Computing with many encoded logical qubits beyond break-even

Adam P. Reed; Akhil Isanaka; Alex Chernoguzov; Alex Hall; Ali A. Husain; Ali Lavasani; Alistair R. Milne; Andrew C. Potter; Andrew Y. Guo; Annie J. Park

REVIEW

Computing with many encoded logical qubits beyond break-even

Shival Dasu, Matthew DeCross, Andrew Y. Guo, Ali Lavasani, Jan Behrends, Asmae Benhemou, Yi-Hsiang Chen, Karl Mayer

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Chris N. Self, Selwyn Simsek, Basudha Srivastava, M.S. Allman, Jake Arkinstall, Justin G. Bohnet, Nathaniel Q. Burdick, J.P. Campora III, Alex Chernoguzov, Samuel F. Cooper, Robert D. Delaney, Joan M. Dreiling, Brian Estey, Caroline Figgatt, Cameron Foltz, John P. Gaebler, Alex Hall, Craig A. Holliman, Ali A. Husain, Akhil Isanaka, Colin J. Kennedy, Yuga Kodama, Nikhil Kotibhaskar, Nathan K. Lysne, Ivaylo S. Madjarov, Michael Mills, Alistair R. Milne, Brian Neyenhuis, Annie J. Park, Anthony Ransford, Adam P. Reed, Steven J. Sanders, Charles H. Baldwin, David Hayes, Ben Criger, Andrew C. Potter, David Amaro

Quantum Physics · Submitted 25 Feb 2026 · 55 references

Pith's verdict: A genuine hardware milestone—beyond-break-even at up to 94 logical qubits—whose strongest d=4 claim rests on a fault-tolerance proof enumerated only for a 16-qubit code and extrapolated by analogy.

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arXiv ID2602.22211 (version 1)

Pith IDUOKNVJVU, Pith's permanent record of this paper and its review

CitationAdam P. Reed, Akhil Isanaka, Alex Chernoguzov, Alex Hall, Ali A. Husain, Ali Lavasani, Alistair R. Milne, Andrew C. Potter, Andrew Y. Guo, Annie J. Park, Anthony Ransford, Asmae Benhemou, Basudha Srivastava, Ben Criger, Brian Estey, Brian Neyenhuis, Cameron Foltz, Caroline Figgatt, Charles H. Baldwin, Chris N. Self, Colin J. Kennedy, Craig A. Holliman, David Amaro, David Hayes, Ivaylo S. Madjarov, Jake Arkinstall, Jan Behrends, Joan M. Dreiling, John P. Gaebler, J.P. Campora III, Justin G. Bohnet, Karl Mayer, Matthew DeCross, Michael Mills, M.S. Allman, Nathaniel Q. Burdick, Nathan K. Lysne, Nikhil Kotibhaskar, Robert D. Delaney, Samuel F. Cooper, Selwyn Simsek, Shival Dasu, Steven J. Sanders, Yi-Hsiang Chen, Yuga Kodama. "Computing with many encoded logical qubits beyond break-even." arXiv:2602.22211 (2026). https://pith.science/paper/UOKNVJVU

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Editor's note

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Worth your time. This is the real thing on scale: 94 logical qubits in distance-2 iceberg QED, 48 in a distance-4 concatenated code, on Helios, with unencoded baselines measured on the same device for SPAM, GHZ, gate benchmarks, and the XY-model simulation. The beyond-break-even claim is actually supported in the data, not just asserted.

The new material is genuine: variable-block-size concatenated iceberg codes, GHZ-based parallel syndrome extraction that uses Helios' eight gate zones well, a constant-overhead FT FANOUT gate, and a low-overhead d=4 QEC cycle with a circuit-level decoder instead of Knill-style blocks. Reporting is honest where it counts: no-logical-error results are given as Wilson upper bounds, acceptance and leakage rates are disclosed everywhere, and postselection conditions are explicit. That is more discipline than most hardware papers show.

