论文标题
QAOA的多项式缩放，用于完全连接的P-Spin Ferromagnet的地面制备
Polynomial scaling of QAOA for ground-state preparation of the fully-connected p-spin ferromagnet
论文作者
论文摘要
我们表明，量子近似优化算法（QAOA）可以用多条件缩放资源构建完全连接的p旋转p-spin ising iSing ferromagnet的基础状态，这一问题由于$ $ c的第一个小小的转移而闻名，臭名昭著地构成了量子退火（QA）的严重困难（QA）。对于任意横向场处的目标基态，我们发现，当变量参数的数量$ 2 {\ rm p} $时，需要适当的QAOA参数初始化才能实现算法的良好性能，这比系统大小$ {\ rm n} $小得多，因为大量的亚ip-optimaptimaptimal local Minima。相反，当$ {\ rm p} $超过临界值$ {\ rm p}^*_ {\ rm n} \ propto {\ rm n} $，参数空间的结构就会简化，因为所有minima都变得变性。这允许以$ {\ rm n} $的多个参数进行大量扩展，并以$ {\ rm n} $多数缩放的方式来实现基础状态。
We show that the quantum approximate optimization algorithm (QAOA) can construct with polynomially scaling resources the ground state of the fully-connected p-spin Ising ferromagnet, a problem that notoriously poses severe difficulties to a Quantum Annealing (QA) approach, due to the exponentially small gaps encountered at first-order phase transition for ${\rm p} \ge 3$. For a target ground state at arbitrary transverse field, we find that an appropriate QAOA parameter initialization is necessary to achieve a good performance of the algorithm when the number of variational parameters $2{\rm P}$ is much smaller than the system size ${\rm N}$, because of the large number of sub-optimal local minima. Instead, when ${\rm P}$ exceeds a critical value ${\rm P}^*_{\rm N} \propto {\rm N}$, the structure of the parameter space simplifies, as all minima become degenerate. This allows to achieve the ground state with perfect fidelity with a number of parameters scaling extensively with ${\rm N}$, and with resources scaling polynomially with ${\rm N}$.
