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Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing
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Benchmarks of a quantum information processor establish, for the first time, an advantage for a quantum annealer over classical simulated annealing, an important milestone in the development of quantum optimizers and in the journey towards demonstrating a quantum speedup over classical computers.
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“A comparison with SA, spin-vector-monte-carlo [215], and simulated QA suggests that QA possesses the best scaling properties [7].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [7]
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“QA shows superior scaling properties compared to SA, where both are significantly inferior to simulated QA [7].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [7]
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Cites
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“This advance allows us furthermore to demonstrate the first certifiable observation of an algorithmic scaling advantage obtained using quantum annealing hardware over an important general purpose classical algorithm, namely, over simulated annealing with single-spin updates (SA) [36].”
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MethodAlgorithms for quantum computation: discrete logarithms and factoring
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“Here we check a polynomial-time algorithm for solving the minimumweight perfect-matching (MWPM) problem [70, 71] and show that it cannot be used to efficiently determine the ground state of the logical planted instances defined on Chimera with the gadget.”
MethodQuantum annealing in the transverse Ising model
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“The SA and SVMC algorithms can both be viewed not only as classical analogues of QA, but also as implementing two of its possible classical limits [15,38,58].”
BackgroundA Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
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“Unlike universal quantum computers that operate using quantum gates and the principles of the circuit model [14], these devices specialize primarily in solving combinatorial optimization problems, and are designed to represent physical implementations of quantum annealing (QA) [15] and the quantum adiabatic algorithm…”
BackgroundQuantum annealing with manufactured spins
Johnson, M. W., Amin, M. H. S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A. J., Johansson, J., Bunyk, P., et al. (2011) · Nature · doi:10.1038/nature10012 · Cited by 1,891 · cited 1×
“We answer this question in the affirmative and report on the first observation of a quantum hardware scaling advantage when comparing simulated annealing with singlespin updates (SA) [8] to a quantum annealer [9], for a specific problem class we introduce here.”
BackgroundObservation of a many-body dynamical phase transition with a 53-qubit quantum simulator
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Evidence for quantum annealing with more than one hundred qubits
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“In (a) and (b) error bars represent 95% confidence intervals (2σ) calculated using 1000 bootstraps of 100 gauge transformations [17].”
MethodResultSelf-citationTheory of Quantum Annealing of an Ising Spin Glass
Santoro, G. E., Martoňák, R., Tosatti, E., & Car, R. (2002) · Science · doi:10.1126/science.1068774 · Cited by 734 · cited 2×
“2, where we compare the DW2KQ results to three classical algorithms: SA with single-spin updates [36], SQA based on the discrete-time path-integral quantum Monte Carlo algorithm [37], and the SVMC algorithm [38].”
MethodQuantum computational supremacy
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BackgroundDefining and detecting quantum speedup
Rønnow, T. F., Wang, Z., Job, J., Boixo, S., Isakov, S. V., Wecker, D., Martinis, J. M., Lidar, D. A., & Troyer, M. (2014) · Science · doi:10.1126/science.1252319 · Cited by 601 · cited 4×
“We note that our results are robust to modifying the SA annealing schedule from a quadratic to a linear function in β (seeAppendixE), and under a change of themetric to the socalled “quantile-of-ratios speedup” [18] (see Appendix F).”
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A blueprint for demonstrating quantum supremacy with superconducting qubits
Neill, C., Roushan, P., Kechedzhi, K., Boixo, S., Isakov, S. V., Smelyanskiy, V., Megrant, A., Chiaro, B., Dunsworth, A., Arya, K., et al. (2018) · Science · doi:10.1126/science.aao4309 · Cited by 468 · cited 1×
“However, there is reason for optimism [11] that current “noisy intermediate scale quantum” (NISQ) era [12] quantum computers will be capable of demonstrating the important milestone of “quantum supremacy” [13], a less ambitious quantum speedup Published by the American Physical Society under the terms of the Creative…”
BackgroundBlossom V: a new implementation of a minimum cost perfect matching algorithm
Kolmogorov, V. (2009) · Mathematical Programming Computation · doi:10.1007/s12532-009-0002-8 · Cited by 435 · cited 2×
“In order to do so, we map the Ising Hamiltonian on the square grid to a MWPM problem [92], run the Blossom V algorithm [91] to determine the solution to the MWPM problem, and finally map the solution of the MWPM problem to a ground state of the Ising Hamiltonian.”
