We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-$1/2 XXZ$ quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an $L$-qubit state with $M$ down-spins using $\binom{L}{M}-1$ multi-controlled rotation gates and $2M(L-M)$ CNOT-gates.

中文翻译：

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确定性 Bethe 状态准备


我们提出了一个显式量子电路，它在量子计算机上准备任意 $U（1）$-特征态，包括具有开放或封闭边界条件的自旋 $1/2 XXZ$ 量子自旋链的确切特征态。该算法是确定性的，不需要辅助量子比特，也不需要 QR 分解。该电路使用 $\binom{L}{M}-1$ 多控制旋转门和 $2M（L-M）$ CNOT 门准备这样一个 $L$ 量子比特状态，其中包含 $M$ 次下旋。