We prove several new lower bounds for constant depth quantum circuits. The main result is that parity (and hence fanout) requires log depth circuits, when the circuits are composed of single qubit and arbitrary size Toffoli gates, and when they use only constantly many ancillæ. Under this constraint, this bound is close to optimal. In the case of a non-constant number $a$ of ancillae, we give a tradeoff between $a$ and the required depth, that results in a non-trivial lower bound for fanout when $a = n^{1-o(1)}$.
Quantum Fanout Gates in Constant Depth via Resonance Engineering
ETH Zürich（苏黎世联邦理工学院）；Institute for Quantum Electronics, ETH Zürich（苏黎世联邦理工学院量子电子学研究所）；Fraunhofer Institute for Applied Solid State Physics IAF（弗劳恩霍夫应用固态物理研究所）
The quantum query complexity of read-many formulas
The quantum query complexity of evaluating any read-once formula with n black-box input bits is Theta(sqrt(n)). However, the corresponding problem for read-many formulas (i.e., formulas in which the inputs have fanout) is not well understood. Although the optimal read-once formula evaluation algorithm can be applied to any formula, it can be suboptimal if the inputs have large fanout. We give an algorithm for evaluating any formula with n inputs, size S, and G gates using O(min{n, sqrt{S}, n^{1/2} G^{1/4}}) quantum queries. Furthermore, we show that this algorithm is optimal, since for any n,S…
Lower bounds on non-local computation from controllable correlation
Institute for Quantum Computing and School of Computer Science, University of Waterloo（量子计算研究所与滑铁卢大学计算机科学学院）；Institute for Quantum Computing and Perimeter Institute for Theoretical Physics（量子计算研究所与珀西瓦尔理论物理研究所）