MethodMinor-embedding in adiabatic quantum computation: I. The parameter setting problem
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Denchev, V. S., Boixo, S., Isakov, S. V., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., & Neven, H. (2016) · Physical Review X · doi:10.1103/physrevx.6.031015 · Cited by 399
Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor
Bunyk, P. I., Hoskinson, E., Johnson, M. W., Tolkacheva, E., Altomare, F., Berkley, A. J., Harris, R., Hilton, J. P., Lanting, T., Przybysz, A. J., et al. (2014) · IEEE Transactions on Applied Superconductivity · doi:10.1109/tasc.2014.2318294 · Cited by 374 · cited 2×
“The σi and σi are the Pauli matrices acting on superconducting flux qubits that occupy the vertices V of a Chimera hardware graph G with edge set E [43,44] and the local fields hi and couplings Jij are programmable analog parameters.”
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Experimental signature of programmable quantum annealing
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Self-citationQuantum adiabatic Markovian master equations
Albash, T., Boixo, S., Lidar, D. A., & Zanardi, P. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/12/123016 · Cited by 274 · cited 1×
“The same is true for master equation simulations [41,74], even when implemented using the quantum trajectories method [75].”
MethodSelf-citationFault-Tolerant Quantum Computation with Long-Range Correlated Noise
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“Another concern we face is that while the accuracy threshold theorem provides a theoretical guarantee that for sufficiently low noise levels and through the use of quantum error correction a finite-size device can be scaled up fault tolerantly [57], in the absence of such an asymptotic guarantee for quantum annealing…”
BackgroundComputational multiqubit tunnelling in programmable quantum annealers
Boixo, S., Smelyanskiy, V., Shabani, A., Isakov, S. V., Dykman, M. I., Denchev, V. S., Amin, M. H. S., Smirnov, A. Y., Mohseni, M., & Neven, H. (2016) · Nature Communications · doi:10.1038/ncomms10327 · Cited by 232 · cited 3×
“We emphasize that the appropriate energy landscape for tunneling is not the classical energy landscape associated with simulated annealing [26] but rather the semiclassical landscape associated with transverse-field annealing [41,42].”
BackgroundMethodAdiabatic Quantum Computation in Open Systems
Sarandy, M. S., & Lidar, D. A. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.250503 · Cited by 219 · cited 1×
“In the case where the system is very weakly coupled to its thermal environment, we can expect a competition between adiabaticity (unitary dynamics) and open system effects such as thermal excitations [48,49], resulting in a peak in the success probability and a minimum in the TTS.”
BackgroundSelf-citationQuantum versus classical annealing of Ising spin glasses
Heim, B., Rønnow, T. F., Isakov, S. V., & Troyer, M. (2015) · Science · doi:10.1126/science.aaa4170 · Cited by 215 · cited 1×
“It has been demonstrated that time discretization may result in improved residual energy minimization performance over the continuum case [70], although this does not necessarily translate into a scaling performance advantage.”
