近日，意大利罗马大学的Giorgio Parisi及其研究小组与西班牙马德里康普顿斯大学的Isidoro González-Adalid Pemartín等人合作并取得一项新进展。经过不懈努力，他们对二维伊辛自旋玻璃的量子跃迁进行研究。相关研究成果已于2024年7月10日在国际权威学术期刊《自然》上发表。

据悉，量子退火炉是一种商用设备，旨在解决非常困难的计算问题，特别是那些涉及自旋玻璃的问题。就像在冶金退火中，铁质金属被缓慢冷却一样，量子退火通过在尽可能低的温度下缓慢地去除横向磁场来寻求良好的解决方案。移除场会减少量子涨落，但会迫使系统越过将无序相(在大场)与自旋玻璃相(在小场)分开的临界点。对这一相变的充分认识仍然缺乏。一个有争议的关键问题是关于基态和第一激发态之间能隙的闭合。与经典计算机相比，实现指数级加速的所有希望都建立在这样一个假设上，即自旋的数量会以代数方式关闭能隙。然而，重整化群计算预测存在一个无限随机不动点。

该研究团队通过极端尺度的数值模拟来解决这个争论，发现双方都掌握了部分真相。虽然在临界点处能隙的闭合确实是超代数的，但如果限制可能激发的对称性，它仍然是代数的。由于这种对称性限制在实验上是可以实现的(至少在名义上)，量子退火范式仍然有希望。

附：英文原文

Title: The quantum transition of the two-dimensional Ising spin glass

Author: Bernaschi, Massimo, Gonzlez-Adalid Pemartn, Isidoro, Martn-Mayor, Vctor, Parisi, Giorgio

Issue&Volume: 2024-07-10

Abstract: Quantum annealers are commercial devices that aim to solve very hard computational problems, typically those involving spin glasses. Just as in metallurgic annealing, in which a ferrous metal is slowly cooled, 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 spins. However, renormalization group calculations predict instead that there is an infinite-randomness fixed point. 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 paradigm.

DOI: 10.1038/s41586-024-07647-y

Source: https://www.nature.com/articles/s41586-024-07647-y