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, and simulated QA suggests that QA possesses the best scaling properties.
“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]
The Introduction says simulated quantum annealing (SQA), not quantum-annealing hardware, had the best scaling among the algorithms tested on logical-planted instances. The Discussion and Outlook likewise says SQA overwhelmingly outperformed the DW2KQ device, although the device outperformed simulated annealing. The supplied passages have section labels but no page numbers. (LLM, conf=0.91)
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Experimental — accuracy not yet measuredQA shows superior scaling properties compared to SA, where both are significantly inferior to simulated QA.
“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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“In particular, at sufficiently low temperatures SQA can mimic tunneling [39,40] and describe entangled ground states such as those followed by QA.”
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“In particular, at sufficiently low temperatures SQA can mimic tunneling [39,40] and describe entangled ground states such as those followed by QA.”
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“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…”
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“Addressing this question provides another approach for searching for a quantum advantage beyond the standard optimization approach [60,82].”
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“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
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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].”
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Self-citation
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Cited by
Sorted by citations
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 2,056 · see citing works
Perspectives of quantum annealing: methods and implementations
Hauke, P., Katzgraber, H. G., Lechner, W., Nishimori, H., & Oliver, W. D. (2020) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab85b8 · Cited by 507 · see citing works
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 · see citing works
“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 · see citing works
“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).”
BackgroundHamerly, R., Inagaki, T., McMahon, P. L., Venturelli, D., Marandi, A., Onodera, T., Ng, E., Langrock, C., Inaba, K., Honjo, T., et al. (2019) · CaltechAUTHORS (California Institute of Technology) · Cited by 257 · see citing works
Reverse quantum annealing approach to portfolio optimization problems
Venturelli, D., & Kondratyev, A. (2019) · Quantum Machine Intelligence · doi:10.1007/s42484-019-00001-w · Cited by 233 · see citing works
“In particular, the annealing time is expected to be suboptimal for N ≤ 50, leading to a measurement of a flatter slope for the median TTS [33].”
BackgroundThe prospects of quantum computing in computational molecular biology
Outeiral, C., Strahm, M., Shi, J., Morris, G. M., Benjamin, S. C., & Deane, C. M. (2021) · WIREs Computational Molecular Science · doi:10.1002/wcms.1481 · Cited by 232 · see citing works
“Despite these concerns, it has been used widely as an optimization metaheuristic and has recently been shown to overperform simulated annealing [188].”
MethodChallenges and opportunities in quantum optimization
Abbas, A., Ambainis, A., Augustino, B., Bärtschi, A., Buhrman, H., Coffrin, C., Cortiana, G., Dunjko, V., Egger, D. J., Elmegreen, B. G., et al. (2024) · Nature Reviews Physics · doi:10.1038/s42254-024-00770-9 · Cited by 201 · see citing works
“Hence, quantum annealing research tends to focus on empirical studies of the behaviour of the algorithm in ideal 47 and noisy computational settings 48,49 .”
Bando, Y., Susa, Y., Oshiyama, H., Shibata, N., Ohzeki, M., Gómez-Ruiz, F. J., Lidar, D. A., Suzuki, S., del Campo, A., & Nishimori, H. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033369 · Cited by 147 · see citing works
“We first consider a Boltzmann distribution of the kink density of the classical Ising chain, then the classical spin-vector Monte Carlo model [80], which has been successfully applied to at least partially describe the outcomes of experiments using the D-Wave devices in past studies [8,13,56,66,67,71,81], and also in…”
MethodSelf-citationProspects for quantum enhancement with diabatic quantum annealing
Crosson, E., & Lidar, D. A. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00313-6 · Cited by 137 · see citing works
Self-citationCarapito, R., Li, R. Y., Helms, J., Carapito, C., Gujja, S., Rolli, V., Guimaraes, R., Malagon-Lopez, J., Spinnhirny, P., Lederle, A., et al. (2021) · Science Translational Medicine · doi:10.1126/scitranslmed.abj7521 · Cited by 119 · see citing works
“The advantage of running the optimization problem on a QA is that, since the QA samples from the quantum distribution, it retains both the lowest energy solution and some of the next lowest-energy solutions (Albash and Lidar, 2018).”
