{ "version": "1.2", "frozen": true, "frozen_note": "Dataset frozen pending the next scheduled update", "title": "Q-Day Monitor: published resource estimates to break RSA-2048 vs. demonstrated hardware", "maintainer": "Product Lab, The Quantum Investor's Notebook", "date_checked": "2026-10-26", "metrics": { "physical_qubits": { "units": "physical qubits", "label": "Physical qubits" }, "logical_qubits": { "units": "logical qubits", "label": "Logical qubits" }, "runtime": { "units": "as stated (hours, days, months)", "label": "Runtime" }, "two_qubit_fidelity_pct": { "units": "percent", "label": "Two-qubit gate fidelity" }, "two_qubit_error": { "units": "probability per gate", "label": "Two-qubit gate error" }, "lambda": { "units": "factor per code-distance step", "label": "Error suppression factor (Lambda)" }, "magic_state_fidelity": { "units": "fidelity (0 to 1)", "label": "Magic state fidelity" } }, "estimates": [ { "id": "est-fowler-2012", "date": "2012-08-04", "date_basis": "arXiv v1 posted", "label": "Fowler et al. 2012", "authors": "A. G. Fowler, M. Mariantoni, J. M. Martinis, A. N. Cleland", "affiliation": "University of Melbourne; UC Santa Barbara", "problem": "Factoring a 2,000-bit number (not exactly 2,048)", "values": [ { "metric": "physical_qubits", "value": 1000000000, "qualifier": "about", "quote": "the full quantum computer needs about a billion physical qubits, operating for about one day" }, { "metric": "logical_qubits", "value": 4000, "qualifier": "about", "quote": "the number of computational logical qubits, which for this circuit is about 2N = 4,000" }, { "metric": "runtime", "value": 26.7, "units": "hours", "qualifier": "about", "quote": "it will take about 26.7 hours to complete the exponentiation" } ], "assumptions": { "physical_error_rate": "about one-tenth of the threshold; the appendix works at p = 10^-3 (\"Here we assume an error rate approximately one-tenth the threshold rate\")", "cycle_time": "physical qubit measurement time 100 ns; surface code cycle about 200 ns (\"a 200 ns time for this cycle is not unreasonable\")", "reaction_time": "not stated as a separate parameter", "connectivity": "2D nearest-neighbor surface code array", "code": "surface code with magic-state distillation", "other": "about 14,500 physical qubits per logical qubit; most of the machine generates |A> magic states" }, "source_url": "https://arxiv.org/abs/1208.0928", "source_title": "Surface codes: Towards practical large-scale quantum computation", "venue": "Physical Review A 86, 032324 (2012)", "peer_reviewed": true, "date_checked": "2026-10-20", "notes": "Problem size is N = 2000 bits. Gidney and Ekera 2019 (Table 2) restate this estimate at n = 2048 as 1,000 million qubits and 1.1 days. Counts the 4,000 logical qubits as less than 6% of the machine.", "chart": true }, { "id": "est-gidney-ekera-2019", "date": "2019-05-23", "date_basis": "arXiv v1 posted", "label": "Gidney & Ekera 2019", "authors": "C. Gidney, M. Ekera", "affiliation": "Google; KTH Royal Institute of Technology", "problem": "Factoring 2048-bit RSA integers", "values": [ { "metric": "physical_qubits", "value": 20000000, "qualifier": "about", "quote": "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (title); Table 2, (ours) 2019 (parallel): 20 million physical qubits" }, { "metric": "runtime", "value": 8, "units": "hours", "qualifier": "about", "quote": "in 8 hours (title); Table 2 expected runtime 0.31 days" } ], "assumptions": { "physical_error_rate": "10^-3 (\"a characteristic physical gate error rate of 10^-3\")", "cycle_time": "1 microsecond surface code cycle", "reaction_time": "10 microseconds", "connectivity": "planar grid, nearest-neighbor", "code": "surface code; CCZ magic-state factories", "other": "abstract-circuit cost given as a formula: 3n + 0.002n lg n logical qubits; no single logical-qubit count is plotted here" }, "source_url": "https://arxiv.org/abs/1905.09749", "source_title": "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits", "venue": "Quantum 5, 433 (2021)", "peer_reviewed": true, "date_checked": "2026-10-20", "notes": "Peer-reviewed version published April 15, 2021; plotted at the first public (arXiv) date.", "chart": true }, { "id": "est-gouzien-sangouard-2021", "date": "2021-03-10", "date_basis": "arXiv v1 posted", "label": "Gouzien & Sangouard 2021", "authors": "E. Gouzien, N. Sangouard", "affiliation": "Universite Paris-Saclay, CEA, CNRS", "problem": "Factoring a 2048-bit RSA integer", "values": [ { "metric": "physical_qubits", "value": 13436, "qualifier": "exact (processor only)", "quote": "factoring a 2 048-bit RSA integer is shown to be possible in 177 days with 3D gauge color codes assuming a threshold of 0.75 % with a processor made with 13 436 physical qubits and a memory that can store 28 million spatial modes and 45 temporal modes with 2 hours' storage time" }, { "metric": "logical_qubits", "value": 8284, "qualifier": "exact", "quote": "Table I, n = 2 048 row: logical qubits 8 284" }, { "metric": "runtime", "value": 177, "units": "days", "qualifier": "about", "quote": "177 days" } ], "assumptions": { "physical_error_rate": "10^-3 (\"a characteristic physical gate error rate of 10^-3\")", "cycle_time": "processor cycle time 1 microsecond", "reaction_time": "not stated in the abstract", "connectivity": "small processor plus a separate multimode quantum memory", "code": "3D gauge color codes, assumed threshold 0.75%", "other": "requires a memory storing 28 million spatial modes and 45 temporal modes with 2 hours of storage time; the memory is not counted in the 13,436" }, "source_url": "https://arxiv.org/abs/2103.06159", "source_title": "Factoring 2048-bit RSA Integers in 177 Days with 13436 Qubits and a Multimode Memory", "venue": "Physical Review Letters 127, 140503 (2021)", "peer_reviewed": true, "date_checked": "2026-10-20", "notes": "Different architecture: the qubit count covers only the processor. Not directly comparable to whole-machine counts; drawn with an open marker.", "chart": true }, { "id": "est-chevignard-2024", "date": "2024-02-13", "date_basis": "IACR ePrint received", "label": "Chevignard, Fouque & Schrottenloher 2024", "authors": "C. Chevignard, P.