Quantum annealing (QA) is a computational optimization technique that has gained significant attention for solving extremely difficult combinatorial optimization problems.

In QA, the optimization problem is encoded into a Hamiltonian and initialized in a superposition of all possible states using a strong transverse field. This field is then adiabatically reduced, guiding the system to its lowest-energy ground state, which corresponds to the optimal solution.

However, in the presence of quantum phase transitions, especially first-order phase transitions, the energy gap becomes exponentially small, causing computation times to grow exponentially. Unfortunately, transverse-field Ising model formulations of most practical combinatorial optimization problems suitable for QA, exhibit first-order phase transitions.

In a recent study, published in the Journal of the Physical Society of Japan, researchers who first introduced QA proposed an innovative solution to this problem. Consequently, this study was honored with The 30^th Outstanding Paper Award of the Physical Society of Japan.

Instead of applying a uniform transverse field, the new method introduces an inhomogeneously driven transverse field, where the field strength is reduced sequentially, one spin at a time.

Specifically, an additional time-dependent parameter  is introduced to the transverse field term of the conventional QA Hamiltonian, causing the transverse field to be turned off one by one as the system evolves. This modification allows the system to avoid quantum phase transitions altogether, ensuring the energy gap remains constant even for large system sizes, which leads to an exponential speedup in QA. The researchers successfully applied this technique to the uniformly interacting p-spin model, as well as the random-field Ising model, demonstrating its effectiveness. The findings of this study has the potential to inspire the next generation of QA devices, making them significantly more powerful for solving real-world optimization problems across various fields.

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