BackgroundSelf-citationPower of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers
Marshall, J., Venturelli, D., Hen, I., & Rieffel, E. G. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.11.044083 · Cited by 119 · see citing works
“03] GHz, when the problem Hamiltonian is re-scaled by [1, 2, 4, 8] re-”
InfluentialQuantum Annealing amid Local Ruggedness and Global Frustration
King, J., Yarkoni, S., Raymond, J., Ozfidan, I., King, A. D., Nevisi, M. M., Hilton, J., & McGeoch, C. C. (2019) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.88.061007 · Cited by 104 · see citing works
Practical Annealing-Based Quantum Computing
McGeoch, C. C., Harris, R., Reinhardt, S. P., & Bunyk, P. (2019) · Computer · doi:10.1109/mc.2019.2908836 · Cited by 70 · see citing works
“12 Note that results about quantum speedup also tend to have little relevance to practice: the synthetic inputs do not resemble real-world inputs, and the scaling analysis ignores constant-factor speedups (sometimes favoring the QPU by many orders of magnitude 13 ), which are of keen interest to…”
BackgroundBiology and medicine in the landscape of quantum advantages
Cordier, B. A., Sawaya, N. P. D., Guerreschi, G. G., & McWeeney, S. K. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0541 · Cited by 87 · see citing works
Bokhan, D., Mastiukova, A. S., Boev, A. S., Trubnikov, D. N., & Fedorov, A. K. (2022) · Frontiers in Physics · doi:10.3389/fphy.2022.1069985 · Cited by 83 · see citing works
“ranking DNA to RNA transcription factors [36] using a quantum annealer, weather forecasting [37] on the basis of the superconducting quantum computer, and many others [38].”
MethodSU(2) lattice gauge theory on a quantum annealer
Rahman, S. A., Lewis, R., Mendicelli, E., & Powell, S. J. M. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.034501 · Cited by 80 · see citing works
Detecting multiple communities using quantum annealing on the D-Wave system
Negre, C. F. A., Ushijima-Mwesigwa, H., & Mniszewski, S. M. (2020) · PLOS ONE · doi:10.1371/journal.pone.0227538 · Cited by 80 · see citing works
“Problems having many local minima (that could come from large sized system) would require longer annealing times for QA [44].”
BackgroundBenchmarking Quantum Annealing Controls with Portfolio Optimization
Grant, E., Humble, T. S., & Stump, B. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.15.014012 · Cited by 90 · see citing works
“[18] Tameem Albash and Daniel A Lidar.”
BackgroundNishi, H., Kosugi, T., & Matsushita, Y. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00409-y · Cited by 78 · see citing works
Dynamics of reverse annealing for the fully connected p -spin model
Yamashiro, Y., Ohkuwa, M., Nishimori, H., & Lidar, D. A. (2019) · Physical Review A · doi:10.1103/physreva.100.052321 · Cited by 76 · see citing works
Self-citationAnnealing-Based Quantum Computing for Combinatorial Optimal Power Flow
Morstyn, T. (2022) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2022.3200590 · Cited by 77 · see citing works
“Theoretically demonstrating when noisy quantum annealing has a definitive advantage over classical alternatives is challenging [34], but a performance advantage has been demonstrated for specific applications [35], [36].”
BackgroundTheory versus practice in annealing-based quantum computing
McGeoch, C. C. (2020) · Theoretical Computer Science · doi:10.1016/j.tcs.2020.01.024 · Cited by 69 · see citing works
Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits
Ozfidan, I., Deng, C., Smirnov, A. Y., Lanting, T. M., Harris, R., Swenson, L. J., Whittaker, J. D., Altomare, F., Babcock, M. C., Baron, C., et al. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.13.034037 · Cited by 66 · see citing works
“[13] T.”
BackgroundKarimi-Rizvandi, S., Goodarzi, H. V., Hatamiafkoueieh, J., Chung, I.-M., Kişi, Ö., Kim, S., & Linh, N. T. T. (2021) · Water · doi:10.3390/w13050658 · Cited by 64 · see citing works
“The dvant ge of the SA algorithm was v ry low memory consumption and the ability to pass local optimization due to a randomized process [72].”