-A. Fouque, A. Schrottenloher", "affiliation": "Univ Rennes, Inria, CNRS, IRISA", "problem": "Factoring an RSA-2048 instance", "values": [ { "metric": "logical_qubits", "value": 1730, "qualifier": "exact", "quote": "To factor an RSA-2048 instance, we estimate that 1730 logical qubits and 2^36 Toffoli gates will suffice for a single run, and the algorithm needs on average 40 runs." } ], "assumptions": { "physical_error_rate": "not applicable (logical-level estimate)", "cycle_time": "not applicable", "reaction_time": "not applicable", "connectivity": "not applicable", "code": "none; abstract circuit model", "other": "2^36 Toffoli gates per run, 40 runs on average" }, "source_url": "https://eprint.iacr.org/2024/222", "source_title": "Reducing the Number of Qubits in Quantum Factoring", "venue": "CRYPTO 2025 (LNCS 16001); IACR ePrint 2024/222", "peer_reviewed": true, "date_checked": "2026-10-20", "notes": "Logical-qubit count only; no physical-qubit estimate. Its approximate residue arithmetic is one of the ingredients of Gidney 2025.", "chart": true }, { "id": "est-gidney-2025", "date": "2025-05-21", "date_basis": "arXiv v1 posted", "label": "Gidney 2025", "authors": "C. Gidney", "affiliation": "Google Quantum AI", "problem": "Factoring a 2048-bit RSA integer", "values": [ { "metric": "physical_qubits", "value": 897864, "qualifier": "less than a million", "quote": "I estimate that a 2048 bit RSA integer could be factored in less than a week by a quantum computer with less than a million noisy qubits. ... The total number of physical qubits is 897864." }, { "metric": "logical_qubits", "value": 1399, "qualifier": "exact", "quote": "Table 5, n = 2048 row: Qubits 1399 (1,537 logical qubits including idle hot patches, Section 3)" }, { "metric": "runtime", "value": 4.96, "units": "days", "qualifier": "less than a week", "quote": "the actual time estimate per factoring: 4.96 days. Which I round up to a week for slack." } ], "assumptions": { "physical_error_rate": "0.1% (\"a uniform gate error rate of 0.1%\")", "cycle_time": "1 microsecond surface code cycle", "reaction_time": "10 microseconds", "connectivity": "square grid, nearest-neighbor", "code": "surface code; yoked surface codes for idle qubits; magic state cultivation", "other": "same assumptions as Gidney & Ekera 2019" }, "source_url": "https://arxiv.org/abs/2505.15917", "source_title": "How to factor 2048 bit RSA integers with less than a million noisy qubits", "venue": "arXiv preprint", "peer_reviewed": false, "date_checked": "2026-10-20", "notes": "Savings come from approximate residue arithmetic (Chevignard et al. 2024), yoked surface codes and magic state cultivation, per the abstract. This is the estimate the Q-Day Note cites.", "chart": true }, { "id": "est-pinnacle-2026", "date": "2026-02-12", "date_basis": "arXiv v1 posted (values from v2, May 5, 2026)", "label": "Webster et al. 2026 (Pinnacle)", "authors": "P. Webster, L. Berent, O. Chandra, E. T. Hockings, N. Baspin, F. Thomsen, S. C. Smith, L. Z. Cohen", "affiliation": "Iceberg Quantum", "problem": "Factoring 2048-bit RSA integers", "values": [ { "metric": "physical_qubits", "value": 94000, "qualifier": "fewer than 100,000", "quote": "2048-bit RSA integers can be factored with fewer than one hundred thousand physical qubits (abstract); Table VI (v2), 1 us cycle, 10^-3 error: 94 kq for a runtime of 1 month or less (135 kq for 1 week, 381 kq for 1 day)" }, { "metric": "runtime", "value": 1, "units": "month", "qualifier": "at most", "quote": "fewer than one hundred thousand physical qubits are required for factoring at a physical error rate of p = 10^-3 in an expected runtime of one month" } ], "assumptions": { "physical_error_rate": "10^-3", "cycle_time": "1 microsecond code cycle", "reaction_time": "10 microseconds", "connectivity": "quasi-local connections between physical qubits (not a planar nearest-neighbor grid)", "code": "quantum LDPC (generalized bicycle) codes", "other": "uses an algorithm based on Gidney 2025" }, "source_url": "https://arxiv.org/abs/2602.11457", "source_title": "The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "notes": "v2 (May 5, 2026) corrected a technical error in v1, per its acknowledgements. v2 text says one week needs 139 thousand qubits while its Table VI says 135 kq; recorded as stated. Requires connectivity that today's fixed-layout superconducting chips do not have; see est-frozen-pinnacle-2026.", "chart": true }, { "id": "est-cain-2026", "date": "2026-03-30", "date_basis": "arXiv v1 posted", "label": "Cain et al. 2026", "authors": "M. Cain, Q. Xu, R. King, L. R. B. Picard, H. Levine, M. Endres, J. Preskill, H.-Y. Huang, D. Bluvstein", "affiliation": "Oratomic; Caltech; UC Berkeley", "problem": "Factoring RSA-2048 integers", "values": [ { "metric": "physical_qubits", "value": 102000, "qualifier": "about", "quote": "our most time-efficient architectures can potentially enable runtimes of ... 