The soft spot is the one the stress test flags, and it is real. Prop. 1 in SI Sec. IV—the fault-tolerance proof that makes the d=4 QEC result a QEC result rather than a favorable accepted-noise draw—is verified by exhaustive enumeration of single and double faults only for I2∘I2 = [[16,4,4]]. The headline [[80,48,4]] claim inherits it via "the decoding for other sizes of iceberg layers is entirely analogous." Larger blocks differ in lower-level block size, in the geometry of hook-error strings, and in decoder bookkeeping; an unenumerated hook or ambiguity pattern would break the interpretation of the 4e-5 bound and the below-pseudo-threshold comparison. The authors disclose the enumeration basis, so this is a missing-support gap, not an internal inconsistency—but it is the load-bearing unverified step, and a referee should push on it.

Secondary issues: the abstract's "beyond-classical-scale computation" framing overreaches, since mirror benchmarking is classically simulable (the authors acknowledge it is a proxy, but the abstract says more than that), and the Outlook sentence "We demonstrate computations below break-even" has the direction inverted—presumably a typo, but sloppy. The pseudo-threshold comparison leans on the self-cited companion hardware paper [8]; fine as a data source given overlapping authors, but it is worth noting the comparison is only as good as that paper. Free parameters are standard fit summaries; nothing invented.

Who it is for: the QEC and quantum-hardware community, and anyone tracking the logical-vs-physical crossover. The core is solid, the scale is genuinely new, and the weaknesses are fixable. Deserves a serious referee: send it out, and ask for either a verification of the FT enumeration at the larger block size or an explicit statement of which claims are and are not covered by the proof.

Referee report

Significance

If the claims hold, this is a significant experimental advance: high-rate codes at 48–94 logical qubits outperform unencoded circuits on several benchmarks on current hardware, and a distance-4 concatenated code is presented as operating below its pseudo-threshold. The paper is strengthened by direct in-paper unencoded baselines for the SPAM, GHZ, and XY-model experiments, by systematic disclosure of acceptance rates and Wilson confidence intervals, and by reporting no-logical-error results as upper bounds rather than point estimates. The main risks are the extrapolation of the fault-tolerance proof from the smallest code to the headline code, an apparent inconsistency in the logical-gate benchmarking comparison, and the need to define precisely what 'below pseudo-threshold' means when 38% of shots are rejected.

Major objections (3)

[SI Sec. IV, Prop. 1] The circuit-level fault-tolerance proof of the d=4 QEC cycle is verified by exhaustive enumeration of single- and double-fault configurations only for I2∘I2 = [[16,4,4]]; the extension to the headline I8∘I6 = [[80,48,4]] code rests on the sentence 'the decoding for other sizes of iceberg layers is entirely analogous.' These codes differ in lower-level block size (I6 vs I2), in the dimensions n1,n2 over which hook-error strings and decoder coordinates are defined, and in the number of rows and columns in the stabilizer grid. An unenumerated hook error or decoder ambiguity unique to the larger code could convert a single internal fault into an undetected logical error on an accepted shot. Because Prop. 1 is the basis for interpreting the accepted-shot no-logical-error result as a fault-tolerant QEC error rate and for the below-pseudo-threshold comparison, this missing verification is load-bearing. Please provide an explicit circuit-level enumeration or simulation for I8∘I6 (or a rigorous argument that the enumeration for I2∘I2 covers all size-dependent cases), or qualify the d=4 claims accordingly.
[Main text (Fig. 2b); Methods C; SI Sec. VI] The reported logical gate infidelities of 1.0–1.2×10^-4 are claimed to 'significantly outperform the bare physical two-qubit gate errors of ~8×10^-4', but as written this comparison appears internally inconsistent. As stated in SI Sec. VI, the intra-block logical UZZ(π/2) is implemented by a single physical UZZ(π/2) between two data qubits, and the paper also states that the Helios two-qubit error model has essentially all weight-2 errors of ZZ type. A ZZ error on that physical gate is the undetectable logical operator Z_i Z_j for this code, so syndrome-based postselection cannot remove it; the logical gate infidelity would then be bounded below by the undetectable component of the physical gate error, which the cited model implies is close to the full 8×10^-4. The manuscript should reconcile this, either by explaining how the twirling/fitting procedure or the in-situ gate error budget evades that bound, or by revising the comparison and the 'outperform physical gates' claim for gate benchmarking. The authors acknowledge this: “However, it fails to be fully FT for the same reason that theU ZZ (θ) gate alone fails to be FT in the iceberg code; namely, weight-2XX,YY, orZZerrors on theU ZZ (θ) are undetectable.”
[Main text (QEC cycle benchmarking); Methods B] The below-pseudo-threshold statement compares the accepted-shot logical error upper bound of 4×10^-5 with the unconditional physical memory error of 1.1(3)×10^-4. With an acceptance rate of 0.62(2), an unconditional logical failure rate that counts rejected shots as failures would be many orders of magnitude above the physical rate. The authors do disclose the postselection, and the retry interpretation is defensible, but the standard term 'pseudo-threshold' is usually defined without this conditioning. Please state explicitly that 'below pseudo-threshold' refers to the accepted-run error rate, define this postselected pseudo-threshold, and optionally report the unconditional per-cycle rate so that readers can compare with standard usage.

