Brooke, J., Bitko, D., Rosenbaum, T. F. & Aeppli, G. Quantum annealing of a disordered magnet. Science 284, 779–781 (1999).
Aeppli, G. & Rosenbaum, T. F. in Quantum Annealing and Related Optimization Methods (eds Das, A. & Chakrabarti, B.) Ch. 6 (Springer, 2005).
Das, A. & Chakrabarti, B. K. Colloquium: quantum annealing and analog quantum computation. Rev. Mod. Phys. 80, 1061–1081 (2008).
Kadowaki, T. & Nishimori, H. Quantum annealing in the transverse Ising model. Phys. Rev. E 58, 5355 (1998).
Santoro, G. E., Martonák, R., Tosatti, E. & Car, R. Theory of quantum annealing of an Ising spin glass. Science 295, 2427–2430 (2002).
Harris, R. et al. Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor. Phys. Rev. B 82, 024511 (2010).
Rønnow, T. F. et al. Defining and detecting quantum speedup. Science 345, 420–424 (2014).
Katzgraber, H. G., Hamze, F. & Andrist, R. S. Glassy chimeras could be blind to quantum speedup: designing better benchmarks for quantum annealing machines. Phys. Rev. X 4, 021008 (2014).
Hen, I. et al. Probing for quantum speedup in spin-glass problems with planted solutions. Phys. Rev. A 92, 042325 (2015).
Heim, B., Rønnow, T. F., Isakov, S. V. & Troyer, M. Quantum versus classical annealing of Ising spin glasses. Science 348, 215–217 (2015).
Boixo, S. et al. Computational multiqubit tunnelling in programmable quantum annealers. Nat. Commun. 7, 10327 (2016).
Denchev, V. S. et al. What is the computational value of finite-range tunneling? Phys. Rev. X 6, 031015 (2016).
Albash, T. & Lidar, D. A. Demonstration of a scaling advantage for a quantum annealer over simulated annealing. Phys. Rev. X 8, 031016 (2018).
Mezard M. & Montanari, A. Information, Physics, and Computation (Oxford Univ. Press, 2009).
Stein, D. L. & Newman, C. M. Spin Glasses and Complexity (Princeton Univ. Press, 2013).
Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. Optimization by simulated annealing. Science 220, 671–680 (1983).
Tan, C. M. (ed.) Simulated Annealing (InTech, 2008).
Albash, T. & Lidar, D. A. Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018).
Arnab Das, A. & Chakrabarti, B. (eds) Quantum Annealing and Related Optimization Methods (Springer, 2005).
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).
Johnson, M. W. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011).
Lechner, W., Hauke, P. & Zoller, P. A quantum annealing architecture with all-to-all connectivity from local interactions. Sci. Adv. 1, e15008 (2015).
Weber, S. J. et al. Coherent coupled qubits for quantum annealing. Phys. Rev. Appl. 8, 014004 (2017).
Novikov, S. et al. Exploring more-coherent quantum annealing. In 2018 IEEE International Conference on Rebooting Computing (ICRC) 1–7 (IEEE, 2018).
Hauke, P., Katzgraber, H. G., Lechner, W., Nishimori, H. & Oliver, W. D. Perspectives of quantum annealing: methods and implementations. Rep. Prog. Phys. 83, 054401 (2020).
Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).
Monroe, C. et al. Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys. 93, 025001 (2021).
Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).
Scholl, P. et al. Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms. Nature 595, 233–238 (2020).
Ebadi, S. et al. Quantum optimization of maximum independent set using Rydberg atom arrays. Science 376, 1209–1215 (2022).
Harris, R. et al. Phase transitions in a programmable quantum spin glass simulator. Science 361, 162–165 (2018).
King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nat. Phys. 18, 1324–1328 (2022).
Suzuki, M. Relationship between d-dimensional quantal spin systems and (d + 1)-dimensional Ising systems: equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56, 1454–1469 (1976).
Isakov, S. V. et al. Understanding quantum tunneling through quantum Monte Carlo simulations. Phys. Rev. Lett. 117, 180402 (2016).
King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018).
Nishimura, K., Nishimori, H. & Katzgraber, H. G. Griffiths–McCoy singularity on the diluted chimera graph: Monte Carlo simulations and experiments on quantum hardware. Phys. Rev. A 102, 042403 (2020).
Weinberg, P. et al. Scaling and diabatic effects in quantum annealing with a D-Wave device. Phys. Rev. Lett. 124, 090502 (2020).
Zhou, S., Green, D., Dahl, E. D. & Chamon, C. Experimental realization of classical ({rho }_{E}^{{rm{f}}}) spin liquids in a programmable quantum device. Phys. Rev. B 104, L081107 (2021).
Farhi, E. et al. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–475 (2001).
Kibble, T. W. B. Topology of cosmic domains and strings. J. Phys. A Math. Gen. 9, 1387–1398 (1976).
Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985).
Polkovnikov, A. Universal adiabatic dynamics in the vicinity of a quantum critical point. Phys. Rev. B 72, 161201 (2005).
Dziarmaga, J. Dynamics of a quantum phase transition: exact solution of the quantum Ising model. Phys. Rev. Lett. 95, 245701 (2005).
Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005).
Deng, S., Ortiz, G. & Viola, L. Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions. Europhys. Lett. 84, 67008 (2008).
De Grandi, C., Polkovnikov, A. & Sandvik, A. W. Universal nonequilibrium quantum dynamics in imaginary time. Phys. Rev. B 84, 224303 (2011).
Chandran, A., Erez, A., Gubser, S. S. & Sondhi, S. L. Kibble–Zurek problem: universality and the scaling limit. Phys. Rev. B 86, 064304 (2012).
Liu, C.-W., Polkovnikov, A., Sandvik, A. W. & Young, A. P. Universal dynamic scaling in three-dimensional Ising spin glasses. Phys. Rev. E 92, 022128 (2015).
Miyazaki, R. & Nishimori, H. Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions. Phys. Rev. E 87, 032154(2013).
Matoz-Fernandez, D. A. & Romá, F. Unconventional critical activated scaling of two-dimensional quantum spin glasses. Phys. Rev. B 94, 024201 (2016).
Guo, M., Bhatt, R. N. & Huse, D. A. Quantum critical behavior of a three-dimensional Ising spin glass in a transverse magnetic field. Phys. Rev. Lett. 72, 4137–4140 (1994).
Hartmann, A. K. Ground-state behavior of the three -dimensional ±J random-bond Ising model. Phys. Rev. B 59, 3617–3623 (1999).
Hasenbusch, M., Toldin, F. P., Pelissetto, A. & Vicari, E. Critical behavior of the three-dimensional ±J Ising model at the paramagnetic-ferromagnetic transition line. Phys. Rev. B 76, 094402 (2007).
Hasenbusch, M., Toldin, F. P., Pelissetto, A. & Vicari, E. Magnetic-glassy multicritical behavior of the three-dimensional ±J Ising model. Phys. Rev. B 76, 184202 (2007).
Nishimori, H. Boundary between the ferromagnetic and spin glass phases. J. Phys. Soc. Jpn 61, 1011–1012 (1992).
Schmitt, M., Rams, M. M., Dziarmaga, J., Heyl, M. & Zurek, W. H. Quantum phase transition dynamics in the two-dimensional transverse-field Ising model. Sci. Adv. 8, eabl6850 (2022).
Harris, R. et al. Experimental demonstration of a robust and scalable flux qubit. Phys. Rev. B 81, 134510 (2010).
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