通过稠密编码再次将QROM成本减半
Halving the cost of QROM again via dense encoding
- Xanadu
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出QROM的稠密编码构造，利用Z和X基在脏量子比特中存储两位信息，结合顺序比特包，将领先Toffoli计数降至$\tfrac12(1+1/b)N/\lambda$，较SelectSwap实现约4倍改进。
AI中文摘要：
量子只读存储器（QROM）是容错量子算法中非克利福德成本的重要来源。借用脏量子比特可以降低这一成本，前提是其未知的初始状态得到恢复。我们考虑实际相关的量子比特受限场景，其中有限的工作空间限制了表块大小，且表加载主导成本。对于$N$个$b$比特的条目和大约$b\lambda$个脏量子比特，SelectSwap的领先Toffoli计数为$2N/\lambda$。最近使用顺序比特包的工作将其减少到$(1+1/b)N/\lambda$。在本工作中，我们引入了一种QROM的稠密编码构造，通过利用$Z$和$X$基，在每个脏量子比特中存储两位经典信息，而非一位。单独来看，稠密编码通过将领先Toffoli计数减少到$N/\lambda$，提供了相对于SelectSwap的$2\times$改进。将其与顺序比特包结合，得到$\tfrac12(1+1/b)N/\lambda$，进一步将顺序构造的领先成本减半，并在大$N$极限下，对于实际的$b$值，相对于SelectSwap实现了约$4\times$的改进。
英文摘要：
Quantum read only memory (QROM) is a substantial source of non-Clifford cost in fault-tolerant quantum algorithms. Borrowing dirty qubits can reduce this cost, provided their unknown initial states are restored. We consider the practically relevant qubit-constrained regime, where limited workspace restricts the table-block size and table loading dominates the cost. For $N$ entries of $b$ bits and approximately $bλ$ dirty qubits, SelectSwap has leading Toffoli count $2N/λ$. Recent work using sequential bit packets reduces this to $(1+1/b)N/λ$. In this work we introduce a dense encoding construction of QROM, where two bits of classical information are stored in each dirty qubit instead of one by utilizing both the $Z$ and $X$ bases. On its own, dense encoding provides a $2\times$ improvement over SelectSwap by reducing the leading Toffoli count to $N/λ$. Combining it with sequential bit packets gives $\tfrac12(1+1/b)N/λ$, a further halving of the sequential construction's leading cost, and an approximately $4\times$ improvement over SelectSwap in the large-$N$ limit for practical values of $b$.