97 days for RSA-2048 with approximately 102,000 qubits" }, { "metric": "runtime", "value": 97, "units": "days", "qualifier": "about", "quote": "97 days for RSA-2048" } ], "assumptions": { "physical_error_rate": "0.1% circuit-level depolarizing noise (p = 0.1%)", "cycle_time": "1 ms stabilizer measurement cycle (\"Here we assume a 1 ms stabilizer measurement cycle\")", "reaction_time": "not stated in the summary", "connectivity": "reconfigurable neutral-atom arrays (qubits moved by optical tweezers)", "code": "high-rate lifted-product codes with surgery-based logic", "other": "time-efficient architecture with up to P = 1,160 Toffoli gates in parallel; the authors call these estimates preliminary" }, "source_url": "https://arxiv.org/abs/2603.28627", "source_title": "Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits", "venue": "arXiv preprint (company and university authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "notes": "The headline 10,000-qubit figure refers to the smallest architectures (ECC-256); for RSA-2048 the paper says 11,000 to 14,000 qubits give runtimes roughly two orders of magnitude longer, with no single runtime stated in the text, so only the 102,000-qubit point is plotted. Slow (1 ms) cycle assumed, unlike the 1 us estimates.", "chart": true }, { "id": "est-mundada-2026", "date": "2026-04-07", "date_basis": "arXiv v1 posted", "label": "Mundada et al. 2026", "authors": "P. S. Mundada, A. Khindanov, Y. Wang, C. L. Edmunds, P. Coote, M. J. Biercuk, Y. Baum, M. Hush", "affiliation": "Q-CTRL", "problem": "Factoring 2048-bit RSA integers", "values": [ { "metric": "physical_qubits", "value": 381000, "qualifier": "about", "quote": "using an experimentally demonstrated grid-coupling topology, factoring RSA-2048 requires 381k physical qubits and 9.2 days, which can be reduced to 4.9 days via addition of an algorithm-specific accelerator for the Adder subroutine (requiring 439k qubits)" }, { "metric": "logical_qubits", "value": 1399, "qualifier": "exact (Gidney 2025 program)", "quote": "the 1,399-logical-qubit program" }, { "metric": "runtime", "value": 9.2, "units": "days", "qualifier": "about", "quote": "381k physical qubits and 9.2 days" } ], "assumptions": { "physical_error_rate": "5 x 10^-4 for the superconducting processors (\"We assume physical error rates of 5 x 10^-4 and code threshold of 6 x 10^-3\")", "cycle_time": "1 microsecond", "reaction_time": "not stated in the summary", "connectivity": "grid coupling for processors; separate quantum memory modules", "code": "surface code processors; memory in a long-coherence modality without active error correction", "other": "heterogeneous design: rare-earth-ion memory parameters T1 ~ 23 days, T2 > 10 hr; 190k qubits if hypothetical long-range coupling allows qLDPC memory" }, "source_url": "https://arxiv.org/abs/2604.06319", "source_title": "Heterogeneous architectures enable a 138x reduction in physical qubit requirements for fault-tolerant quantum computing under detailed accounting", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "notes": "Assumes a lower physical error rate (5 x 10^-4) than the 10^-3 used by most other estimates, plus a memory technology of a different kind. Compiles Gidney 2025's algorithm.", "chart": true }, { "id": "est-frozen-pinnacle-2026", "date": "2026-09-18", "date_basis": "arXiv v1 posted", "label": "Webster et al. 2026 (fixed connectivity)", "authors": "P. Webster, T. Peham, L. Z. Cohen", "affiliation": "Iceberg Quantum", "problem": "Factoring a 2048-bit RSA integer", "values": [ { "metric": "physical_qubits", "value": 120000, "qualifier": "approximately", "quote": "we show that a 2048-bit RSA integer can be factored in one month with approximately 120 000 physical qubits" }, { "metric": "runtime", "value": 1, "units": "month", "qualifier": "about", "quote": "factored in one month" } ], "assumptions": { "physical_error_rate": "10^-3", "cycle_time": "1 microsecond code cycle", "reaction_time": "10 microseconds", "connectivity": "fixed connectivity of degree eight (compatible with fabricated superconducting chips)", "code": "quantum LDPC (Pinnacle variant)", "other": "adapts est-pinnacle-2026 to fixed wiring" }, "source_url": "https://arxiv.org/abs/2609.21249", "source_title": "The Pinnacle Architecture with fixed connectivity of degree eight", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "notes": "Same authors' company as est-pinnacle-2026. Part of Iceberg Quantum's Pinnacle 1.1 release (Sept 22, 2026).", "chart": true } ], "hardware": [ { "id": "hw-google-sycamore-2019", "date": "2019-10-23", "date_basis": "journal publication", "series": "physical_qubits", "platform": "superconducting", "organization": "Google", "system": "Sycamore", "values": [ { "metric": "physical_qubits", "value": 53, "qualifier": "exact", "quote": "a processor with programmable superconducting qubits to create quantum states on 53 qubits" } ], "conditions": "54-qubit chip; one qubit did not function, so the device used 53 qubits and 86 couplers", "source_url": "https://www.nature.com/articles/s41586-019-1666-5", "source_title": "Quantum supremacy using a programmable superconducting processor", "venue": "Nature 574, 505 (2019)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Gate-model processor running full-array circuits.", "notes": "" }, { "id": "hw-ibm-eagle-2021", "date": "2021-11-16", "date_basis": "company announcement", "series": "physical_qubits", "platform": "superconducting", "organization": "IBM", "system": "Eagle", "values": [ { "metric": "physical_qubits", "value": 127, "qualifier": "exact", "quote": "127-qubit