论文标题
旋转不变的电路：交换互动和两个Ancilla Qubits的普遍性
Rotationally-Invariant Circuits: Universality with the exchange interaction and two ancilla qubits
论文作者
论文摘要
局部统一转换的通用性是量子计算的基石之一，具有许多应用程序和含义超出了该领域。但是，最近已经显示，这种普遍性在存在连续对称的情况下不存在：复合系统上的通用对称单位也无法使用子系统上的局部对称单位[I. I.即使大致实现。 Marvian，《自然物理学》（2022）]。在这项工作中，我们研究了由k-局部旋转不变的单位者形成的量子电路，并充分表征了当地对可实现的单位施加的约束。我们还根据具有固定角动量的状态的平均能量来对这些约束进行解释。有趣的是，尽管有这些限制，我们表明，使用一对Ancilla Qubits，可以通过Heisenberg Exchange相互作用来实现任何旋转不变的单一统一，该相互作用是2局部和旋转不变的。我们还表明，一个Ancilla不足以实现普遍性。最后，我们通过半导体量子点，量子参考框架和资源理论讨论这些结果用于量子计算的应用。
Universality of local unitary transformations is one of the cornerstones of quantum computing with many applications and implications that go beyond this field. However, it has been recently shown that this universality does not hold in the presence of continuous symmetries: generic symmetric unitaries on a composite system cannot be implemented, even approximately, using local symmetric unitaries on the subsystems [I. Marvian, Nature Physics (2022)]. In this work, we study qubit circuits formed from k-local rotationally-invariant unitaries and fully characterize the constraints imposed by locality on the realizable unitaries. We also present an interpretation of these constraints in terms of the average energy of states with a fixed angular momentum. Interestingly, despite these constraints, we show that, using a pair of ancilla qubits, any rotationally-invariant unitary can be realized with the Heisenberg exchange interaction, which is 2-local and rotationally-invariant. We also show that a single ancilla is not enough to achieve universality. Finally, we discuss applications of these results for quantum computing with semiconductor quantum dots, quantum reference frames, and resource theories.
