作者：Simon C. Marshall Jordi Tura Vedran Dunjko
少量量子位是有利量子计算近期部署的主要制约因素之一。为了缓解这种限制，已经开发了将大型量子计算分解为小型计算的技术。虽然这项工作有时被称为电路编织或量子，但我们通常将其称为电路切割（CC）。现有的许多工作都集中在开发更有效的电路切割方案上，留下了理论上最优方案所能达到的极限的悬而未决的问题。我们通过将可能的方法分解为两种不同的模式来开发边界：第一种模式，输入状态和测量是固定的和已知的，第二种模式，需要给定的切割工作来获得输入状态和度量的完整基础。对于第一种情况，很容易看出，解决任何电路切割方法效率的界限相当于解决BPP$\stackrel｛？｝｛＝｝$BQP。我们因此限制了自己
Small numbers of qubits are one of the primary constraints on the near-termdeployment of advantageous quantum computing. To mitigate this constraint,techniques have been developed to break up a large quantum computation intosmaller computations. While this work is sometimes called circuit knitting ordivide and quantum we generically refer to it as circuit cutting (CC). Much ofthe existing work has focused on the development of more efficient circuitcutting schemes, leaving open questions on the limits of what theoreticallyoptimal schemes can achieve. We develop bounds by breaking up possibleapproaches into two distinct regimes: the first, where the input state andmeasurement are fixed and known, and the second, which requires a given cuttingto work for a complete basis of input states and measurements. For the firstcase, it is easy to see that bounds addressing the efficiency of any approachesto circuit cutting amount to resolving BPP$\stackrel{?}{=}$BQP. We thereforerestrict ourselves to a simpler question, asking what \textit{locally-acting}circuit cutting schemes can achieve, a technical restriction which stillincludes all existing circuit cutting schemes. In our first case we show thatthe existence of a locally-acting circuit cutting scheme which couldefficiently partition even a single qubit from the rest of a circuit wouldimply BPP$=$BQP. In our second case, we obtain more general results, showinginefficiency unconditionally. We also show that any (local or otherwise)circuit cutting scheme cannot function by only applying unital channels.
论文链接：http://arxiv.org/pdf/2303.13422v1
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