Eagle processor" } ], "conditions": "", "source_url": "https://newsroom.ibm.com/2021-11-16-IBM-Unveils-Breakthrough-127-Qubit-Quantum-Processor", "source_title": "IBM Unveils Breakthrough 127-Qubit Quantum Processor", "venue": "IBM newsroom", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Company announcement; the release does not give gate fidelities.", "notes": "" }, { "id": "hw-ibm-osprey-2022", "date": "2022-11-09", "date_basis": "company announcement", "series": "physical_qubits", "platform": "superconducting", "organization": "IBM", "system": "Osprey", "values": [ { "metric": "physical_qubits", "value": 433, "qualifier": "exact", "quote": "The new 433 qubit 'Osprey' processor" } ], "conditions": "", "source_url": "https://newsroom.ibm.com/2022-11-09-IBM-Unveils-400-Qubit-Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System-Two", "source_title": "IBM Unveils 400 Qubit-Plus Quantum Processor and Next-Generation IBM Quantum System Two", "venue": "IBM newsroom", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Company announcement; the release does not give gate fidelities.", "notes": "" }, { "id": "hw-atom-computing-2023", "date": "2023-10-24", "date_basis": "company announcement", "series": "physical_qubits", "platform": "neutral atoms", "organization": "Atom Computing", "system": "next-generation platform (1,225-site array)", "values": [ { "metric": "physical_qubits", "value": 1180, "qualifier": "exact (array populated with)", "quote": "Atom Computing announced it has created a 1,225-site atomic array, currently populated with 1,180 qubits" } ], "conditions": "array sites populated with atoms", "source_url": "https://www.prnewswire.com/news-releases/quantum-startup-atom-computing-first-to-exceed-1-000-qubits-301964712.html", "source_title": "Quantum Startup Atom Computing First to Exceed 1,000 Qubits", "venue": "Press release (PR Newswire)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Press release; it reports atoms held in the array, not gate benchmarks across all 1,180.", "notes": "" }, { "id": "hw-ibm-condor-2023", "date": "2023-12-04", "date_basis": "company announcement", "series": "physical_qubits", "platform": "superconducting", "organization": "IBM", "system": "Condor", "values": [ { "metric": "physical_qubits", "value": 1121, "qualifier": "exact", "quote": "We have introduced IBM Condor, a 1,121 superconducting qubit quantum processor based on our cross-resonance gate technology." } ], "conditions": "", "source_url": "https://www.ibm.com/quantum/blog/quantum-roadmap-2033", "source_title": "The hardware and software for the era of quantum utility is here", "venue": "IBM Quantum blog", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "IBM describes it as a scale milestone: \"With performance comparable to our previous 433-qubit Osprey, it serves as an innovation milestone\".", "notes": "" }, { "id": "hw-caltech-6100-2024", "date": "2024-03-18", "date_basis": "arXiv v1 posted", "series": "physical_qubits", "platform": "neutral atoms", "organization": "Caltech", "system": "tweezer array (Manetsch et al.)", "values": [ { "metric": "physical_qubits", "value": 6100, "qualifier": "over", "quote": "optical tweezers trapping over 6,100 neutral atoms in around 12,000 sites" } ], "conditions": "atoms trapped as qubits with coherence time of 12.6 s reported", "source_url": "https://arxiv.org/abs/2403.12021", "source_title": "A tweezer array with 6100 highly coherent atomic qubits", "venue": "Nature (2025), doi:10.1038/s41586-025-09641-4", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Trapping and coherence demonstration; it does not report entangling gates across the array. Not a computer of 6,100 working qubits.", "notes": "" }, { "id": "hw-google-willow-2024", "date": "2024-08-24", "date_basis": "arXiv v1 posted", "series": "physical_qubits", "platform": "superconducting", "organization": "Google", "system": "Willow", "values": [ { "metric": "physical_qubits", "value": 105, "qualifier": "exact", "quote": "using a 105-qubit processor with similar performance, we realize a distance-7 surface code" } ], "conditions": "", "source_url": "https://arxiv.org/abs/2408.13687", "source_title": "Quantum error correction below the surface code threshold", "venue": "Nature 638, 920 (2025)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Gate-model processor used for error-correction experiments.", "notes": "Google announced the chip by name (Willow) on December 9, 2024." }, { "id": "hw-harvard-3000-2025", "date": "2025-06-25", "date_basis": "arXiv v1 posted", "series": "physical_qubits", "platform": "neutral atoms", "organization": "Harvard / MIT / QuEra", "system": "continuously reloaded atom array (Chiu et al.)", "values": [ { "metric": "physical_qubits", "value": 3000, "qualifier": "over", "quote": "maintain an array of over 3,000 atoms for more than 2 hours" } ], "conditions": "continuous reloading of atoms", "source_url": "https://arxiv.org/abs/2506.20660", "source_title": "Continuous operation of a coherent 3,000-qubit system", "venue": "Nature (2025), doi:10.1038/s41586-025-09596-6", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Demonstrates keeping a large array loaded and coherent; not gate operations across all 3,000.", "notes": "" }, { "id": "hw-quantinuum-helios-2025", "date": "2025-11-07", "date_basis": "arXiv v1 posted", "series": "physical_qubits", "platform": "trapped ions", "organization": "Quantinuum", "system": "Helios", "values": [ { "metric": "physical_qubits", "value": 98, "qualifier": "exact", "quote": "We report on