BackgroundMethodEngineering Reflective Metasurfaces With Ising Hamiltonian and Quantum Annealing
Ross, C., Gradoni, G., Lim, Q. J., & Peng, Z. (2021) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2021.3137424 · Cited by 64 · see citing works
“The probability of reaching the ground state (global optimal solution) is around 95%, which is often referred to as the success probability of a single-instance run, Ps [55], [56].”
BackgroundOptimization Applications as Quantum Performance Benchmarks
Lubinski, T., Coffrin, C., McGeoch, C. C., Sathe, P., Apanavicius, J., Bernal, D. E., & Quantum Economic Development Consortium Collaboration (2024) · ACM Transactions on Quantum Computing · doi:10.1145/3678184 · Cited by 66 · see citing works
“The time-to-solution (TTS) metric determines the expected wall-clock time required to solve a problem to optimality [48, 82–85].”
Quantum Optimization: Potential, Challenges, and the Path Forward
Abbas, A., (NNSA), U. N. N. S. A., Ambainis, A., Augustino, B., Bärtschi, A., Buhrman, H., Coffrin, C., Cortiana, G., Dunjko, V., Egger, D., et al. (2023) · doi:10.2172/2229681 · Cited by 63 · see citing works
Multilevel Combinatorial Optimization across Quantum Architectures
Ushijima-Mwesigwa, H., Shaydulin, R., Negre, C. F. A., Mniszewski, S. M., Alexeev, Y., & Safro, I. (2021) · ACM Transactions on Quantum Computing · doi:10.1145/3425607 · Cited by 57 · see citing works
Demonstration of Algorithmic Quantum Speedup
Pokharel, B., & Lidar, D. A. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.210602 · Cited by 56 · see citing works
“Quantum annealing hardware based on superconducting flux qubits was used to demonstrate a speedup against simulated annealing for certain specially crafted spin-glass problems [55].”
MethodSelf-citationBoundaries of quantum supremacy via random circuit sampling
Zlokapa, A., Villalonga, B., Boixo, S., & Lidar, D. A. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00703-x · Cited by 54 · see citing works
Self-citationScalable Emulation of Sign-Problem–Free Hamiltonians with Room-Temperature p -bits
Camsari, K. Y., Chowdhury, S., & Datta, S. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.12.034061 · Cited by 55 · see citing works
3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers
Kowalsky, M., Albash, T., Hen, I., & Lidar, D. A. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac4d1b · Cited by 52 · see citing works
“Since the solvers we study are stochastic, we use the optimal time-to-solution (TTS) metric [21, 24].”
Self-citationQFold: quantum walks and deep learning to solve protein folding
Casares, P. A. M., Campos, R., & Martin-Delgado, M. A. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac4f2f · Cited by 53 · see citing works
“Similar metrics have also been defined previously in the literature [37].”
Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers
Pelofske, E., Bärtschi, A., & Eidenbenz, S. (2023) · Lecture Notes in Computer Science · doi:10.1007/978-3-031-32041-5_13 · Cited by 47 · see citing works
“Simulated annealing is a standard high accuracy and general purpose classical heuristic algorithm [57], and has been used as a reasonable comparison against quantum algorithms [13].”
MethodChallenges of variational quantum optimization with measurement shot noise
Scriva, G., Astrakhantsev, N., Pilati, S., & Mazzola, G. (2024) · Physical Review A · doi:10.1103/physreva.109.032408 · Cited by 49 · see citing works
“However, it is not easy to prove systematic quantum speedups with analog quan-∗ tum annealers [8, 9], also because quantum Monte Carlo algorithms appear to be able to emulate their tunneling dynamics [10–13].”
BackgroundMethodImproving quantum annealing of the ferromagnetic p -spin model through pausing
Passarelli, G., Cataudella, V., & Lucignano, P. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.024302 · Cited by 47 · see citing works
Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning
Böhm, F., Alonso-Urquijo, D., Verschaffelt, G., & der Sande, G. V. (2022) · Nature Communications · doi:10.1038/s41467-022-33441-3 · Cited by 51 · see citing works
“(16), and (17) with a step width of h = 1 at α = 0.”
