Observation of topological phenomena in a programmable lattice of 1,800 qubits

Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems having a continous symmetry group II: quantum systems. Sov. Phys. JETP 34, 610–616 (1972).

Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181–1203 (1973).

Moessner, R., Sondhi, S. L. & Chandra, P. Two-dimensional periodic frustrated Ising models in a transverse field. Phys. Rev. Lett. 84, 4457–4460 (2000).

Moessner, R. & Sondhi, S. L. Ising models of quantum frustration. Phys. Rev. B 63, 224401 (2001).

Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Phys. Rev. B 68, 104409 (2003).

Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).

Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).

Paraoanu, G. S. Recent progress in quantum simulation using superconducting circuits. J. Low Temp. Phys. 175, 633–654 (2014).

Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006).

Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).

Hensgens, T. et al. Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array. Nature 548, 70–73 (2017).

Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

Mohseni, M. et al. Commercialize quantum technologies in five years. Nature 543, 171–175 (2017).

Preskill, J. Quantum Computing in the NISQ era and beyond. Preprint at https://arxiv.org/abs/1801.00862 (2018).

Johnson, M. W. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011).

Harris, R. et al. Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor. Phys. Rev. B 82, 024511 (2010).

Bunyk, P. I. et al. Architectural considerations in the design of a superconducting quantum annealing processor. IEEE Trans. Appl. Supercond. 24, 1–10 (2014).

Mott, A., Job, J., Vlimant, J.-r., Lidar, D. & Spiropulu, M. Solving a Higgs optimization problem with quantum annealing for machine learning. Nature 550, 375–379 (2017).

Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B. & Melko, R. Quantum Boltzmann machine. Phys. Rev. X 8, 021050 (2018). 

Moessner, R. & Ramirez, A. P. Geometrical frustration. Phys. Today 59, 24–29 (2006).

Kosterlitz, J. M. & Thouless, D. J. Early work on defect driven phase transitions. Int. J. Mod. Phys. B 30, 1630018 (2016).

Han, Z. et al. Collapse of superconductivity in a hybrid tin-graphene Josephson junction array. Nat. Phys. 10, 380–386 (2014).

Jiang, Y. & Emig, T. Ordering of geometrically frustrated classical and quantum triangular Ising magnets. Phys. Rev. B 73, 104452 (2006).

Wang, Y.-C., Qi, Y., Chen, S. & Meng, Z. Y. Caution on emergent continuous symmetry: a Monte Carlo investigation of the transverse-field frustrated Ising model on the triangular and honeycomb lattices. Phys. Rev. B 96, 115160 (2017).

Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Phys. Rev. B 29, 5250–5252 (1984).

José, J. V., Kadanoff, L. P., Kirkpatrick, S. & Nelson, D. R. Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model. Phys. Rev. B 16, 1217–1241 (1977).

Lanting, T., King, A. D., Evert, B. & Hoskinson, E. Experimental demonstration of perturbative anticrossing mitigation using nonuniform driver Hamiltonians. Phys. Rev. A 96, 042322 (2017).

Herbut, I. A Modern Approach to Critical Phenomena (Cambridge Univ. Press, Cambridge, 2007).

Chancellor, N. Modernizing quantum annealing using local searches. New J. Phys. 19, 023024 (2017).

Babbush, R., Love, P. J. & Aspuru-Guzik, A. Adiabatic quantum simulation of quantum chemistry. Sci. Rep. 4, 6603 (2014).

Nishimori, H. & Takada, K. Exponential enhancement of the efficiency of quantum annealing by non-stochastic Hamiltonians. Front. ICT 4, 1–11 (2017).

Korshunov, S. E. Finite-temperature phase transitions in the quantum fully frustrated transverse-field Ising models. Phys. Rev. B 86, 014429 (2012).

Rieger, H. & Kawashima, N. Application of a continuous time cluster algorithm to the two-dimensional random quantum Ising ferromagnet. Eur. Phys. J. B 9, 233–236 (1999).

Swendsen, R. H. & Wang, J.-S. Replica Monte Carlo simulation of spin-glasses. Phys. Rev. Lett. 57, 2607–2609 (1986).

Andriyash, E. & Amin, M. H. Can quantum Monte Carlo simulate quantum annealing? Preprint at https://arxiv.org/abs/1703.09277 (2017).

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).