模拟特殊但自然的量子电路
Simulating Special but Natural Quantum Circuits
摘要：
我们确定了一个子类的BQP，捕捉到许多量子算法，包括肖尔的算法之间的某些结构共性。这个类不包含所有的BQP（例如Grover算法不属于这个类）。我们的主要结果是，在这一类的任何算法，措施在最多O（log n）量子位可以模拟经典的随机多项式时间算法。这并不意味着Shor的算法（因为后者测量n个量子位），但我们的工作也突出了一个新的加密应用程序的潜在硬函数。我们的主要技术贡献是（据我们所知）一个新的确切表征某些款项的傅立叶型系数（指数许多被加数）。
英文摘要：
We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our main result is that any algorithm in this class that measures at most O(log n) qubits can be simulated by classical randomized polynomial time algorithms. This does not dequantize Shor's algorithm (as the latter measures n qubits) but our work also highlights a new potentially hard function for cryptographic applications. Our main technical contribution is (to the best of our knowledge) a new exact characterization of certain sums of Fourier-type coefficients (with exponentially many summands).
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