论文标题
量子绝热优化中的对角线催化剂
Diagonal Catalysts in Quantum Adiabatic Optimization
论文作者
论文摘要
我们提出了一种量子绝热优化的方案，在插值过程中，在计算基础上是对角的中介哈密顿量。这种“对角线催化剂”有助于偏向给定的旋转构型，我们展示了如何删除铁磁$ p $ -spin和弱的群集群问题的标准方案中存在的一阶相变。协议的成功还清楚了它如何失败：将能源格局偏向一个状态，只有与基态的锤距离距离距离距离距离距离距离和偏见状态的能量是否相关，才有助于找到基态。我们列举了示例，尽管与标准协议相比，与基态距离距离距离很远的低能状态的偏见可能会严重恶化该算法的效率。我们针对对角线催化剂方案的结果类似于绝热反向退火的结果，因此我们的结论也应适用于该方案。
We propose a protocol for quantum adiabatic optimization, whereby an intermediary Hamiltonian that is diagonal in the computational basis is turned on and off during the interpolation. This `diagonal catalyst' serves to bias the energy landscape towards a given spin configuration, and we show how this can remove the first-order phase transition present in the standard protocol for the ferromagnetic $p$-spin and the Weak-Strong Cluster problems. The success of the protocol also makes clear how it can fail: biasing the energy landscape towards a state only helps in finding the ground state if the Hamming distance from the ground state and the energy of the biased state are correlated. We present examples where biasing towards low energy states that are nonetheless very far in Hamming distance from the ground state can severely worsen the efficiency of the algorithm compared to the standard protocol. Our results for the diagonal catalyst protocol are analogous to results exhibited by adiabatic reverse annealing, so our conclusions should apply to that protocol as well.
