arXiv 2406.031472024-06-11hep-thnucl-thquant-ph

量子计算机上正则二次量子化的动力学实现

A dynamical implementation of canonical second quantization on a quantum computer

Juan José Gálvez-Viruet, Felipe J. Llanes-Estrada

备注：: 35 pages, 7 figures

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AI总结：

针对粒子数可变的二次量子化问题，提出在独立寄存器中动力学实现产生与湮灭算符的理论框架，并给出对易关系、对称化算符及多体 Hamiltonian 幺正演化公式。

摘要：

我们发展了在量子计算机的独立寄存器中实现产生与湮灭算符的理论方法，从而能够在粒子数可变问题中，以透明且动力学的方式二次量子化地产生和湮灭粒子模式。我们建立了有限存储库上对易（反对易）关系的定理，并给出所需的对称化与反对称化算符。最后，我们利用这些算符给出了常规两体和四体 Hamiltonian 项以及改变粒子数的项之下幺正演化的公式。在此形式体系中，编码每个粒子具有 N_p 个模式的 n 个粒子所需的量子比特数为 n log_2 N_p 量级。当粒子数量适中而每个粒子可用状态数很大时，这种标度比需要 O(N_p) 个量子比特的 Jordan-Wigner 变换更高效（而在粒子数量很大、每个粒子可用状态很少时则不占优势）。尽管其效率较低，但它也比紧致编码更简便。

英文摘要：

We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second quantization in problems with variable particle number. We establish theorems for the commutation (anticommutation) relations on a finite memory bank and provide the needed symmetrizing and antisymmetrizing operators. Finally, we provide formulae in terms of these operators for unitary evolution under conventional two- and four-body Hamiltonian terms, as well as terms varying the particle number. In this formalism, the number of qubits needed to codify $n$ particles with $N_p$ modes each is of order $n\log_2 N_p$. Such scaling is more efficient than the Jordan-Wigner transformation which requires $O(N_p)$ qubits, whenever there are a modest number of particles with a large number of states available to each (and less advantageous for a large number of particles with few states available to each). And although less efficient, it is also less cumbersome than compact encoding.

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