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arXiv 2408.04007quant-ph
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减少基于Pauli的计算中的深度和测量权重

Reducing depth and measurement weights in Pauli-based computation

International Iberian Nanotechnology Laboratory (INL)(伊比利亚纳米技术实验室);Quantum Thermodynamics and Computation Group, Electromagnetism and Matter Physics Department, University of Granada(格拉纳达大学电磁与物质物理系量子热力学与计算组);Instituto de Fı́sica, Universidade Federal Fluminense(弗鲁米嫩塞联邦大学物理研究所)

Filipa C. R. Peres, Ernesto F. Galvão

AI总结:

本文提出了一种减少基于Pauli计算中Pauli测量权重和计算深度的方法,通过预编译步骤和启发式算法,显著降低了CNOT计数,尤其在Clifford主导的随机量子电路中表现优异。

摘要:

基于Pauli的计算(PBC)是一种通用性的测量基量子计算模型,其通过在可分离的魔法态量子比特上进行适应性序列的独立且兼容的Pauli测量来引导。本文提出了几种新的技术,用于减少Pauli测量的权重及其相关CNOT复杂度;我们还展示了如何降低该模型的计算深度。我们首先通过预编译步骤证明了新的上界,这些上界限定了所需的权重和计算深度。我们还提出了一种启发式算法,当模拟和编译以Clifford主导的随机量子电路,最多包含22个T门和超过20%的T门数量时,该算法可以为Pauli测量的平均权重(以及相关的CNOT计数)带来超过30%的减少。这种PBC编译方案,借助启发式算法,优于当前最先进的编译器,对于前类电路,将CNOT计数减少了18%至96%,相较于其他技术所达到的数值。相比之下,对于后者具有更大T门数量的电路,它导致的CNOT数量大约大30%。最后,受已知的状态转移方法启发,我们引入了incPBC,一种通用的量子计算模型,需要更多的(现在不兼容的)Pauli测量,其权重最多为2。

英文摘要:

Pauli-based computation (PBC) is a universal measurement-based quantum computation model steered by an adaptive sequence of independent and compatible Pauli measurements on separable magic-state qubits. Here, we propose several new techniques for reducing the weight of the Pauli measurements and their associated \textsc{cnot} complexity; we also demonstrate how to decrease this model's computational depth. We start by proving new upper bounds on the required weights and computational depth, obtained via a pre-compilation step. We also propose a heuristic algorithm that can contribute reductions of over 30\% to the average weight of Pauli measurements (and associated \textsc{cnot} count) when simulating and compiling Clifford-dominated random quantum circuits with up to 22 $T$ gates and over 20\% for instances with larger $T$ counts. This PBC-compilation scheme, boosted by the heuristic algorithm, outperforms state-of-the-art compilers for the former circuits, reducing the \textsc{cnot} count by 18\% to 96\% compared with the values achieved by other techniques. In contrast, for the latter circuits with larger $T$ counts, it leads to a number of \textsc{cnot}s roughly 30\% larger. Finally, inspired by known state-transfer methods, we introduce incPBC, a universal model for quantum computation requiring a larger number of (now incompatible) Pauli measurements of weight at most 2.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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