MethodAgile Earth Observation Satellite Scheduling With a Quantum Annealer
Stollenwerk, T., Michaud, V., Lobe, E., Picard, M., Basermann, A., & Botter, T. (2021) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2021.3088490 · Cited by 49 · see citing works
Mishra, A., Albash, T., & Lidar, D. A. (2018) · Nature Communications · doi:10.1038/s41467-018-05239-9 · Cited by 46 · see citing works
Self-citationQuantum Annealing versus Digital Computing
Jünger, M., Lobe, E., Mutzel, P., Reinelt, G., Rendl, F., Rinaldi, G., & Stollenwerk, T. (2021) · ACM Journal of Experimental Algorithmics · doi:10.1145/3459606 · Cited by 51 · see citing works
From Charge to Spin and Spin to Charge: Stochastic Magnets for Probabilistic Switching
Camsari, K. Y., Debashis, P., Ostwal, V., Pervaiz, A. Z., Shen, T., Chen, Z., Datta, S., & Appenzeller, J. (2020) · Proceedings of the IEEE · doi:10.1109/jproc.2020.2966925 · Cited by 44 · see citing works
“There is emerging evidence on relative benefits of SQA compared to CA [57], attributed to the SQA’s ability to mimick “tunneling” out of local minima which is not possible in CA though it has also been noted that there might be observable scaling differences between QA and SQA [58].”
BackgroundQuantum processor-inspired machine learning in the biomedical sciences
Li, R. Y., Gujja, S., Bajaj, S. R., Gamel, O., Cilfone, N. A., Gulcher, J. R., Lidar, D. A., & Chittenden, T. W. (2021) · Patterns · doi:10.1016/j.patter.2021.100246 · Cited by 49 · see citing works
“16 While the computational role of quantum effects in these processors remains controversial and the subject of intensive study, quantum annealing is currently one of the few paradigms of quantum computing that are approaching a scale useful for practical applications.”
Self-citationOn the emerging potential of quantum annealing hardware for combinatorial optimization
Tasseff, B., Albash, T., Morrell, Z., Vuffray, M., Lokhov, A. Y., Misra, S., & Coffrin, C. (2024) · Journal of Heuristics · doi:10.1007/s10732-024-09530-5 · Cited by 42 · see citing works
“Due to the challenges associated with mapping established optimization test cases to specific QA hardware [11], the QA benchmarking community has adopted the practice of building instance generation algorithms that are tailored to specific quantum processing units (QPUs) [48, 36, 49, 19, 2, 66].”
InfluentialSelf-citationWhy and When Pausing is Beneficial in Quantum Annealing
Chen, H., & Lidar, D. A. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.14.014100 · Cited by 41 · see citing works
“Today’s commercial quantum annealers feature thousands of superconducting flux qubits and are being used routinely to test whether this approach can provide a quantum advantage over classical computing [5–11].”
BackgroundSelf-citationCharged particle tracking with quantum annealing optimization
Zlokapa, A., Anand, A., Vlimant, J.-R., Duarte, J. M., Job, J., Lidar, D. A., & Spiropulu, M. (2021) · Quantum Machine Intelligence · doi:10.1007/s42484-021-00054-w · Cited by 42 · see citing works
“To test the effect of the annealing time (which in principle must be optimized in order to extract the true time to solution (Albash and Lidar 2018; Rønnow et al. 2014)), we compare runs from 5 to 800 μs.”
BackgroundMethodInfluentialSelf-citationEmbedding Overhead Scaling of Optimization Problems in Quantum Annealing
Könz, M. S., Lechner, W., Katzgraber, H. G., & Troyer, M. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040322 · Cited by 43 · see citing works
Two-parameter counter-diabatic driving in quantum annealing
Prielinger, L., Hartmann, A., Yamashiro, Y., Nishimura, K., Lechner, W., & Nishimori, H. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.013227 · Cited by 39 · see citing works
“[40] T.”
MethodMean field analysis of reverse annealing for code-division multiple-access multiuser detection
Arai, S., Ohzeki, M., & Tanaka, K. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033006 · Cited by 36 · see citing works
Photonic Ising machines for combinatorial optimization problems
Gao, Y., Chen, G., Luo, Q., Fu, W., Yuan, Z., & Danner, A. J. (2024) · Applied Physics Reviews · doi:10.1063/5.0216656 · Cited by 34 · see citing works
Scaling Advantage in Approximate Optimization with Quantum Annealing
Munoz-Bauza, H., & Lidar, D. A. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.160601 · Cited by 46 · see citing works
“It is well known that the TTS metric generates unreliable results unless the annealing time is optimized for each size N [8, 13].”