Minor objections (3)

[Outlook] The first sentence of the Outlook says 'We demonstrate computations below break-even on many logical qubits'; this should read 'beyond break-even' to match the title, abstract, and the rest of the paper.
[SI Sec. IV, Algorithm 3] The condition 'if (length(Xcoords) > 1) or (4 > length(Ycoords) > 1)' is hard to parse and appears to contain a typo; it should presumably be '1 < length(Ycoords) < 4'. Also, the variable 'CurrInputErrorAllowed' is not defined in the pseudocode and should be aligned with 'InputErrorAllowed' for clarity.
[Main text, QEC cycle result] The phrase 'no logical errors recorded in five thousand shots in each basis' is potentially misleading because the no-error statement applies to the accepted shots (708 and 958 respectively in SI Table III), not to all 5000 submitted shots. Please rephrase to 'no logical errors in the accepted shots' for precision, even though Table III already provides the breakdown.

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The paper

The paper claims

High-rate iceberg codes let encoded circuits outperform their unencoded counterparts on a 98-qubit trapped-ion processor, with a distance-4 code recording no logical errors in 10,000 shots.

The reading

This paper is trying to establish that high-rate quantum error correction has crossed from overhead to advantage on current hardware: encoding circuits in iceberg codes made them more accurate than running the same circuits on unencoded physical qubits. The authors demonstrate this beyond-break-even behaviour on the 98-qubit Helios trapped-ion processor at up to 94 logical qubits with distance-2 error-detecting codes and at 48 logical qubits with a newly devised distance-4 concatenated code, across state preparation, logical-gate benchmarking, GHZ state preparation, and a partial-fault-tolerant simulation of the three-dimensional XY model of magnetism. The load-bearing evidence is a QEC cycle for the $[[80,48,4]]$ code with average infidelity per logical qubit upper-bounded by $4\times 10^{-5}$, no logical errors in 5,000 shots in each basis, and a $0.62(2)$ acceptance rate after discarding uncorrectable errors. A sympathetic reading: if the results hold, all-to-all-connected hardware can already run circuits on tens of logical qubits more reliably than on bare qubits, and raising the code distance via concatenation shrinks rather than grows the postselection cost.

What carries the argument

The central object is the iceberg code, a high-rate quantum error-detecting code that encodes $k$ logical qubits into $k+2$ physical qubits using just two global stabilizers, $S_X$ and $S_Z$ (products of $X$ or $Z$ over every physical qubit); concatenating two iceberg codes yields a distance-4 QEC code with parameters $[[(k_2+2)(k_1+2),k_2k_1,4]]$, drawn as a grid whose rows carry the inner stabilizers and whose column pairs carry the outer ones. The new machinery is a low-overhead QEC cycle for these concatenated codes: instead of the two full ancilla code blocks of Knill-style QEC, it uses one lower-level iceberg block (18 physical ancilla qubits and depth 18 for $I_8\circ I_6$) followed by ordinary distance-2 syndrome extraction, decoded by classifying error strings as 'generalized weight-one' or 'generalized weight-two' — vertical or horizontal lines through the grid that meet any weight-4 logical operator in at most two qubits. Fault-tolerance is argued by showing this decoder satisfies distance-3 QEC and distance-4 QED extended-rectangle conditions, verified by exhaustive enumeration of single- and double-fault configurations on the smallest instance $I_2\circ I_2 = [[16,4,4]]$. Supporting gadgets — fault-tolerant log-depth state preparation with repeat-until-success, GHZ-based syndrome extraction matched to the hardware's eight gate zones, a constant-overhead logical FANOUT gate, and leakage-heralded measurement — are what let the demonstrations run at up to 94 logical qubits.

