有界宽度的量子和随机分支程序
Quantum and Stochastic Branching Programs of Bounded Width
摘要：
在本文中，我们表明，一个量子位的多项式时间计算至少是强大的$\NC^1$电路。更确切地说，我们定义的句法模型的量子和随机分支程序的有界宽度和证明其权力的上界和下界。我们表明任何$\NC^1$语言可以接受的宽度为2的量子分支程序的多项式长度，在经典的情况下，宽度5是必要的，除非$\NC^1=\ACC$。这将宽度-2量子程序与宽度-2双随机程序区分开来，因为我们证明了后者不能计算乘法的中间位。最后，我们表明，有界宽度的量子和随机程序可以模拟的经典程序较大，但有界宽度，因此在$\NC^1$。修订本的变化是增加了句法条件。
英文摘要：
In this paper we show that one qubit polynomial time computations are at least as powerful as $\NC^1$ circuits. More precisely, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show any $\NC^1$ language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless $\NC^1=\ACC$. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in $\NC^1$. The change in the revised version is the addition of the syntactic condition.
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