We describe a matrix product state (MPS) extension for the Fermionic Quantum Emulator (FQE) software library. We discuss the theory behind symmetry-adapted MPSs for approximating many-body wave functions of spin-1/2 Fermions, and we present an open-source, MPS-enabled implementation of the FQE interface (MPS-FQE). The software uses the open-source pyblock3 and block2 libraries for most elementary tensor operations, and it can largely be used as a drop-in replacement for FQE that allows for more efficient but approximate emulation of larger Fermionic circuits. Finally, we show several applications relevant to both near-term and fault-tolerant quantum algorithms where approximate emulation of larger systems is expected to be useful: characterization of state preparation strategies for quantum phase estimation, the testing of different variational quantum eigensolver ansätze, the numerical evaluation of Trotter errors, and the simulation of general quantum dynamics problems. In all these examples, approximate emulation with MPS-FQE allows us to treat systems that are significantly larger than those accessible with a full statevector emulator.

中文翻译：

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具有矩阵积状态的费米子电路的快速仿真

我们描述了费米子量子仿真器 (FQE) 软件库的矩阵积态 (MPS) 扩展。我们讨论了用于近似自旋 1/2 费米子多体波函数的对称适应 MPS 背后的理论，并提出了一种开源的、支持 MPS 的 FQE 接口实现 (MPS-FQE)。该软件使用开源 pyblock3 和 block2 库来进行大多数基本张量运算，并且它在很大程度上可以用作 FQE 的直接替代品，从而可以更有效地近似模拟更大的费米子电路。最后，我们展示了与近期和容错量子算法相关的几个应用，其中较大系统的近似仿真预计将是有用的：量子相位估计的状态准备策略的表征、不同变分量子本征解算器的测试、 Trotter 误差的数值评估以及一般量子动力学问题的模拟。在所有这些示例中，使用 MPS-FQE 进行近似仿真使我们能够处理比使用完整状态向量仿真器可访问的系统大得多的系统。