BackgroundSelf-citationQuantum annealing for systems of polynomial equations
Chang, C. C., Gambhir, A. S., Humble, T. S., & Sota, S. (2019) · Scientific Reports · doi:10.1038/s41598-019-46729-0 · Cited by 36 · see citing works
Compressed Quadratization of Higher Order Binary Optimization Problems
Mandal, A., Roy, A., Upadhyay, S., & Ushijima‐Mwesigwa, H. (2020) · DCC · doi:10.1109/dcc47342.2020.00090 · Cited by 33 · see citing works
Spintronic devices as next-generation computation accelerators
González, V. H., Litvinenko, A. N., Kumar, A., Khymyn, R., & Åkerman, J. J. (2024) · Current Opinion in Solid State and Materials Science · doi:10.1016/j.cossms.2024.101173 · Cited by 31 · see citing works
“…technology [13, 14], electrical oscillators [15], interfering light [16], optical pulses [17, 18, 19, 20], memristor crossbar arrays [21, 22], Josephson junctions [23, 24], and even single atoms [25]; with the latter two making use of the quantum adiabatic theorem to tunnel to the ground state.”
BackgroundStrategic Portfolio Optimization Using Simulated, Digital, and Quantum Annealing
Lang, J. B., Zielinski, S., & Feld, S. (2022) · Applied Sciences · doi:10.3390/app122312288 · Cited by 31 · see citing works
“Parallel rejection algorithms on GPU (see [29,30]) are examples of similar efforts in the literature to address the low acceptance probability problem in Monte Carlo methods [28].”
MethodAccelerated quantum Monte Carlo with probabilistic computers
Chowdhury, S., Çamsarı, K. Y., & Datta, S. (2022) · Communications Physics · doi:10.1038/s42005-023-01202-3 · Cited by 39 · see citing works
“This is interesting because until this result, results on TFI, a well-known stoquastic Hamiltonian, have been routinely benchmarked with quantum Monte Carlo algorithms [40] with no clear scaling differences for practical problems [41].”
ResultWishart planted ensemble: A tunably rugged pairwise Ising model with a first-order phase transition
Hamze, F., Raymond, J., Pattison, C. A., Biswas, K., & Katzgraber, H. G. (2020) · Physical review. E · doi:10.1103/physreve.101.052102 · Cited by 29 · see citing works
“Often, it is faster to carry out many short attempts taking run time R with a lower success probability p(R, {φ}) which motivates the definition [79–81]”
BackgroundAn Application of Quantum Annealing Computing to Seismic Inversion
Souza, A. M., Martins, E. O., Roditi, I., Sá, N., Sarthour, R. S., & Oliveira, I. S. (2022) · Frontiers in Physics · doi:10.3389/fphy.2021.748285 · Cited by 30 · see citing works
“Recent works have proposed that, in some cases, quantum annealing is advantageous over classical computing [27–30], on the other hand, no advantage was reported in references [24, 31].”
BackgroundBenchmarking Digital Quantum Simulations Above Hundreds of Qubits Using Quantum Critical Dynamics
Miessen, A., Egger, D. J., Tavernelli, I., & Mazzola, G. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.040320 · Cited by 29 · see citing works
“For instance, variational algorithms [46, 83] for many-body spin systems feature circuits very similar to the ones considered in the previous section.”
BackgroundMethodLimitations of error corrected quantum annealing in improving the performance of Boltzmann machines
Li, R. Y., Albash, T., & Lidar, D. A. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab9aab · Cited by 29 · see citing works
“In reference [62], simulations demonstrated that at high temperature SQA and SVMC performed similarly, but at lower temperatures the two performed differently, most likely because SQA is able to simulate tunneling events, whereas SVMC can only make use of thermal hopping.”