Quantinuum Helios, a 98-qubit trapped-ion quantum processor" } ], "conditions": "", "source_url": "https://arxiv.org/abs/2511.05465", "source_title": "Helios: A 98-qubit trapped-ion quantum computer", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Gate-model processor with all-to-all connectivity.", "notes": "The Q-Day Note's 98-qubit figure." }, { "id": "hw-tsinghua-11000-2026", "date": "2026-06-01", "date_basis": "arXiv v1 posted", "series": "physical_qubits", "platform": "neutral atoms", "organization": "Tsinghua University / Qosmos", "system": "metasurface tweezer array (Wang et al.)", "values": [ { "metric": "physical_qubits", "value": 11000, "qualifier": "exact (atoms trapped)", "quote": "Here, we robustly trap 11,000 individual atoms in a tweezer array" } ], "conditions": "atoms trapped in a tweezer array generated by a single metasurface", "source_url": "https://arxiv.org/abs/2606.02715", "source_title": "Trapping 11,000 Atoms in a Tweezer Array Generated by a Single Metasurface", "venue": "arXiv preprint", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Trapping demonstration; it does not report entangling gates across the array. Not a computer of 11,000 working qubits.", "notes": "Cross-checked with TQINB analysis." }, { "id": "hw-barends-2014", "date": "2014-02-19", "date_basis": "arXiv v1 posted", "series": "two_qubit_error", "platform": "superconducting", "organization": "UC Santa Barbara / Google", "system": "5-qubit Xmon array", "values": [ { "metric": "two_qubit_fidelity_pct", "value": 99.4, "qualifier": "up to", "quote": "a two-qubit gate fidelity up to 99.4%" } ], "conditions": "CZ gate, randomized benchmarking", "source_url": "https://arxiv.org/abs/1402.4848", "source_title": "Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing", "venue": "Nature 508, 500 (2014)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Best pair on a small device (\"up to\").", "notes": "" }, { "id": "hw-ballance-2016", "date": "2015-12-14", "date_basis": "arXiv v1 posted", "series": "two_qubit_error", "platform": "trapped ions", "organization": "University of Oxford", "system": "laser-driven 43Ca+ gates", "values": [ { "metric": "two_qubit_fidelity_pct", "value": 99.9, "qualifier": "99.9(1)%", "quote": "two-qubit and single-qubit logic gates with fidelities 99.9(1)% and 99.9934(3)% respectively" } ], "conditions": "two ions", "source_url": "https://arxiv.org/abs/1512.04600", "source_title": "High-fidelity quantum logic gates using trapped-ion hyperfine qubits", "venue": "Physical Review Letters 117, 060504 (2016)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Two-ion laboratory demonstration.", "notes": "" }, { "id": "hw-gaebler-2016", "date": "2016-03-31", "date_basis": "arXiv v1 posted", "series": "two_qubit_error", "platform": "trapped ions", "organization": "NIST", "system": "9Be+ ion gates", "values": [ { "metric": "two_qubit_error", "value": 0.0008, "qualifier": "8(4) x 10^-4", "quote": "By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of 8(4) x 10^-4." } ], "conditions": "two ions; error deduced from Bell-state fidelity", "source_url": "https://arxiv.org/abs/1604.00032", "source_title": "High-Fidelity Universal Gate Set for 9Be+ Ion Qubits", "venue": "Physical Review Letters 117, 060505 (2016)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Two-ion laboratory demonstration; large uncertainty (plus or minus 4 x 10^-4).", "notes": "" }, { "id": "hw-google-sycamore-2q-2019", "date": "2019-10-23", "date_basis": "journal publication", "series": "two_qubit_error", "platform": "superconducting", "organization": "Google", "system": "Sycamore (53 qubits)", "values": [ { "metric": "two_qubit_error", "value": 0.0062, "qualifier": "average, simultaneous operation", "quote": "we repeat the same procedure while simultaneously running two-qubit circuits for the entire array ... we find an average e2 of 0.62%" } ], "conditions": "average Pauli error over all pairs, all gates running at once (0.36% average in isolation)", "source_url": "https://www.nature.com/articles/s41586-019-1666-5", "source_title": "Quantum supremacy using a programmable superconducting processor", "venue": "Nature 574, 505 (2019)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Whole-chip average, not a best pair; Pauli error is not identical to 1 minus average fidelity.", "notes": "" }, { "id": "hw-evered-2023", "date": "2023-04-11", "date_basis": "arXiv v1 posted", "series": "two_qubit_error", "platform": "neutral atoms", "organization": "Harvard / MIT / QuEra", "system": "Rydberg CZ gates", "values": [ { "metric": "two_qubit_fidelity_pct", "value": 99.5, "qualifier": "99.52(4)%", "quote": "two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel" } ], "conditions": "parallel CZ gates on up to 60 atoms", "source_url": "https://arxiv.org/abs/2304.05420", "source_title": "High-fidelity parallel entangling gates on a neutral atom quantum computer", "venue": "Nature 622, 268 (2023)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Parallel gates on up to 60 atoms.", "notes": "" }, { "id": "hw-quantinuum-h1-2024", "date": "2024-04-16", "date_basis": "company announcement", "series": "two_qubit_error", "platform": "trapped ions", "organization": "Quantinuum", "system": "H1-1", "values": [ { "metric": "two_qubit_fidelity_pct", "value": 99.914, "qualifier": "99.914(3)%", "quote": "the first demonstration of 99.914(3)% 2-qubit gate fidelity, showing repeatable performance across all qubit pairs on our H1-1 system" } ], "conditions": "commercial system, randomized benchmarking across five gate