论文标题
定制的量子模拟代码
Custom fermionic codes for quantum simulation
论文作者
论文摘要
在量子计算机上模拟费米子系统需要将反向交易的费米子变量编码到作用于Qubit Hilbert空间的操作员中。其中最熟悉的Jordan-Wigner Transformation将Fermionic操作员编码为非本地Qubbit Operators。由于非本地运算符导致量子模拟较慢，最近的工作提出了在本地编码费米子系统的方法。在这项工作中，我们表明，实际上可能对条件过于严格，并且可以通过以下地编码系统准分子来减小操作员的大小。我们提供了与与量子重力相关的冷凝物和系统晶格模型（例如SYK模型）相关的示例。此外，我们为设计代码提供了一般构造，以适合当前的问题和资源，并展示如何将一类准本地编码视为由于截断了本地编码的状态准备电路而引起的。我们以对设备连接约束存在的设计代码进行设计结尾。
Simulating a fermionic system on a quantum computer requires encoding the anti-commuting fermionic variables into the operators acting on the qubit Hilbert space. The most familiar of which, the Jordan-Wigner transformation, encodes fermionic operators into non-local qubit operators. As non-local operators lead to a slower quantum simulation, recent works have proposed ways of encoding fermionic systems locally. In this work, we show that locality may in fact be too strict of a condition and the size of operators can be reduced by encoding the system quasi-locally. We give examples relevant to lattice models of condensed matter and systems relevant to quantum gravity such as SYK models. Further, we provide a general construction for designing codes to suit the problem and resources at hand and show how one particular class of quasi-local encodings can be thought of as arising from truncating the state preparation circuit of a local encoding. We end with a discussion of designing codes in the presence of device connectivity constraints.
