checks and fresh atoms from a reservoir. It is Fig. 1 of Wu, Kolkowitz, Puri and Thompson, Nature Communications (2022). It shows how a metastable qubit turns most gate errors into detectable erasures. “Fig. 1 — Fig. 1: Overview of a fault-tolerant neutral atom quantum computer using erasure conversion.a Schematic of a neutral atom quantum computer, with a plane of…” by Wu, Yue; Kolkowitz, Shimon; Puri, Shruti; Thompson, Jeff D., www.nature.com/articles/s41467-022-32094-6, CC BY 4.0 (creativecommons.org/licenses/by/4.0/)
ro_erasure · layer 6 Readout · centrality 20.6 · demonstrated · since 2023 · updated 2026-09-30

Mid-circuit erasure check

Ancilla- or fluorescence-based test of whether a qubit is still in its code space, flagging decay/leakage as a located erasure without reading the logical state.

Verdict. The check is solved on transmons (384 ns, residual 6×10⁻⁴); unsolved are erasure fraction under two-qubit gates, false negatives and the cycle-time tax. Demote if no erasure system shows logical Λ > 2 by end-2027.

Key references

Λ = error-suppression factor per code-distance step; QBI = DARPA Quantum Benchmarking Initiative (Stage A concept → B R&D plan → C government V&V); G1–G7 = the report's goal classes (see Actors & economics).

Identity & lineage

A mid-circuit erasure check asks "is this qubit still inside its code space?" and returns a one-bit herald with the qubit's location without disturbing the logical state. It needs an encoding whose dominant decay leaves the code space: dual-rail (one excitation in two transmons or two cavities; loss leaves the detectable vacuum) or a metastable atomic qubit (³P₀ in ¹⁷¹Yb, D₅/₂ in ⁴⁰Ca⁺) whose ground-state decay fluoresces under a beam the qubit does not see. Proposals: Princeton/Yale, 2022-01 — 98% of ¹⁷¹Yb errors convertible, surface-code threshold 0.937%→4.15% S[8]; AWS dual-rail transmons, 2022-08 S[334]; Yale cavities, 2022-12 S[399]. Demonstrations: Princeton ¹⁷¹Yb D[141] and Caltech ⁸⁸Sr D[143] in 2023-05; AWS transmons D[400] and Yale cavities D[401] in 2023-07.

Attributes from the technology graph (legend: a affinity natural↔fabricated; b time, deterministic/heralded; c readout mechanism, time, destructive?, mid-circuit?; d mobility; e control @ placement; f error structure; g manufacturing):

  • a = 0.5, carrier-agnostic.
  • b = n/a.
  • c = ancilla erasure check, ≈400 ns (10^−6.4 s), non-destructive, mid-circuit — the transmon record D[85], not the atomic 20 µs D[141].
  • d = none.
  • e = microwave @ room temperature (atoms: optical).
  • f = erasure-convertible (located, heralded loss).
  • g = none (a protocol, not an object).
    Rank 1 of 111; shared by the superconducting and neutral-atom families.

Physics & limits

In a transmon dual-rail pair the logical states are |10⟩ and |01⟩, so a T1 decay of either transmon lands in |00⟩. The check is a joint dispersive readout tuned so that both logical states pull the shared resonator equally while the vacuum pulls it differently; AWS reaches a residual logical splitting of −0.7(5) kHz against a −4.25 MHz dispersive shift D[85]. In a cavity pair an ancilla sensitive to the total photon number does the same job in 1.82 µs D[404]. For atoms a decay from ³P₀ to ¹S₀ is caught by 20 µs of fluorescence on ¹S₀–¹P₁, invisible to the metastable qubit, so survivors pick up less than 10⁻⁵ error per check D[141].

Each check costs one exposure to T1: AWS measures 2.54(1)×10⁻² erasure per 384 ns check against a residual undetected error of 6.0(2)×10⁻⁴; their ratio, the erasure bias of 42(1), is what a code cares about D[85].

Three floors are intrinsic. False negatives re-enter the code as leakage: Yale's 3.7% false-negative rate times its erasure rate gives a missed-erasure fraction of 9.0(5)×10⁻⁴ D[404]; AWS's are the readout's ≈0.8% separation error D[85]. Back-action: residual χ mismatch dephases the qubit by 8(3)×10⁻⁵ per check and the readout tone halves the erasure lifetime while on D[85]. Time: in atoms the 20 µs check stretches to 420 µs when Rydberg population must decay before imaging — hence 56(4)% of single-qubit but only ≈33% of two-qubit errors are converted D[141]. The code sees a located erasure p_e, a Pauli residual ≈p_e/40 and an unheralded leakage tail ≈FN×p_e; under that channel the surface-code threshold is 4.15% S[8] and biased-erasure codes reach 8.2–10.3% S[643]. The floor moves with longer T1, stronger readout and, for atoms, faster Rydberg-leakage detection.