BackgroundSelf-citationQuickSim: Efficient and Accurate Physical Simulation of Silicon Dangling Bond Logic
Drewniok, J., Walter, M., Ng, S. S. H., Walus, K., & Wille, R. (2023) · IEEE International Conference on Nanotechnology (IEEE-NANO) · doi:10.1109/nano58406.2023.10231266 · Cited by 28 · see citing works
“This trade-off is captured by the Time-To-Solution (TTS) metric that provides the total runtime needed to derive a solution of a certain confidence level η [31].”
MethodSu, Y., Kim, T. T.-H., & Kim, B. (2024) · IEEE Journal of Solid-State Circuits · doi:10.1109/jssc.2024.3352907 · Cited by 26 · see citing works
“Recently, Ising machines have been demonstrated in various technologies, including quantum computing [26], [27], [28], [29], coherent optics [30], [31], [32], and CMOS technologies [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17].”
BackgroundQuantum computation and simulation with superconducting qubits*
He, K., Geng, X., Huang, R., Liu, J., & Chen, W. (2021) · Chinese Physics B · doi:10.1088/1674-1056/ac16cf · Cited by 24 · see citing works
Equation Planting: A Tool for Benchmarking Ising Machines
Hen, I. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.12.011003 · Cited by 25 · see citing works
“[50–52]).”
Benchmarking Quantum(-Inspired) Annealing Hardware on Practical Use Cases
Huang, T., Xu, J., Luo, T., Gu, X., Goh, R. S. M., & Wong, W. (2022) · IEEE Transactions on Computers · doi:10.1109/tc.2022.3219257 · Cited by 25 · see citing works
“[16] compares the scalability of quantum and classical annealing.”
BackgroundTaming a nonconvex landscape with dynamical long-range order: Memcomputing Ising benchmarks
Sheldon, F. C., Traversa, F. L., & Ventra, M. D. (2019) · Physical review. E · doi:10.1103/physreve.100.053311 · Cited by 25 · see citing works
Benchmarking Quantum Annealing Against “Hard” Instances of the Bipartite Matching Problem
Vert, D., Sirdey, R., & Louise, S. (2021) · SN Computer Science · doi:10.1007/s42979-021-00483-1 · Cited by 23 · see citing works
“Such an advantage has furthermore recently been experimentally demonstrated by Albash and Lidar [1].”
BackgroundResultIsing Model Optimization Problems on a FPGA Accelerated Restricted Boltzmann MachinePreprint
Patel, S., Chen, L., Canoza, P., & Salahuddin, S. (2020) · Research Square · doi:10.21203/rs.3.rs-122016/v1 · Cited by 23 · see citing works
Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study
Gemeinhardt, F., Garmendia, A., Wimmer, M., Weder, B., & Leymann, F. (2024) · ACM Computing Surveys · doi:10.1145/3620668 · Cited by 22 · see citing works
“SA, spin-vector-monte-carlo [215], and simulated QA suggests that QA possesses the best scaling properties [7].”
BackgroundComputational hardness of spin-glass problems with tile-planted solutions
Perera, D., Hamze, F., Raymond, J., Weigel, M., & Katzgraber, H. G. (2020) · Physical review. E · doi:10.1103/physreve.101.023316 · Cited by 22 · see citing works
Wauters, M. M., Mbeng, G. B., & Santoro, G. E. (2020) · Physical Review A · doi:10.1103/physreva.102.062404 · Cited by 30 · see citing works
Blueprint for All-to-All-Connected Superconducting Spin Qubits
Pita‐Vidal, M., Wesdorp, J. J., & Andersen, C. K. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.010308 · Cited by 22 · see citing works
“Flux qubit systems have been used to approach the so-lution of some problems using quantum annealing [61– 63].”
