论文标题
建造Qutrit对角门
Building Qutrit Diagonal Gates from Phase Gadgets
论文作者
论文摘要
事实证明，相位小工具是用于推理ZX-DAGRAM，用于量子电路的优化和模拟以及基于测量的量子计算理论的必不可少的工具。在本文中，我们研究了Qutrits的阶段小工具。我们介绍了原始Qutrit ZX-Calculus的屈曲对称变体，该变体允许在精神上更接近原始（Qubit）ZX-Calculus。在这种演算期，小工具看起来如您所期望的，但是它们的性质存在非平凡的差异。我们设计了新的QUTRIT特定技巧来扩展Qubits的图形傅立叶理论，从而导致“添加”相位小工具和“乘法”对应器之间的翻译我们配音相位乘数。 这使我们能够以两种方式将多控制的量子概念概括为Qutrits。 第一种类型是控制单个TRITSTRING，而第二种类型则在控制Qutrits的tritwise乘法模量3中应用门数。第一个需要多项式的大门和指数的小相，而第二个则需要指数级的门，但需要恒定的阶段。这很有趣，因为在量子设置中不可能进行这种结构。 作为这些结果的应用，我们找到了模拟任意量子对角线统一的构造，并特别找到了量子CCZ门的无actilla仿真，该仿真仅需要三个单Qutrit非clifford闸门，证明比具有Ancilla Qubits所需的四个T门要低。
Phase gadgets have proved to be an indispensable tool for reasoning about ZX-diagrams, being used in optimisation and simulation of quantum circuits and the theory of measurement-based quantum computation. In this paper we study phase gadgets for qutrits. We present the flexsymmetric variant of the original qutrit ZX-calculus, which allows for rewriting that is closer in spirit to the original (qubit) ZX-calculus. In this calculus phase gadgets look as you would expect, but there are non-trivial differences in their properties. We devise new qutrit-specific tricks to extend the graphical Fourier theory of qubits, resulting in a translation between the 'additive' phase gadgets and a 'multiplicative' counterpart we dub phase multipliers. This enables us to generalise the qubit notion of multiple-control to qutrits in two ways. The first type is controlling on a single tritstring, while the second type applies the gate a number of times equal to the tritwise multiplication modulo 3 of the control qutrits.We show how both types of control can be implemented for any qutrit Z or X phase gate, ancilla-free, and using only Clifford and phase gates. The first requires a polynomial number of gates and exponentially small phases, while the second requires an exponential number of gates, but constant sized phases. This is interesting, because such a construction is not possible in the qubit setting. As an application of these results we find a construction for emulating arbitrary qubit diagonal unitaries, and specifically find an ancilla-free emulation for the qubit CCZ gate that only requires three single-qutrit non-Clifford gates, provably lower than the four T gates needed for qubits with ancilla.