Engineering state of the art

Best demonstrated: one dual-rail transmon qubit checked in 384 ns with a 6×10⁻⁴ residual (2026-04) D[85]; a cavity CZ with 0.5% erasure and 0.03% Pauli error (2026-08) D[84]. Typical at scale (3 Sep 2026): nothing above ten erasure qubits except OQC GENESIS, 16 dual-rail sites with error-detected readout — SUSTech's four dual-rail transmons at 98.8% logical Bell fidelity (2025-04) D[406], Quantum Circuits' 8-qubit Seeker (2024-11) C[86]. On atoms, Princeton's [[4,2,2]] blocks D[142] and JILA's 20-atom GHZ state D[644] (2025-06) are the largest erasure-checked circuits; Microsoft/Atom Computing's 24 logical qubits use end-of-round loss imaging, not mid-circuit checks D[149].

table
Year Figure Who Tag Src
2023-05 20 µs check at 0.986 detection fidelity; 56(4)% of 1Q errors converted Princeton ¹⁷¹Yb D [141]
2023-07 Erasure 2.19(2)×10⁻³ per gate, residual ≈40× lower, <0.1% dephasing per check AWS transmons D [400]
2024-06 1.82 µs mid-circuit check, FP 0.51%, FN 3.7% Yale cavities D [404]
2024-11 ⁴⁰Ca⁺ Bell 98.56→99.14% with erasure excision; 1 ms check Oregon D [393]
2025-06 ¹⁷¹Yb error-detected CZ 99.78(4)%, >90% Rydberg-decay detection JILA D [644]
2025-06 [[4,2,2]] teleportation 0.771→0.802 with erasure-selected ancillas Princeton D [142]
2026-04 384 ns check, residual 6.0(2)×10⁻⁴, bias 42(1) AWS D [85]
2026-08 Dual-rail CZ 500 ns, erasure ≈0.5% per gate, Pauli 0.029(6)%, bit-flip 2.8(4)×10⁻⁶ Quantum Circuits D [84]

Dominant term today: on transmons the idling erasure during the check (T1 ≈25 µs); on cavities the ancilla's decoherence; on atoms undetectable two-qubit errors and the Rydberg dead time.

Manufacturing, materials & supply chain

Transmon dual-rail uses standard superconducting lithography, but the pair must be flux-tunable to find a χ-matched point and dodge two-level systems, and both must be good — a yield-squared problem; AWS's five-day samples fluctuate with near-resonant TLSs D[85]. Cavity dual-rail needs two machined high-Q cavities plus an ancilla per qubit, hand-assembled — hence Quantum Circuits' plan of 8 → 17 → 49 → 181 qubits over 2024–2028 R[94]. The atomic check needs only an imaging beam and a camera. Cost and energy per checked qubit are unpublished. The transmon check inherits the dispersive-readout chain, whose amplifiers and refrigerators are the concentrated items. Export exposure: the BIS rule of 2024-09-06 G[301] fact lists parametric amplifiers and cryo-CMOS (3A901), refrigerators of ≥600 µW at ≤0.1 K (3A904) and quantum computers (4A906), these only when their qubit count and C-NOT error fall in the same band, from 34–99 qubits at ≤ 10⁻⁴ to any error from 2,000 qubits fact; the rule does not say whether a dual-rail qubit counts as one or two.

Control, readout & I/O burden

Superconducting: one readout resonator per dual-rail qubit on a multiplexed feedline, two flux lines per qubit, one TWPA per line — twice a transmon's I/O. Replacing an erased qubit within the cycle needs feed-forward of a few hundred ns. At 10³ qubits the wiring is the transmon wall doubled; at 10⁴ only cold multiplexing or cryo-CMOS works, helped by the one-bit flag; at 10⁶ the 384 ns per cycle and 2×10⁶ transmons are the price of the 40× bias. Atoms: one global 20 µs pulse and one camera frame per check — lines do not grow with N, but camera readout and processing (0.1–1 ms) set the loop latency, and fast frames cost survival (98.80(44)% for Kyoto's 17.6 µs ¹⁷⁴Yb imaging D[261]); the wall beyond 10⁴ atoms is frame budget.