Nested quantum annealing correction at finite temperature: p -spin models
Matsuura, S., Nishimori, H., Vinci, W., & Lidar, D. A. (2019) · Physical Review A · doi:10.1103/physreva.99.062307 · Cited by 21 · see citing works
Self-citationQuantum adiabatic machine learning by zooming into a region of the energy surface
Zlokapa, A., Mott, A., Job, J., Vlimant, J.-R., Lidar, D. A., & Spiropulu, M. (2020) · Physical Review A · doi:10.1103/physreva.102.062405 · Cited by 22 · see citing works
Self-citationCryogenic Electronics and Quantum Information Processing
Holmes, D. S. (2021) · doi:10.1109/irds54852.2021.00012 · Cited by 23 · see citing works
Perils of embedding for sampling problems
Marshall, J., Gioacchino, A. D., & Rieffel, E. G. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023020 · Cited by 20 · see citing works
A superconducting adiabatic neuron in a quantum regime
Bastrakova, M. V., Pashin, D. S., Rybin, D. A., Schegolev, A. E., Klenov, N. V., Soloviev, I. I., Gorchavkina, A. A., & Михайлович, С. А. (2022) · Beilstein Journal of Nanotechnology · doi:10.3762/bjnano.13.57 · Cited by 19 · see citing works
Quantum annealing for vehicle routing problem with weighted segment
Tambunan, T. D., Suksmono, A. B., Edward, I. J. M., & Mulyawan, R. (2023) · AIP conference proceedings · doi:10.1063/5.0178362 · Cited by 22 · see citing works
Continuous quantum error correction for evolution under time-dependent Hamiltonians
Atalaya, J., Zhang, S., Niu, M. Y., Babakhani, A., Chan, C. H. H., Epstein, J. M., & Whaley, K. B. (2021) · Physical Review A · doi:10.1103/physreva.103.042406 · Cited by 19 · see citing works
“This TTS metric, which is applied to both algorithmic and error mitigation protocols, reflects a trade-off between a high single-run success probability with a long operation time, and a low single-run success probability with a short operation time [59].”
MethodA Quantum Annealer-Enabled Decoder and Hardware Topology for NextG Wireless Polar Codes
Kasi, S., Kaewell, J., & Jamieson, K. (2023) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2023.3311204 · Cited by 18 · see citing works
“It is computed as [30]: where T a is the annealing time and P 1 is the probability of R 1 , the minimum energy solution.”
MethodVolpe, D., Cirillo, G. A., Zamboni, M., & Turvani, G. (2023) · IEEE Access · doi:10.1109/access.2023.3260765 · Cited by 18 · see citing works
“This figure of merit is commonly employed in the literature for comparing heuristic algorithms and in particular, for detecting quantum speed-up [96], [97], [98], [99], [100] given by quantum, quantum-inspired and quantum-compliant optimization approaches.”
MethodEfficient low temperature Monte Carlo sampling using quantum annealing
Sandt, R., & Spatschek, R. (2023) · Scientific Reports · doi:10.1038/s41598-023-33828-2 · Cited by 17 · see citing works
Improving performance of logical qubits by parameter tuning and topology compensation
Raymond, J., Ndiaye, N., Rayaprolu, G., & King, A. D. (2020) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce49297.2020.00044 · Cited by 19 · see citing works
A Quantum Algorithm for Model-Independent Searches for New Physics
Matchev, K. T., Shyamsundar, P., & Smolinsky, J. (2023) · Letters in High Energy Physics · doi:10.31526/lhep.2023.301 · Cited by 16 · see citing works
“A promising approach to tackle large N cases is offered by current and future AQO implementations on quantum computers [55–57].”
The potential of quantum annealing for rapid solution structure identification
Pang, Y., Coffrin, C., Lokhov, A. Y., & Vuffray, M. (2020) · Constraints · doi:10.1007/s10601-020-09315-0 · Cited by 18 · see citing works
Multilevel Combinatorial Optimization Across Quantum Architectures
Ushijima‐Mwesigwa, H., Shaydulin, R., Negre, C. F. A., Mniszewski, S. M., Alexeev, Y., & Safro, I. (2019) · TigerPrints (Clemson University) · Cited by 15 · see citing works
Hamerly, R., Inagaki, T., McMahon, P. L., Venturelli, D., Marandi, A., Onodera, T., Ng, E., Langrock, C., Inaba, K., Honjo, T., et al. (2018) · arXiv (Cornell University) · Cited by 14 · see citing works
Schulz, S., Willsch, D., & Michielsen, K. F. L. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013312 · Cited by 14 · see citing works
“Panels (a)–(e) present the averaged results for the EC problems with sizes N ∈ { 12 , 15 , 18 , 21 , 24 } , respectively.”