zones", "source_url": "https://www.quantinuum.com/blog/quantinuum-extends-its-significant-lead-in-quantum-computing-achieving-historic-milestones-for-hardware-fidelity-and-quantum-volume", "source_title": "Quantinuum extends its significant lead in quantum computing, achieving historic milestones for hardware fidelity and Quantum Volume", "venue": "Quantinuum blog", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Company blog; a system-wide figure across all qubit pairs of a smaller commercial machine.", "notes": "" }, { "id": "hw-oxford-ionics-2025", "date": "2025-10-20", "date_basis": "arXiv v1 posted", "series": "two_qubit_error", "platform": "trapped ions", "organization": "Oxford Ionics (an IonQ company)", "system": "electronically controlled 40Ca+ gates", "values": [ { "metric": "two_qubit_error", "value": 8.4e-05, "qualifier": "8.4(7) x 10^-5", "quote": "We demonstrate electronically controlled two-qubit gates with an estimated error of 8.4(7) x 10^-5 without ground-state cooling." } ], "conditions": "a pair of ions; subspace-benchmarked", "source_url": "https://arxiv.org/abs/2510.17286", "source_title": "Trapped-ion two-qubit gates with >99.99% fidelity without ground-state cooling", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Two-ion demonstration, not a full processor. IonQ's press release (Oct 21, 2025) calls it a world record; we do not rank records.", "notes": "" }, { "id": "hw-quantinuum-helios-2q-2025", "date": "2025-11-07", "date_basis": "arXiv v1 posted", "series": "two_qubit_error", "platform": "trapped ions", "organization": "Quantinuum", "system": "Helios (98 qubits)", "values": [ { "metric": "two_qubit_error", "value": 0.00079, "qualifier": "7.9(2) x 10^-4 average", "quote": "Averaged over all operational zones in the system, we achieve average infidelities of 2.5(1) x 10^-5 for single-qubit gates, 7.9(2) x 10^-4 for two-qubit gates" } ], "conditions": "average over all operational zones of a 98-qubit system", "source_url": "https://arxiv.org/abs/2511.05465", "source_title": "Helios: A 98-qubit trapped-ion quantum computer", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "System-wide average on a 98-qubit machine; not comparable one-to-one with two-ion records.", "notes": "" }, { "id": "hw-evered-2026", "date": "2026-04-28", "date_basis": "arXiv v1 posted", "series": "two_qubit_error", "platform": "neutral atoms", "organization": "Harvard / MIT / QuEra", "system": "Rydberg CZ gates", "values": [ { "metric": "two_qubit_fidelity_pct", "value": 99.854, "qualifier": "99.854(4)% raw", "quote": "achieve state-of-the-art fidelities of 99.854(4)% which improve to 99.941(3)% upon loss postselection" } ], "conditions": "raw value plotted; 99.941(3)% if shots with lost atoms are discarded", "source_url": "https://arxiv.org/abs/2604.25987", "source_title": "High-fidelity entangling gates and nonlocal circuits with neutral atoms", "venue": "arXiv preprint", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Raw fidelity plotted; the higher figure needs postselection.", "notes": "" }, { "id": "hw-harvard-48-logical-2023", "date": "2023-12-07", "date_basis": "arXiv v1 posted", "series": "logical_qubits", "platform": "neutral atoms", "organization": "Harvard / MIT / QuEra", "system": "reconfigurable atom array (Bluvstein et al.)", "values": [ { "metric": "logical_qubits", "value": 48, "qualifier": "up to", "quote": "Using three-dimensional [[8,3,2]] code blocks, we realize computationally complex sampling circuits with up to 48 logical qubits" } ], "conditions": "[[8,3,2]] codes: distance 2, which detect but cannot correct an error", "source_url": "https://arxiv.org/abs/2312.03982", "source_title": "Logical quantum processor based on reconfigurable atom arrays", "venue": "Nature 626, 58 (2024)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Error-detecting code with postselection; not the kind of logical qubit a factoring estimate assumes.", "notes": "" }, { "id": "hw-microsoft-atom-2024", "date": "2024-11-18", "date_basis": "arXiv v1 posted", "series": "logical_qubits", "platform": "neutral atoms", "organization": "Microsoft / Atom Computing", "system": "neutral-atom processor", "values": [ { "metric": "logical_qubits", "value": 28, "qualifier": "up to", "quote": "we demonstrate the entanglement of 24 logical qubits encoded into 48 atoms ... with up to 28 logical qubits encoded into 112 atoms, showing better-than-physical error rates" } ], "conditions": "24 logical qubits entangled; up to 28 in an algorithm", "source_url": "https://arxiv.org/abs/2411.11822", "source_title": "Fault-tolerant quantum computation with a neutral atom processor", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Small codes; compare code distance before comparing counts.", "notes": "" }, { "id": "hw-quantinuum-helios-logical-2026", "date": "2026-02-25", "date_basis": "arXiv v1 posted", "series": "logical_qubits", "platform": "trapped ions", "organization": "Quantinuum", "system": "Helios (98 qubits)", "values": [ { "metric": "logical_qubits", "value": 94, "qualifier": "up to (error-detected)", "quote": "benchmarks with between 48 and 94 logical qubits ... 