Role in the stack

Two architectures: superconducting dual-rail erasure and alkaline-earth(-like) neutral atoms. It requires an erasure-detectable encoding — dual-rail, or the metastable "omg" (optical–metastable–ground) encoding — and provides the flags that dual-rail encodings and erasure-adapted codes consume. It displaces leakage removal and post-selection on bare transmons. The price of switching is 2× transmons plus a check every cycle; on atoms the metastable manifold costs single-qubit fidelity (99.12(4)% in ³P₀ against 99.968(3)% in the ground state of JILA's omg device D[645]). The pairing "fabricated carrier with an erasure error structure" is genuine; "natural carrier with ≤10 µs readout" is inherited from the transmon time, not earned by the 20 µs atomic check. Derived clock = sum of the syndrome round: gate layers + transport + readout + reset: dual-rail architecture 2.8 µs, set by the gate layers, with the 0.40 µs check a seventh of it; atom architecture 1.3 ms, set by transport, the check ≈1.5% of it. Neighbouring empty slots: the cold-stage decoder (a natural consumer of one-bit heralds) and the microwave–optical transducer.

Evidence — how the numbers were measured

FP/FN (false-positive/false-negative rates) come from preparing |0_L⟩, |1_L⟩ and the erased state and repeating the check; AWS quotes FP ≈ FN ≈0.8% and derives residual and bias from repeated-check and interleaved sequences under continuous detection D[85]. Gate-level erasure fractions are flag statistics and the residual Pauli error a low-depth linear fit D[84]. Atomic conversion fractions rest on the 0.986 detection fidelity D[141]; Caltech's ≥0.9971 Bell fidelity is a post-excision, SPAM-corrected bound D[143].

Not captured: survival (every headline fidelity is conditioned on "no erasure"; at 2.5% per check, forty checks halve the sample); false negatives, visible only as leakage in a multi-round code; spectator dephasing on shared feedlines, unbenchmarked beyond four qubits; drift (TLS-driven swings over 5–18 days D[85]); the time tax. Independent replications: AWS (2023, 2026) D[85], [400], Yale (2023, 2024) D[401], [404], Quantum Circuits (2026) D[84], SUSTech (2025) D[406], UMass (2026) D[405]; Princeton (2023, 2025) D[141], [142], Caltech (2023) D[143], JILA (2025) D[644]; Oregon (2024) D[393].

Conflicts. D-Wave says its qubits detect "approximately 90% of errors" C[94]; at gate level the fraction is 83–94% depending on whether the Pauli residual is the <0.1% bound or the 0.029% fit D[84]. Atomic two-qubit conversion is 33–38% D[141], [142] against the proposal's 98% S[8]. The [[4,2,2]] gain from erasure information is 1.9(4)× in the 2025-06 arXiv text D[142] but 3.6× as carried in the graph from the 2026-06 Nature Physics version D[142]; the arXiv value is used pending the published text.

Quantum Circuits' cumulative funding of ≈ $84 M to May 2024 is a trade-press figure P[646]; the company's release states no total. Oregon's metastable-ion Bell fidelities read 98.61 → 99.16 % in abstract summaries and 98.56 → 99.14 % in the arXiv v1 full text, the values used here D[393]. Not published: whether Quantum Circuits is the unnamed 18th DARPA QBI Stage A company — DARPA names 17 of 18 fact; the cost or energy per checked qubit, from any actor; a patent count for the Yale/Quantum Circuits dual-rail cavity families beyond two individual patents; AWS's spending on its dual-rail programme, and the grants attributable to this primitive behind the Princeton, Caltech, Yale, Oregon and SUSTech groups; and the atomic species of Google's neutral-atom track.

Actors & economics

Who.
Organisation Role Country What it does with the check Evidence
Quantum Circuits Inc. developer US Cavity dual-rail qubits; 8-qubit Seeker; 17-qubit system due 2026; D-Wave unit since 2026-01 D[84] C[86] fact
AWS Center for Quantum Computing developer US 384 ns χ-matched transmon check D[85], [400]
Yale University research US Cavity dual-rail origin; ancilla check D[401], [403], [404]
SUSTech (Shenzhen) research China Four dual-rail transmon qubits D[406]
Princeton University research US ¹⁷¹Yb metastable conversion; [[4,2,2]] D[141], [142]
Google Quantum AI developer US Atom track under Kaufman (ex-JILA ¹⁷¹Yb omg), 2026-03 fact P[158] D[644], [645]
Atom Computing developer US ¹⁷¹Yb 1,225-atom systems; loss by imaging; Magne with Microsoft D[149] fact

Money.