BackgroundSolving a Higgs optimization problem with quantum annealing for machine learning
Mott, A., Job, J., Vlimant, J.-R., Lidar, D. A., & Spiropulu, M. (2017) · Nature · doi:10.1038/nature24047 · Cited by 210 · cited 1×
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Self-citationExperimental Implementation of an Adiabatic Quantum Optimization Algorithm
Steffen, M., van Dam, W., Hogg, T., Breyta, G., & Chuang, I. L. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.067903 · Cited by 180
Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
Benedetti, M., Realpe-Gómez, J., Biswas, R., & Perdomo‐Ortiz, A. (2017) · Physical Review X · doi:10.1103/physrevx.7.041052 · Cited by 172
Stochastic series expansion method for quantum Ising models with arbitrary interactions
Sandvik, A. W. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.056701 · Cited by 171
On the ground states of the frustration model of a spin glass by a matching method of graph theory
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Probing for quantum speedup in spin-glass problems with planted solutions
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“Without the identification of an optimal annealing time, one can certify a scaling disadvantage for the hardware quantum annealer, but not an advantage [20]; this holds for all earlier scaling analyses presented for quantum annealing hardware [17–25].”
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Houdayer, J. (2001) · The European Physical Journal B · doi:10.1007/pl00011151 · Cited by 155
Searching for quantum speedup in quasistatic quantum annealers
Amin, M. H. S. (2015) · Physical Review A · doi:10.1103/physreva.92.052323 · Cited by 154 · cited 1×
“Another mechanism, that appears to be more consistent with the fact that the DW2KQ is not operating in the weakcoupling regime, is that thermal relaxation is fast for small tf and then slows down for sufficiently large tf, presumably since the system has already entered the quasistatic regime [56].”
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Error-correcting codes for adiabatic quantum computation
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Consistency tests of classical and quantum models for a quantum annealer
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“[46] Tameem Albash, Walter Vinci, Anurag Mishra, Paul A.”
BackgroundSelf-citationComplexity of Stoquastic Frustration-Free Hamiltonians
Bravyi, S. B., & Terhal, B. M. (2009) · SIAM Journal on Computing · doi:10.1137/08072689x · Cited by 144
Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension.
Zhu, Z., Ochoa, A., & Katzgraber, H. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.077201 · Cited by 126 · cited 2×
“, we do not consider the isoenergetic cluster updates algorithm [80]).”
BackgroundSeeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
Katzgraber, H. G., Hamze, F., Zhu, Z., Ochoa, A. J., & Munoz-Bauza, H. (2015) · Physical Review X · doi:10.1103/physrevx.5.031026 · Cited by 112 · cited 1×
“We emphasize that the appropriate energy landscape for tunneling is not the classical energy landscape associated with simulated annealing [26] but rather the semiclassical landscape associated with transverse-field annealing [41,42].”
BackgroundMandrà, S., Zhu, Z., Wang, W., Perdomo‐Ortiz, A., & Katzgraber, H. G. (2016) · Physical Review A · doi:10.1103/physreva.94.022337 · Cited by 108 · cited 2×
“For example, simulated annealing with both single-spin and multispin updates (SAC), with the latter being simultaneous updates of all the spins comprising a unit cell (superspin approximation [23]), scales significantly better than SA with single-spin updates but still does not perform as well as SQA (see Appendix J).”
BackgroundMethodSimple Glass Models and Their Quantum Annealing
Jörg, T., Krząkała, F., Kurchan, J., & Maggs, A. C. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.147204 · Cited by 107 · cited 1×
“Instead, as proxies for a direct calculation of tunneling transition matrix elements or an instanton analysis [54], we consider the behavior of the SVMC and SQA algorithms.”
MethodUnderstanding Quantum Tunneling through Quantum Monte Carlo Simulations
Isakov, S. V., Mazzola, G., Smelyanskiy, V., Zhang, J., Boixo, S., Neven, H., & Troyer, M. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.180402 · Cited by 102 · cited 4×
“In particular, at sufficiently low temperatures SQA can mimic tunneling [39,40] and describe entangled ground states such as those followed by QA.”