94 logical qubits in iceberg QED codes, and up to 48 logical qubits (the largest for which a full QEC cycle can be executed on Helios)" } ], "conditions": "94 in error-detecting iceberg codes (distance 2); 48 in concatenated error-correcting codes (distance 4); postselection used", "source_url": "https://arxiv.org/abs/2602.22211", "source_title": "Computing with many encoded logical qubits beyond break-even", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "The 94 are error-detected, not error-corrected; the error-corrected count is 48.", "notes": "" }, { "id": "hw-ibm-uchicago-logical-2026", "date": "2026-07-30", "date_basis": "company announcement", "series": "logical_qubits", "claim_type": "company_claim", "platform": "superconducting", "organization": "IBM / University of Chicago", "system": "IBM quantum computer", "values": [ { "metric": "logical_qubits", "value": 70, "qualifier": "exact", "quote": "the team executed 70 logical qubits — shielding them from errors to run 2,415 logical two-qubit operations and 468 logical \"T gates\"" } ], "conditions": "encoded random-circuit-style sampling with error detection during the computation", "source_url": "https://newsroom.ibm.com/2026-07-30-ibm-and-the-university-of-chicago-demonstrate-quantum-advantage,-establishing-trusted-quantum-computation-on-logical-circuits", "source_title": "IBM and The University of Chicago Demonstrate Quantum Advantage, Establishing Trusted Quantum Computation on Logical Circuits", "venue": "IBM newsroom", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Company claim: IBM newsroom announcement only, not checked by us against a paper; the code and distance are not stated in it. Underlying paper: \"Sampling hard circuits with verifiably high fidelity\" (not yet checked by us). Shown with an open, dashed marker, never as a measured result.", "notes": "" }, { "id": "hw-google-willow-lambda-2024", "date": "2024-08-24", "date_basis": "arXiv v1 posted", "series": "error_suppression", "platform": "superconducting", "organization": "Google", "system": "Willow, surface code memory", "values": [ { "metric": "lambda", "value": 2.14, "qualifier": "2.14 +/- 0.02", "quote": "The logical error rate of our larger quantum memory is suppressed by a factor of Lambda = 2.14 +/- 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% +/- 0.003% error per cycle" } ], "conditions": "memory (storing one logical qubit), distance 3 to 7, real-time decoder", "source_url": "https://arxiv.org/abs/2408.13687", "source_title": "Quantum error correction below the surface code threshold", "venue": "Nature 638, 920 (2025)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Memory only, not a computation.", "notes": "" }, { "id": "hw-google-color-lambda-2024", "date": "2024-12-18", "date_basis": "arXiv v1 posted", "series": "error_suppression", "platform": "superconducting", "organization": "Google", "system": "color code memory", "values": [ { "metric": "lambda", "value": 1.56, "qualifier": "1.56(4)", "quote": "suppresses logical errors by a factor of Lambda_3/5 = 1.56(4)" } ], "conditions": "color code, distance 3 to 5", "source_url": "https://arxiv.org/abs/2412.14256", "source_title": "Scaling and logic in the color code on a superconducting quantum processor", "venue": "Nature 645, 614 (2025)", "peer_reviewed": true, "date_checked": "2026-10-20", "caveat": "Memory plus logic tests; one distance step.", "notes": "" }, { "id": "hw-quantinuum-color-lambda-2026", "date": "2026-10-16", "date_basis": "arXiv v1 posted", "series": "error_suppression", "platform": "trapped ions", "organization": "Quantinuum", "system": "Helios-1, color code memory", "values": [ { "metric": "lambda", "value": 12, "qualifier": "12 (+3/-2)", "quote": "error suppression by over an order of magnitude, Lambda = 12 (+3/-2), with each successive increase in code distance" } ], "conditions": "memory over 20 rounds at distance 3, 5 and 7; decoded offline; distance-7 point rests on 3 failures in 29,000 shots", "source_url": "https://arxiv.org/abs/2610.24077", "source_title": "Quantum error correction well below the color code threshold", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Memory and Clifford gates; magic states not tested; offline decoding. See the paper “Quantum error correction well below the color code threshold” (https://arxiv.org/abs/2610.24077).", "notes": "" }, { "id": "hw-ibm-nighthawk-lambda-2026", "date": "2026-10-16", "date_basis": "arXiv v1 posted", "series": "error_suppression", "platform": "superconducting", "organization": "PNNL and partners (on IBM hardware)", "system": "IBM Nighthawk r2 (ibm_phoenix), surface code memory", "values": [ { "metric": "lambda", "value": 1.85, "qualifier": "1.85 X memory (1.68 Z memory)", "quote": "an error-suppression factor (Lambda) of 1.68 and 1.85 under maximum-likelihood decoding" } ], "conditions": "only one code distance grown (3 to 6), the other fixed at 3; short runs of 3 to 13 rounds", "source_url": "https://arxiv.org/abs/2610.23840", "source_title": "Demonstration of Logical Error Suppression in a Surface Code Memory on a Cloud-Accessible IBM Superconducting Processor", "venue": "arXiv preprint (no IBM authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "Independent team on cloud hardware; over 150 rounds the gain shrank. See the paper “Demonstration of Logical Error Suppression in a Surface Code Memory on a Cloud-Accessible IBM Superconducting Processor” (https://arxiv.org/abs/2610.23840).", "notes": "" }, { "id": "hw-google-cultivation-2025", "date": "2025-12-15", "date_basis": "arXiv v1 posted", "series": "magic_state", "platform": "superconducting", "organization": "Google Quantum AI", "system": "magic state cultivation experiment", "values": [ { "metric": "magic_state_fidelity", "value": 0.9999, "qualifier": "0.9999(1), retaining 8% of attempts", "quote": "Cultivation reduces the error by a factor of 40, with a state fidelity of 0.9999(1) (retaining 8% of attempts)." } ], "conditions": "single