多体和电子结构问题的量子近似算法
Quantum approximation algorithms for many-body and electronic structure problems
摘要：
计算多体基态能量和解决电子结构计算是量子化学或凝聚态等领域的基本问题。存在解决这些问题的几种量子计算算法，尽管在它们的性能上建立严格的界限通常是具有挑战性的。在这里，我们详细介绍了三种算法，产生近似基态的多体和电子结构的问题，概括了一些以前已知的结果2-本地哈密顿。每种方法都有其产生的能量的渐近界。第一个产生一个可分离的状态，这改善了随机产品状态。我们在无自旋哈伯德模型上进行了测试，数值验证了理论结果。另外两种算法通过浅回路或深回路产生纠缠态，提高了给定初始态的能量。我们证明了他们的性能，通过数值实验的2维哈伯德模型，从棋盘的产品状态，以及对一些化学哈密顿量，使用Hartree-Fock状态作为参考。在这两种情况下，我们表明，产生的近似能量接近的确切。这些算法提供了一种系统地改善基态能量估计的方法，并且可以单独使用或与现有的基态量子算法结合使用。
英文摘要：
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems exist, although it is often challenging to establish rigorous bounds on their performances. Here we detail three algorithms that produce approximate ground states for many-body and electronic structure problems, generalizing some previously known results for 2-local Hamiltonians. Each method comes with asymptotic bounds on the energies produced. The first one produces a separable state which improves on random product states. We test it on a spinless Hubbard model, validating numerically the theoretical result. The other two algorithms produce entangled states via shallow or deep circuits, improving on the energies of given initial states. We demonstrate their performance via numerical experiments on a 2-dimensional Hubbard model, starting from a checkerboard product state, as well as on some chemistry Hamiltonians, using the Hartree-Fock state as reference. In both cases, we show that the approximate energies produced are close to the exact ones. These algorithms provide a way to systematically improve the estimation of ground state energies and can be used stand-alone or in conjunction with existing quantum algorithms for ground states.
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