BackgroundInfluentialAlbash, T., Rønnow, T. F., Troyer, M., & Lidar, D. A. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02346-0 · Cited by 96
Self-citationTunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems
Muthukrishnan, S., Albash, T., & Lidar, D. A. (2016) · Physical Review X · doi:10.1103/physrevx.6.031010 · Cited by 85
Self-citationTemperature Scaling Law for Quantum Annealing Optimizers
Albash, T., Martín-Mayor, V., & Hen, I. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.110502 · Cited by 73 · cited 2×
“This strongly suggests that the DW2KQ’s performance for this class of instances is severely impacted by its temperature, consistent with general expectations [46].”
MethodResultSelf-citationMandrà, S., Zhu, Z., & Katzgraber, H. G. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.070502 · Cited by 72 · cited 1×
“[77] Salvatore Mandrà, Zheng Zhu, and Helmut G.”
BackgroundObstructions to classically simulating the quantum adiabatic algorithm
Hastings, M. B. (2013) · Quantum Information and Computation · doi:10.26421/qic13.11-12-8 · Cited by 55 · cited 1×
“The fact that SQAperforms sowell for the logical-planted instance class is in itself a significant and novel finding about the class of logical-planted problem instances, since one might reasonably expect that as hardware quantum annealers continue to improve, SQA will become a lower bound on the performance of such h…”
BackgroundScaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations
Zhang, J., Smelyanskiy, V., Isakov, S. V., Boixo, S., Mazzola, G., Troyer, M., & Neven, H. (2017) · Physical Review A · doi:10.1103/physreva.95.012322 · Cited by 47 · cited 4×
“In particular, at sufficiently low temperatures SQA can mimic tunneling [39,40] and describe entangled ground states such as those followed by QA.”
BackgroundInfluentialThe role of symmetries in adiabatic quantum algorithms
Schaller, G., & Schützhold, R. (2010) · Quantum Information and Computation · doi:10.26421/qic10.1-2-9 · Cited by 44 · cited 1×
“[31] Gernot Schaller and Ralf Schützhold, “The role of symmetries in adiabatic quantum algorithms,” Quantum Information & Computation 10, 0109 (2010).”
BackgroundError suppression in Hamiltonian-based quantum computation using energy penalties
Bookatz, A. D., Farhi, E., & Zhou, L. (2015) · Physical Review A · doi:10.1103/physreva.92.022317 · Cited by 42
Non-commuting two-local Hamiltonians for quantum error suppression
Jiang, Z., & Rieffel, E. G. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1527-9 · Cited by 38
The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again)
Mandrà, S., Katzgraber, H. G., & Thomas, C. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa7877 · Cited by 35
Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes
Marvian, M., & Lidar, D. A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.030504 · Cited by 34
Self-citationQuantum Monte Carlo tunneling from quantum chemistry to quantum annealing
Mazzola, G., Smelyanskiy, V., & Troyer, M. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.134305 · Cited by 34
Quantum annealing for problems with ground-state degeneracy
Matsuda, Y., Nishimori, H., & Katzgraber, H. G. (2009) · Journal of Physics Conference Series · doi:10.1088/1742-6596/143/1/012003 · Cited by 33
Owerre, S. A., & Paranjape, M. B. (2014) · Physics Reports · doi:10.1016/j.physrep.2014.09.001 · Cited by 31 · cited 1×
“The semiclassical potential as derived from the spincoherent path-integral formalism [53] is given by the expectation value of HðtÞ in the spin-coherent state jΩðθ⃗;φ⃗Þi1⁄4⊗i1⁄411⁄2cosðθi=2Þj0iiþei sinðθi=2Þj1ii .”
Optimally Stopped Optimization
Vinci, W., & Lidar, D. A. (2016) · Physical Review Applied · doi:10.1103/physrevapplied.6.054016 · Cited by 27
Self-citationOff-diagonal expansion quantum Monte Carlo
Albash, T., Wagenbreth, G., & Hen, I. (2017) · Physical review. E · doi:10.1103/physreve.96.063309 · Cited by 26 · cited 1×
“[57] Tameem Albash, Gene Wagenbreth, and Itay Hen,”
BackgroundSelf-citationAdvantages of Unfair Quantum Ground-State Sampling
Zhang, B. H., Wagenbreth, G., Martín-Mayor, V., & Hen, I. (2017) · Scientific Reports · doi:10.1038/s41598-017-01096-6 · Cited by 25 · cited 1×
“Addressing this question provides another approach for searching for a quantum advantage beyond the standard optimization approach [60,82].”
