干扰的定量测量
A Quantitative Measure of Interference
摘要：
我们引入了一个干扰措施，它允许量化的干扰量存在于任何物理过程中，映射到一个最终的密度矩阵的初始密度矩阵。特别是，干涉测量使人们能够监测量子算法的每个步骤中产生的干扰量。我们证明了作用于单个量子比特的Hadamard门是干扰生成的基本构建块，并实现了一个比特的干扰，即“i比特”。我们使用的干扰措施量化干扰的各种例子，包括Grover的搜索算法和Shor的分解算法。我们区分“潜在可用”和“实际使用”的干扰，并表明，对于这两种算法的潜在可用的干扰是指数大。然而，Grover算法中实际使用的干扰量仅约为3个i比特，并且与量子比特的数量无关，而Shor算法确实使用了指数干扰量。
英文摘要：
We introduce an interference measure which allows to quantify the amount of interference present in any physical process that maps an initial density matrix to a final density matrix. In particular, the interference measure enables one to monitor the amount of interference generated in each step of a quantum algorithm. We show that a Hadamard gate acting on a single qubit is a basic building block for interference generation and realizes one bit of interference, an ``i-bit''. We use the interference measure to quantify interference for various examples, including Grover's search algorithm and Shor's factorization algorithm. We distinguish between ``potentially available'' and ``actually used'' interference, and show that for both algorithms the potentially available interference is exponentially large. However, the amount of interference actually used in Grover's algorithm is only about 3 i-bits and asymptotically independent of the number of qubits, while Shor's algorithm indeed uses an exponential amount of interference.
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