We present an efficient quantum circuit for block encoding pairing Hamiltonians studied in nuclear physics. The new block encoding scheme does not require mapping the creation and annihilation operators to Pauli operators and representing the Hamiltonian as a linear combination of unitaries. Instead, we show how to encode these operators directly using controlled swaps. We analyze the gate complexity of the block encoding circuit and show that it scales polynomially with respect to the number of qubits required to represent a quantum state associated with the pairing Hamiltonian. We also show how the block encoding circuit can be combined with quantum singular value transformation to construct an efficient quantum circuit for approximating the density of state of a pairing Hamiltonian. Athough we focus on block encoding circuit for pair Hamiltonians in this paper, the techniques presented here can be extended to encode more general second quantized Hamiltonians.

翻译：我们提出了一种用于核物理中配对哈密顿量块编码的高效量子电路。这种新的块编码方案无需将产生湮灭算符映射为泡利算符，也无需将哈密顿量表示为酉算符的线性组合。取而代之，我们展示了如何利用受控交换门直接编码这些算符。我们分析了该块编码电路的量子门复杂度，证明其复杂度关于表示配对哈密顿量量子态所需的量子比特数呈多项式增长。我们还展示了如何将该块编码电路与量子奇异值变换结合，构建用于近似配对哈密顿量态密度的高效量子电路。尽管本文聚焦于配对哈密顿量的块编码电路，但所述技术可扩展应用于更一般的二次量子化哈密顿量的编码。