BackgroundQuantum trajectories for time-dependent adiabatic master equations
Yip, K.-W., Albash, T., & Lidar, D. A. (2018) · Physical Review A · doi:10.1103/physreva.97.022116 · Cited by 22 · cited 1×
“The same is true for master equation simulations [41,74], even when implemented using the quantum trajectories method [75].”
MethodSelf-citationAnisotropic Landau-Lifshitz-Gilbert models of dissipation in qubits
Crowley, P. J. D., & Green, A. G. (2016) · Physical Review A · doi:10.1103/physreva.94.062106 · Cited by 16 · cited 1×
“The SA and SVMC algorithms can both be viewed not only as classical analogues of QA, but also as implementing two of its possible classical limits [15,38,58].”
BackgroundError suppression for Hamiltonian quantum computing in Markovian environments
Marvian, M., & Lidar, D. A. (2017) · Physical Review A · doi:10.1103/physreva.95.032302 · Cited by 16
Self-citation
Flagged first, then by citations
Research works printed but not linked: 2
- P. W. Shor, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994
- F. Hamze, 2004, UAI
Cited by
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A quantum engineer's guide to superconducting qubits
Krantz, P., Kjærgaard, M., Yan, F., Orlando, T. P., Gustavsson, S., & Oliver, W. D. (2019) · Applied Physics Reviews · doi:10.1063/1.5089550 · Cited by 2,321
Quantum optimization using variational algorithms on near-term quantum devices
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Perspectives of quantum annealing: methods and implementations
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Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer
Aramon, M., Rosenberg, G., Valiante, E., Miyazawa, T., Tamura, H., & Katzgraber, H. G. (2019) · Frontiers in Physics · doi:10.3389/fphy.2019.00048 · Cited by 442
“With the same goal in mind, researchers have been inspired to push the envelope for such problems on novel hardware, such as the coherent Ising machine [32], as well as on graphics processing units (GPU) [27, 28] and application-specific CMOS hardware [34, 35].”
BackgroundHamerly, R., Inagaki, T., McMahon, P. L., Venturelli, D., Marandi, A., Onodera, T., Ng, E., Langrock, C., Inaba, K., Honjo, T., et al. (2019) · Science Advances · doi:10.1126/sciadv.aau0823 · Cited by 366
“It has been observed empirically on D-Wave quantum annealers that, for Chimera graph spin glasses, optimal time to solution scales as Tsoln o exp (O(N )) (18, 19, 49), while Tsoln at fixed anneal times increases more steeply (18).”
Background
Metadata
- Authors
- Albash, T., & Lidar, D. A.
- Affiliations
- University of Southern California (US)
- ORCID
- Albash, Tameem
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2018-07-19
- Volume
- 8
- Issue
- 3
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W2992146840
- Cited by
- 238
- References
- 70
- Citations by year
- 2026: 13 · 2025: 46 · 2024: 33 · 2023: 28 · 2022: 28 · 2021: 28 · 2020: 33 · 2019: 24 · 2018: 4
- FWCI
- 12.50
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- APS March Meeting Abstracts
- Funders
- Army Research Office (W911NF-12-1-0523, W911NF-11-1-0268, W911NF-15-1-0582, W911NF-17-C-0050)
- National Science Foundation (INSPIRE-1551064)
- U.S. Department of Energy (DE-AC05-00OR22725)
- Office of the Director of National Intelligence
- Intelligence Advanced Research Projects Activity
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum annealing, simulated annealing, quantum advantage, benchmarking, combinatorial optimization, quantum annealers
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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