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Paper 1

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, Chris N. Self, Selwyn Simsek, Basudha Srivastava, M. S. Allman, Jake Arkinstall, Justin G. Bohnet, Nathaniel Q. Burdick, J. P. Campora, 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

Year

2026

Journal

arXiv preprint

DOI

arXiv:2602.22211

arXiv

2602.22211

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.

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Paper 2

Tradeoffs on the volume of fault-tolerant circuits

Anirudh Krishna, Gilles Zémor

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.03057

arXiv

2510.03057

Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial as it must balance several requirements. Increasing the rate of the code reduces the relative number of redundant bits used in the fault-tolerant circuit, while increasing the distance of the code ensures robustness against faults. If the rate and distance were the only concerns, we could use asymptotically optimal codes as is done in communication settings. However, choosing a code for computation is challenging due to an additional requirement: The code needs to facilitate accessibility of encoded information to enable computation on encoded data. This seems to conflict with having large rate and distance. We prove that this is indeed the case, namely that a code family cannot simultaneously have constant rate, growing distance and short-depth gadgets to perform encoded CNOT gates. As a consequence, achieving good rate and distance may necessarily entail accepting very deep circuits, an undesirable trade-off in certain architectures and applications.

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