Extended reading notes

Core claim

The central claim, on the paper's own terms, is that the iceberg code family has become a practical tool: on the 98-qubit Helios trapped-ion processor, logical computations encoded in $[[k+2,k,2]]$ iceberg codes and in $[[(k_2+2)(k_1+2),k_2k_1,4]]$ two-level concatenated iceberg codes outperform their unencoded counterparts. For the distance-4 code $I_8\circ I_6 = [[80,48,4]]$ the authors report an average QEC-cycle infidelity per logical qubit upper-bounded by $4\times 10^{-5}$, with no logical errors in 5,000 shots in each basis and an acceptance rate of $0.62(2)$ after postselecting out uncorrectable errors; compared with the unencoded depth-1 memory error of $1.1(3)\times 10^{-4}$ from the hardware specification, the device sits below the pseudo-threshold for this code. The same pattern repeats across benchmarks: logical gate infidelities of $(1.0$–$1.2)\times 10^{-4}$ beat the bare physical two-qubit error of about $8\times 10^{-4}$, the 94-logical-qubit GHZ state reaches about 95% fidelity, and encoding reduces the effective per-gate error in the 64-logical-qubit XY-model simulation by about 30%. The authors also show that moving from distance 2 to distance 4 via concatenation raises the QEC acceptance rate from $0.945(2)$ to $0.972^{+1}_{-2}$ without worsening fidelity, evidence that postselection overhead is suppressed by code distance.

Load-bearing premise

The proof that the distance-4 error-correction cycle is fault-tolerant checks every possible one- and two-fault pattern by exhaustive enumeration only on the smallest 16-qubit version of the code, then assumes the same decoding behaviour carries over unchanged to the 80-qubit code on which the headline no-logical-errors result was recorded.

Editorial extensions

If this is right

If the central claim is right, current trapped-ion hardware already sits below the pseudo-threshold for the distance-4 concatenated iceberg code, so applying additional rounds of QEC should improve logical memory fidelity rather than degrade it.
Computation at 48 to 94 logical qubits with high encoding rate (48 logical qubits in 80 physical qubits) is available now, a scale the authors argue makes purely forward evolution of the 3D XY model hard for classical simulation.
Postselection need not be a scalability dead end: below threshold, both the accepted-shot error rate and the rejection overhead are exponentially suppressed as code distance grows via concatenation, and the observed acceptance-rate jump from distance 2 to distance 4 supports this.
The benchmarked logical gate set — intra- and inter-block $U_{ZZ}(\theta)$ together with the fault-tolerant FANOUT gate — delivers gate infidelities near $1.1\times 10^{-4}$, more than six times smaller than the bare physical two-qubit error, which is what lets encoded circuits (not just encoded memory) beat break-even.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

My read of the acceptance-rate gain: each concatenation level buys distance and acceptance at the same time, so near-term computations could bootstrap through a 'postselected fault-tolerant' regime toward longer circuits without waiting for a single dramatic threshold crossing.
A portability test the authors do not run: because the iceberg code's power rests on global stabilizers and all-to-all connectivity, re-running the same SPAM and QEC-cycle benchmarks on a reconfigurable neutral-atom device would separate the code's intrinsic merits from Helios-specific gate-zone parallelization and transport overheads.
A scaling check worth running: inject tunable noise (by scaling the $U_{ZZ}$ angle or adding deliberate idling) and verify on the full $[[80,48,4]]$ cycle that accepted-shot logical error scales as $O(p^3)$ and rejection as $O(p^2)$ — the scalings proven by enumeration only on the $[[16,4,4]]$ instance.
The XY-model result hints at a consequence the paper leaves implicit: for the local correlation functions that matter in simulating magnetic materials, encoded break-even may arrive at even shallower depths than global mirror-benchmarking survival probabilities suggest.

