论文标题
优化哈密顿和硬件的费米子编码
Optimizing fermionic encodings for both Hamiltonian and hardware
论文作者
论文摘要
在这项工作中，我们提出了一种生成针对一组目标费米子操作员和目标硬件连接性的费米子编码的方法。我们的方法使用蛮力搜索，在所有编码的空间上，这些编码从Majoraana Moinemials映射到Pauli操作员，以找到优化目标成本函数的编码。与朝着这个方向的早期作品相反，我们的方法搜索了非常广泛的编码类，这些编码涵盖了构成代数同态的所有已知第二个量化编码。为了搜索此类，我们清楚地说明了它的精确表征，以及如何将此特征转化为建设性搜索标准。搜索此类的一个好处是，我们的方法能够在解决方案上提供相当一般的最佳保证。第二个好处是，在主要的方法中，当正在考虑的费米子操作员以较小的代数忠实地表示时，我们的方法能够找到更有效的费米子系统表示。鉴于执行搜索的算法成本很高，我们会适应我们的方法处理翻译不变的系统，该系统可以由成本较低的小型单元细胞描述。我们在各种目标费米子运算符和硬件连接性配对上演示了我们的方法。我们还展示了如何扩展我们的方法以查找此类中的费米子编码的错误。
In this work we present a method for generating a fermionic encoding tailored to a set of target fermionic operators and to a target hardware connectivity. Our method uses brute force search, over the space of all encodings which map from Majorana monomials to Pauli operators, to find an encoding which optimizes a target cost function. In contrast to earlier works in this direction, our method searches over an extremely broad class of encodings which subsumes all known second quantized encodings that constitute algebra homomorphisms. In order to search over this class, we give a clear mathematical explanation of how precisely it is characterized, and how to translate this characterization into constructive search criteria. A benefit of searching over this class is that our method is able to supply fairly general optimality guarantees on solutions. A second benefit is that our method is, in principal, capable of finding more efficient representations of fermionic systems when the set of fermionic operators under consideration are faithfully represented by a smaller quotient algebra. Given the high algorithmic cost of performing the search, we adapt our method to handle translationally invariant systems that can be described by a small unit cell that is less costly. We demonstrate our method on various pairings of target fermionic operators and hardware connectivities. We additionally show how our method can be extended to find error detecting fermionic encodings in this class.