BackgroundCummins, J., Salman, H., & Berloff, N. G. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013150 · Cited by 15 · see citing works
Noise can speed Markov chain Monte Carlo estimation and quantum annealing
Franzke, B., & Kosko, B. (2019) · Physical review. E · doi:10.1103/physreve.100.053309 · Cited by 14 · see citing works
On the Computational Viability of Quantum Optimization for PMU Placement
Jones, E. B., Kapit, E., Chang, C.-Y., Biagioni, D., Vaidhynathan, D., Graf, P. A., & Jones, W. B. (2020) · IEEE Power Engineering Society General Meeting · doi:10.1109/pesgm41954.2020.9281420 · Cited by 15 · see citing works
“…speedups have been demonstrated for AQA against both simulated annealing (SA)– in the form of a scaling advantage– and quantum Monte Carlo (QMC)– as a fixed prefactor– using the D-Wave 2X and 2000Q machines on proof-of-principle problems designed to have tall and narrow energy barriers [8] [9].”
Standard quantum annealing outperforms adiabatic reverse annealing with decoherence
Passarelli, G., Yip, K.-W., Lidar, D. A., & Lucignano, P. (2022) · Physical Review A · doi:10.1103/physreva.105.032431 · Cited by 14 · see citing works
Self-citationPhysics-inspired Ising Computing with Ring Oscillator Activated p-bits
Aadit, N. A., Grimaldi, A., Finocchio, G., & Camsari, K. Y. (2022) · IEEE International Conference on Nanotechnology (IEEE-NANO) · doi:10.1109/nano54668.2022.9928681 · Cited by 14 · see citing works
“We follow the time-to-solution formulation [17], [18] to measure performance of the physics-inspired asynchronous architecture.”
MethodEvidence that PUBO outperforms QUBO when solving continuous optimization problems with the QAOA
Stein, J., Chamanian, F., Zorn, M., Nüßlein, J., Zieliński, S., Kölle, M., & Linnhoff-Popien, C. (2023) · GECCO Companion · doi:10.1145/3583133.3596358 · Cited by 24 · see citing works
“…promising approach to solving such optimization problems is quantum computing, which has already shown results comparable to classical state-of-the-art methods for small problem sizes [Albash and Lidar 2018; Denchev et al. 2016; Ebadi et al. 2022] despite current quantum hardware limitations.”
ResultLeib, D., Seidel, T., Jäger, S., Heese, R., Jones, C. R., Awasthi, A., Niederle, A. E., & Bortz, M. (2023) · Scientific Reports · doi:10.1038/s41598-023-45668-1 · Cited by 16 · see citing works
“Quantum annealing has proven to offer some advantage against the classical simulated annealing algorithm for a spin-glass problem, using D-Wave hardware (Raymond et al. 2023), but this is no conclusive evidence.”
BackgroundOptimization of quantum computing models inspired by D-wave quantum annealing
Wang, B., Hu, F., & Wang, C. (2020) · Tsinghua Science & Technology · doi:10.26599/tst.2019.9010030 · Cited by 13 · see citing works
Investigating the Chinese postman problem on a quantum annealer
Siloi, I., Carnevali, V., Pokharel, B., Fornari, M., & Felice, R. D. (2021) · Quantum Machine Intelligence · doi:10.1007/s42484-020-00031-9 · Cited by 15 · see citing works
Few-qubit quantum refrigerator for cooling a multi-qubit system
Arısoy, O., & Müstecaplıoğlu, Ö. E. (2021) · Scientific Reports · doi:10.1038/s41598-021-92258-0 · Cited by 13 · see citing works
“We take ~ = 1 and set h = 1 GHz for all of our calculations as it is a typical order of magnitude for superconducting qubits [32] and we will assume that g can be in the order of h [33].”
BackgroundDeep recurrent networks predicting the gap evolution in adiabatic quantum computing
Mohseni, N., Navarrete–Benlloch, C., Byrnes, T., & Marquardt, F. (2023) · Quantum · doi:10.22331/q-2023-06-12-1039 · Cited by 13 · see citing works
The Mathematics of Quantum-Enabled Applications on the D-Wave Quantum Computer
Berwald, J. (2019) · Notices of the American Mathematical Society · doi:10.1090/noti1893 · Cited by 11 · see citing works
- 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 · 2017: 1
- 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 › Computer Science › Artificial Intelligence › 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
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