多量子比特系统中动态校正门的几何形式
Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems
摘要：
在多量子比特系统中实现对噪声具有鲁棒性的门的能力对于量子信息技术的进步至关重要。然而，由于时间依赖的薛定谔方程的难解性，特别是在多量子比特系统中，很难找到在执行门的同时消除噪声的控制脉冲。在这里，我们表明，这个问题可以回避使用的形式主义，在门的累积误差表示为几何曲线在多维欧几里德空间。消除噪声误差到前导阶对应于曲线的闭合，这是可以在不求解薛定谔方程的情况下满足的条件。我们开发和揭示这种几何形式主义的一般性质，并推导出一个递归关系，映射控制领域的曲率为任意尺寸的哈密顿。我们演示的例子，通过使用几何方法来设计动态校正门的一类两个量子比特的哈密顿量，这是相关的超导transmon量子比特和半导体自旋量子比特。我们提出这种几何形式主义作为一种通用的技术脉冲引起的误差抑制在量子计算门操作。
英文摘要：
The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrodinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multi-dimensional Euclidean space. Cancellation of noise errors to leading order corresponds to closure of the curve, a condition that can be satisfied without solving the Schrodinger equation. We develop and uncover general properties of this geometric formalism, and derive a recursion relation that maps control fields to curvatures for Hamiltonians of arbitrary dimension. We demonstrate examples by using the geometric method to design dynamically corrected gates for a class of two-qubit Hamiltonians that is relevant for both superconducting transmon qubits and semiconductor spin qubits. We propose this geometric formalism as a general technique for pulse-induced error suppression in quantum computing gate operations.
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