magic state; 8% of attempts kept", "source_url": "https://arxiv.org/abs/2512.13908", "source_title": "Magic state cultivation on a superconducting quantum processor", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "caveat": "One ingredient (the magic state) demonstrated at small scale; Gidney 2025 relies on cultivation at very large scale.", "notes": "Shown in the table, not on a chart. Cross-checked with TQINB analysis." }, { "id": "hw-sydney-ibm-phoenix-logical-2026", "date": "2026-10-23", "date_basis": "arXiv v1 posted", "series": "logical_qubits", "platform": "superconducting", "organization": "University of Sydney (one IBM Quantum co-author)", "system": "IBM Nighthawk r2 (ibm_phoenix, 120 qubits), distance-3 surface codes", "values": [ { "metric": "logical_qubits", "value": 3, "qualifier": "exact (three distance-3 surface codes)", "quote": "With three logical qubits and lattice surgery, we perform logical teleportation of a range of states and gates, observing fidelities in the range 78% - 93%." } ], "conditions": "Three distance-3 surface-code logical qubits with ancilla re-purposing (defect exclusion), entangled by lattice surgery (Sec. II C, Fig. 3). Teleportation fidelities: 78% to 93% in the abstract; the gate-teleportation bars in Fig. 3(d) go as low as 74.2%. Results keep only runs with a clean initial preparation (post-selection yields about 0.85% to 2.4% in Fig. 3(c)-(d); 1.2% for Bell-pair transfer). Separately, a distance-5 surface-code memory reached 0.9% logical error per round with up to three qubits excluded, versus 1.9% without (Sec. I, Sec. II A, Fig. 1; Belief Matching decoder with a noise model; fit over 50 rounds, App. C 1). Two-logical-qubit Bell-state fidelity above 93% via lattice surgery, post-selected on clean preparation (yield 40% +/- 2%), bounded from XX and ZZ only (Fig. 2).", "source_url": "https://arxiv.org/abs/2610.32347", "source_title": "Entangled logical qubits on a superconducting quantum processor", "venue": "arXiv preprint (university authors, one IBM co-author)", "peer_reviewed": false, "date_checked": "2026-10-26", "caveat": "Not below-threshold scaling: the distance-5 memory only matches the best distance-3 codes (Sec. II A), so no Lambda is reported. Fidelities are post-selected on clean preparation.", "notes": "The stability experiment's figure of about 2 x 10^-7 at 170 rounds (8 failures in 50 million runs; walking circuit, Sec. II D, Fig. 4) is not a logical memory error rate and is not plotted. No RSA or ECC resource estimate in the paper." } ], "quote_policy": "Quotes are verbatim from the primary source except: citation markers removed, math and symbols written in plain text (10^-3, +/-, Lambda, us = microseconds), and '...' marks omitted words.", "claim_types": { "company_claim": "A figure that appears only in a company announcement (press release, blog, newsroom) and that we have not checked against a paper or other primary technical document. Rendered with an open, dashed marker and labeled 'company claim' everywhere it appears. Records without claim_type are taken as stated in their source_url, with conditions and caveat." }, "changelog": [ { "version": "1.0", "date": "2026-10-20", "changes": "Initial frozen dataset: 9 estimates, 28 hardware records, 1 context record, 51 sourced values." }, { "version": "1.1", "date": "2026-10-20", "changes": "hw-ibm-uchicago-logical-2026 (70 logical qubits) marked claim_type 'company_claim' (IBM newsroom only; code and distance not stated); caveat reworded. Added top-level claim_types and changelog. No values, dates or ids changed." }, { "version": "1.2", "date": "2026-10-26", "changes": "Added hw-sydney-ibm-phoenix-logical-2026 (3 logical qubits, distance-3 surface codes on IBM Nighthawk r2 ibm_phoenix; arXiv 2610.32347 v1, preprint). Memory, Bell-state and teleportation figures are kept in conditions with their post-selection; the stability-experiment number is in notes and not plotted. Top-level date_checked set to 2026-10-26; no other values, dates, ids or estimates changed." } ], "context": [ { "id": "ctx-ionq-ecdlp-2026", "date": "2026-09-04", "date_basis": "arXiv v1 posted", "label": "Haner et al. 2026 (IonQ), not RSA", "problem": "256-bit elliptic curve discrete logarithm on secp256k1 (not RSA-2048)", "values": [ { "metric": "physical_qubits", "value": 19397, "qualifier": "exact", "quote": "would be able to solve the ECDLP on secp256k1 in approximately 25.7 days using 19,397 physical qubits with an estimated success probability of 63%" }, { "metric": "runtime", "value": 25.7, "units": "days", "qualifier": "approximately", "quote": "approximately 25.7 days" } ], "assumptions": { "physical_error_rate": "two-qubit gate noise 10^-4; single-qubit 10^-5", "cycle_time": "6.7 ms per syndrome extraction cycle (stated in the paper's naive-implementation runtime example)", "reaction_time": "not stated in the summary", "connectivity": "trapped-ion Walking Cat architecture with ion transport", "code": "quantum LDPC codes", "other": "success probability 63% per attempt" }, "source_url": "https://arxiv.org/abs/2609.05625", "source_title": "Computing 256-bit elliptic curve discrete logarithms in 26 days on a fault-tolerant trapped-ion quantum computer with 20,000 qubits", "venue": "arXiv preprint (company authors)", "peer_reviewed": false, "date_checked": "2026-10-20", "notes": "Context only: a different problem (elliptic curves, used by Bitcoin), so it is not plotted against RSA-2048 estimates. Assumes a 10^-4 two-qubit error, ten times lower than the 10^-3 most RSA estimates use." } ] }