面向分子波函数的克利福德高效稀疏态制备
Clifford-efficient sparse state preparation for molecular wavefunctions
AI总结：
该研究提出一种面向分子波函数的稀疏量子态制备方法，利用GF(2)上仿射关系减少非克利福德门与辅助量子比特，在分子基准测试中辅助量子比特用量最少且非克利福德门数量相当。
AI中文摘要：
稀疏量子态制备涉及n量子比特目标态，该态仅为d远小于2ⁿ个计算基态的叠加。现有方法通过将这d个基态及其振幅压缩到一个称为稠密寄存器的更小量子比特集上，再将制备的态扩展到全寄存器，以此利用这种稀疏性。与先前工作中采用的基于置换的压缩不同，我们利用有限域GF(2)上二元构型之间的仿射关系，减少非克利福德门数量和辅助量子比特数量。GF(2)上的可逆仿射变换（包括高斯消元法和全1行移除）仅使用克利福德门且无需辅助量子比特，即可将稠密寄存器从n缩减至秩r。可选的二元编码阶段则以增加额外Toffoli门和辅助量子比特为代价，进一步压缩至表示d个不同构型所需的最小⌈log₂d⌉个稠密量子比特。对于与化学相关的波函数（如通过选定组态相互作用计算得到的波函数），共享电子激发模式会产生许多此类仿射关系，从而在二元编码前实现仅用克利福德门的大幅压缩。在分子基准测试中，我们的方法在被评估的稀疏态制备方法中需要最少的辅助量子比特，且在使用二元编码时保持了相当的非克利福德门数量。
英文摘要：
Sparse quantum state preparation concerns an $n$-qubit target state that is a superposition of only $d \ll 2^n$ computational basis states. Existing approaches exploit this sparsity by compressing these $d$ basis states and their amplitudes onto a smaller set of qubits, called the dense register, before expanding the prepared state to the full register. Rather than relying on the permutation-based compression used in prior work, we exploit affine relationships among the binary configurations over the finite field $\operatorname{GF}(2)$ to reduce both the non-Clifford gate count and the ancillary qubit count. Invertible affine transformations over $\operatorname{GF}(2)$, comprising Gaussian elimination and all-ones-row removal, first reduce the dense register from $n$ to the rank $r$ using only Clifford gates and no ancillary qubits. An optional binary encoding stage then trades additional Toffoli gates and ancillary qubits for further compression to the minimum $\lceil\log_2 d\rceil$ dense qubits needed to represent $d$ distinct configurations. For chemically relevant wavefunctions, such as those obtained from selected configuration interaction calculations, shared electronic excitation patterns produce many of these affine relationships, enabling substantial Clifford-only compression before binary encoding. Across the molecular benchmarks, our method requires the fewest ancillary qubits among the evaluated sparse state preparation methods while maintaining comparable non-Clifford gate counts when using binary encoding.
