并行量子计算与量子码
Parallel Quantum Computation and Quantum Codes
摘要：
我们提出了QNC的定义，有效的并行类NC的量子模拟。我们展示了几个有用的小工具，并证明了各种类型的电路可以并行化到对数深度，包括编码和解码标准量子纠错码的电路，或更一般的任何电路组成的受控非门，受控π移位，和阿达玛门。最后，虽然我们注意到量子傅立叶变换可以并行化到线性深度，但我们推测，一个更简单的“阶梯”电路不能并行化到小于线性深度，并且可能用于证明QNC < QP。
英文摘要：
We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or more generally any circuit consisting of controlled-not gates, controlled pi-shifts, and Hadamard gates. Finally, while we note the Quantum Fourier Transform can be parallelized to linear depth, we conjecture that an even simpler `staircase' circuit cannot be parallelized to less than linear depth, and might be used to prove that QNC < QP.
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