Original abstract

High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers. Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor. Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits. These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism. Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation. Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-26: 1 request, 6,014 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.44 · human participants 0.02 · controlled comparison 0.86 · randomized assignment 0.01 · states quantitative result 0.94 · compares with prior results 0.88 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers. Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor. Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits. These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism. Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation. Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation.	background 1.00	0.05	0.04	asserted 0.63
s1	Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers.	background 0.95	0.07	0.04	asserted 0.98
s2	Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor.	contribution 0.57	0.97	0.64	asserted 1.00
s3	Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits.	result 0.71	0.96	0.46	asserted 1.00
s4	These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism.	contribution 0.72	0.93	0.04	asserted 0.94
s5	Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation.	result 0.97	0.91	0.06	asserted 0.97
s6	Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.	interpretation 0.98	0.92	0.83	asserted 0.89

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Protecting Quantum Computers against Untrusted Users
quant-ph 2026-10 conditional novelty 8.0 of 10

Randomizing the input and revealing only one output bit is conjectured to make a public quantum server unable to factor RSA numbers, while keeping infinite-temperature simulation tasks.
Logical gate set tomography
quant-ph 2026-10 accept novelty 7.0 of 10

Logical GST produces detailed models of logical gate errors and provides the first self-consistent tomographic reconstruction of a universal single-qubit logical gate set.
Error Mitigation From a Single Unmodified Error-Corrected Circuit
quant-ph 2026-10 conditional novelty 7.0 of 10

SOLEM uses naturally occurring syndrome-conditioned logical error channels to estimate ideal expectation values entirely in post-processing, without modifying the error-corrected circuit.
Bounded decoding complexity in transversal circuits with magic state injection
quant-ph 2026-11 accept novelty 6.0 of 10

For random circuits with finite magic state injection density, the space-time correlated decoding volume reaches a stationary average independent of the number of qubits or circuit depth.
End-to-End Optimization of Partial Fault Tolerance in Neutral-Atom Arrays
quant-ph 2026-10 conditional novelty 6.0 of 10

STAR partial fault tolerance on neutral atoms is co-designed end to end, with leading-order coherent logical noise cancelled by the repeat-until-success structure and Rydberg pulses error-selectively optimized.

How the literature uses it

13 arXiv papers cite this in 21 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 13 sentences without a confident label

Uses its method or tool 1 paper

The construction uses the standard identity [equation] as in Fig. 3 of Ref. [ref] .

Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture · Logical Controlled-H gate · 0.89

Cites it as support 1 paper

Recent work has used this approach to demonstrate improvements of encoded circuits over unencoded ones [ref] , and is the approach taken in this work.

The Utility of Sparse Error Detection in Quantum Simulations · A Single Block of [[4,2,2]] · 0.97

Cites it as background 5 papers

The most prevalent QEC paradigm is active QEC [ref] .

Projected logical ensembles in surface codes via the random-matrix theory of quantum dots · Introduction · 0.94
Trapped-ion devices had previously been used to demonstrate various block codes [ref] , and larger concatenated codes [ref] .

Breakeven demonstration of quantum low-density parity-check codes · Introduction · 0.90
This includes IBM using superconducting qubits with LDPC codes [ref] , Google Quantum AI, ETH Zürich, and USTC using superconducting qubits with surface codes [ref] , Quantinuum and the University of Innsbruck using trapped ions [ref] , the Harvard–MIT–QuEra collaboration using neutral atoms [ref] , the Atom Computing–Microsoft collaboration using cold atoms [ref] , and Yale, Amazon (AWS), and Alice & Bob using bosonic codes [ref] .

The Utility of Sparse Error Detection in Quantum Simulations · Introduction · 0.81

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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