  • 2024-05 · Quantum Circuits · Series B extension · $26.5 M · Sequoia · cumulative ≈$84 M · closed P[646] fact
  • 2024-08-15 · Quantum Circuits · Series B close · >$60 M · ARCH, F-Prime, Sequoia, Hither Creek · overlaps the extension · closed C[647] fact
  • 2025-07-17 · QuNorth · Magne order, 50 logical qubits · €80 M · Atom Computing/Microsoft · ordered fact
  • 2025-11-06 · DARPA QBI Stage B · up to $15 M each · eleven teams, no dual-rail vendor · official G[65] fact
  • 2026-01-07 · D-Wave · acquires Quantum Circuits · $550 M ($300 M stock + $250 M cash) · closed 2026-01-19/20 C[14], [648] fact
  • 2026-05-21 · D-Wave; Atom Computing · US DoC CHIPS letters of intent · $100 M each · LOI fact
  • 2026-06-16 · Atom Computing · Series C · $100 M · Third Point Ventures · >$300 M cumulative · closed C[154] fact
  • 2026-08-06 · D-Wave · H1-2026 results · revenue $5.9 M (−67% YoY), cash $546.2 M · reported fact

Market & supply chain. Nobody sells an erasure check; it rides on the amplifiers and refrigerators of dispersive readout (concentrated, BIS-listed G[301]). Unit economics are unpublished; the structural cost is 2× transmons or two cavities plus an ancilla per qubit, against Quantum Circuits' claim of 10–20 physical per logical instead of ~200 C[86]. Only G3 and G4 pay, once codes run 10⁵–10⁶ rounds.

IP & standards. Amazon Technologies: US 11,748,652 B1, "Heralding of amplitude damping decay noise for quantum error correction" (Kubica, Retzker; filed 2021-12-10, granted 2023-09-05): heralded decay via a level outside the code space, dual-rail included G[336]. Yale: US 12,288,135, ancilla with an asymmetric error channel (filed 2019-06-28, granted 2025-04-29) G[408]. The Yale/Quantum Circuits cavity families now sit with D-Wave. No standard; Stim's HERALDED_ERASE instruction P[397] commoditises the decoding side.

Roadmaps & track record.

  • D-Wave: promised 2026-01-07 · initial dual-rail system available in 2026 · not delivered as of 2026-09-03 C[14].
  • D-Wave: promised 2026-06-01 · 17 qubits with logical error 2× below physical (2026), 49 / 20× (2027), 181 / 2,000× (2028), 10 logical (2030), 100 logical (2032), Λ = 10 · pending, no logical data R[94] fact.
    Credibility: Quantum Circuits/D-Wave high on physics, unproven on dates; AWS publishes results and promises no product; Princeton delivered the single-qubit half of its 2022 proposal S[8] D[141]; Atom Computing on schedule, uncommitted to mid-circuit checks.

Strategic reading. If erasure checks scale, the winners own high-T1 fabrication and the readout chain — D-Wave, AWS and the alkaline-earth(-like) camp (Atom Computing, Google); the losers are bare-transmon roadmaps buying threshold with Λ alone. Substitution threats: qutrit erasure qubits D[405] remove the 2× overhead; fast Yb imaging D[261] and loss-aware decoding erode the case for metastable encodings. Bargaining power stays with platform vendors, not suppliers.

Outlook & open questions

Confirm within 12–24 months if: D-Wave ships the 17-qubit system with published logical error 2× below physical by mid-2027 R[94]; any group runs ≥10 rounds of a distance-3 code on dual-rail qubits with survival reported; atomic two-qubit conversion reaches ≥70% with a check ≤50 µs; a χ-matched check reaches ≤250 ns with residual ≤3×10⁻⁴. Demote if by end-2027 no erasure system reports Λ >2 on unconditioned data. Best case by 2029: 100–200 dual-rail qubits at Λ ≈4–10 with 2 µs cycles, and Yb machines running erasure-aware codes. Worst case: erasure stays a two-qubit showpiece while bare transmons reach 10⁻³ and Λ ≈3 without it.

Open questions: (1) does the 40× bias survive parallel checks on qubits sharing feedlines? (2) can Rydberg leakage be made bright within microseconds? (3) what does a decoder do with false negatives at 10⁻³ as leakage accumulates? Watch: D-Wave's 2026 delivery, AWS's next multi-qubit paper, Google/Kaufman Yb results.

