We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution, using mid-circuit measurements on a single ancilla qubit. Imaginary time evolution (ITE) is widely used for obtaining the ground state (GS) of a system on classical hardware, computing thermal averages, and as a component of quantum algorithms that perform non-unitary evolution. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic ITE (PITE) algorithms, which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator—that is, they rely on successful ancillary measurements to evolve the system non-unitarily. Compared with previous PITE proposals, the suggested block encoding in this paper results in shorter circuits and is simpler to implement, requiring only a slight modification of the Pauli gadget primitive. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the GS of the system.

中文翻译：

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用于虚时间演化的非酉 Trotter 电路


我们提出了一种虚时间等价的用于 Trotter 分解实时演化的完善的泡利小工具原语，使用单个辅助量子位的中电路测量。虚时间演化 (ITE) 广泛用于在经典硬件上获取系统的基态 (GS)、计算热平均值以及作为执行非酉演化的量子算法的组成部分。量子硬件的近期实现依赖于启发式方法，从而损害了其准确性。因此，人们对开发更原生的量子算法越来越感兴趣。由于不可能确定性地实现非酉门，因此我们求助于概率 ITE (PITE) 算法的实现，该算法依赖于酉量子电路来模拟 ITE 算子的块编码，也就是说，它们依赖于成功的辅助测量使系统非统一地演化。与之前的 PITE 提案相比，本文建议的块编码可以缩短电路，并且实现起来更简单，只需要对 Pauli gadget 原语进行轻微修改。该方案在横向伊辛模型和费米子哈伯德模型上进行了测试，并被证明可以收敛到系统的 GS。