Stephen David T, Ho Wen Wei, Wei Tzu-Chieh, Raussendorf Robert, Verresen Ruben
Department of Physics and Center for Theory of Quantum Matter, <a href="https://ror.org/02ttsq026">University of Colorado Boulder</a>, Boulder, Colorado 80309 USA.
Department of Physics, <a href="https://ror.org/05dxps055">California Institute of Technology</a>, Pasadena, California 91125, USA.
Phys Rev Lett. 2024 Jun 21;132(25):250601. doi: 10.1103/PhysRevLett.132.250601.
A powerful tool emerging from the study of many-body quantum dynamics is that of dual-unitary circuits, which are unitary even when read "sideways," i.e., along the spatial direction. Here, we show that this provides the ideal framework to understand and expand on the notion of measurement-based quantum computation (MBQC). In particular, applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. We show how the dual-unitary dynamics generated by the dynamics of the paradigmatic one-dimensional kicked Ising chain with certain parameter choices generate resource states for universal deterministic MBQC. Specifically, after k time steps, equivalent to a depth-k quantum circuit, we obtain a resource state for universal MBQC on ∼3k/4 encoded qubits. Our protocol allows generic quantum circuits to be "rotated" in space-time and gives new ways to exchange between resources like qubit number and coherence time in quantum computers. Beyond the practical advantages, we also interpret the dual-unitary evolution as generating an infinite sequence of new symmetry-protected topological phases with spatially modulated symmetries, which gives a vast generalization of the well-studied one-dimensional cluster state and shows that our protocol is robust to symmetry-respecting deformations.
多体量子动力学研究中出现的一个强大工具是双酉电路，即使从“横向”读取，即沿着空间方向读取时，它也是酉的。在此，我们表明这为理解和扩展基于测量的量子计算（MBQC）概念提供了理想框架。特别地，将双酉电路应用于多体状态，随后进行适当测量，可有效地在空间方向上实现量子计算。我们展示了由具有特定参数选择的典型一维踢伊辛链的动力学所产生的双酉动力学如何为通用确定性MBQC生成资源态。具体而言，在经过k个时间步长（相当于一个深度为k的量子电路）后，我们在约3k/4个编码量子比特上获得了用于通用MBQC的资源态。我们的协议允许通用量子电路在时空上“旋转”，并给出了在量子计算机中像量子比特数和相干时间等资源之间进行交换的新方法。除了实际优势外，我们还将双酉演化解释为生成具有空间调制对称性的无限序列新的对称保护拓扑相，这对经过充分研究的一维簇态进行了极大推广，并表明我们的协议对尊重对称性的变形具有鲁棒性。