References
  1. [8] Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, “Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays,” Nat. Commun., vol. 13, Art. no. 4657, 2022, doi: 10.1038/s41467-022-32094-6. arXiv:2201.03540. S
  2. [14] D-Wave Quantum Inc., “D-Wave Announces Agreement to Acquire Quantum Circuits Inc., Establishing World's Leading Quantum Computing Company,” Jan. 7, 2026. [Online]. Available: https://www.dwavequantum.com/company/newsroom/press-release/d-wave-to-acquire-quantum-circuits-inc-establishing-world-s-leading-quantum-computing-company/ C
  3. [65] DARPA, “Stage B selection,” Nov. 6, 2025. [Online]. Available: https://www.darpa.mil/research/programs/quantum-benchmarking-initiative/stage-b-selection G
  4. [84] N. Mehta et al., “An entangling gate for dual-rail erasure qubits,” Nature, vol. 656, no. 8126, pp. 47–53, Aug. 2026, doi: 10.1038/s41586-026-10822-y. arXiv:2503.10935. D
  5. [85] J. S.-C. Hung et al., “Fast, High-Fidelity Erasure Detection of Dual-Rail Qubits with Symmetrically Coupled Readout,” arXiv:2604.16292, Apr. 2026. D
  6. [86] Quantum Circuits, “Quantum Circuits Makes Error-Detecting Qubits,” Nov. 19, 2024. [Online]. Available: https://quantumcircuits.com/resources/quantum-circuits-make-error-detecting-qubits/ C
  7. [94] M. Swayne, “D-Wave's New Gate-Model Roadmap Puts Pin in 2032 For 100 Logical-Qubit System,” The Quantum Insider, Jun. 1, 2026. [Online]. Available: https://thequantuminsider.com/2026/06/01/d-waves-new-gate-model-roadmap-puts-pin-in-2032-for-100-logical-qubit-system/ R
  8. [141] S. Ma et al., “High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit,” Nature, vol. 622, p. 279, 2023, doi: 10.1038/s41586-023-06438-1. arXiv:2305.05493. D
  9. [142] B. Zhang et al., “Logical qubits with erasure conversion using metastable neutral atoms,” Nat. Phys., vol. 22, no. 6, pp. 910–916, Jun. 2026, doi: 10.1038/s41567-026-03309-0. arXiv:2506.13724. D
  10. [143] P. Scholl, A. L. Shaw, R. B.-S. Tsai, R. Finkelstein, J. Choi, and M. Endres, “Erasure conversion in a high-fidelity Rydberg quantum simulator,” Nature, vol. 622, p. 273, 2023, doi: 10.1038/s41586-023-06516-4. arXiv:2305.03406. D
  11. [149] B. W. Reichardt et al., “Fault-tolerant quantum computation with a neutral atom processor,” arXiv:2411.11822, Nov. 2024. D
  12. [154] Atom Computing, “Atom Computing Raises More Than $300 Million to Accelerate Deployment of Fault-Tolerant, Neutral-Atom Quantum Computers,” PR Newswire, Jun. 16, 2026. [Online]. Available: https://www.prnewswire.com/news-releases/atom-computing-raises-more-than-300-million-to-accelerate-deployment-of-fault-tolerant-neutral-atom-quantum-computers-302800832.html C
  13. [158] M. Swayne, “Google Paves a Two-Lane Quantum Roadmap by Adding Neutral Atom Systems,” The Quantum Insider, Mar. 24, 2026. [Online]. Available: https://thequantuminsider.com/2026/03/24/google-paves-a-two-lane-quantum-roadmap-by-adding-neutral-atom-systems/ P
  14. [261] R. Yokoyama et al., “Minimally Destructive Fast Imaging of Single Atoms in an Optical Tweezer Array with Coherent Excitation,” arXiv:2605.24175, Jun. 2026. Also https://arxiv.org/abs/2605.24175. D
  15. [301] US Department of Commerce, Bureau of Industry and Security, “Commerce Control List Additions and Revisions; Implementation of Controls on Advanced Technologies Consistent With Controls Implemented by International Partners,” Federal Register, vol. 89, p. 72926, Sep. 6, 2024. [Online]. Available: https://www.federalregister.gov/documents/2024/09/06/2024-19633/commerce-control-list-additions-and-revisions-implementation-of-controls-on-advanced-technologies G
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