The quantum transition of the two-dimensional Ising spin glass

Massimo Bernaschi, Isidoro González-Adalid Pemartín (), Víctor Martín-Mayor and Giorgio Parisi
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Massimo Bernaschi: CNR
Isidoro González-Adalid Pemartín: Universidad Complutense de Madrid
Víctor Martín-Mayor: Universidad Complutense de Madrid
Giorgio Parisi: Sapienza Università di Roma

Nature, 2024, vol. 631, issue 8022, 749-754

Abstract: Abstract Quantum annealers are commercial devices that aim to solve very hard computational problems1, typically those involving spin glasses2,3. Just as in metallurgic annealing, in which a ferrous metal is slowly cooled4, quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. Removing the field diminishes the quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, compared to classical computers, rest on the assumption that the gap will close algebraically with the number of spins5–9. However, renormalization group calculations predict instead that there is an infinite-randomness fixed point10. Here we solve this debate through extreme-scale numerical simulations, finding that both parties have grasped parts of the truth. Although the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. As this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the quantum annealing paradigm11–13.

Date: 2024
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DOI: 10.1038/s41586-024-07647-y

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