The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to final measurements. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to split any quantum circuit into a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state and local (adaptive) measurement instructions—a so-called standard form—which is executed on a quantum computer. We further process the stabilizer state with the graph state formalism, thus, enabling a significant decrease in circuit depth for certain applications. We show that groups of mutually-commuting operators can be implemented using fully-parallel, i.e. non-adaptive, measurements within our protocol. In addition, we discuss how groups of mutually commuting observables can be simulatenously measured by adjusting the resource state, rather than performing a costly basis transformation prior to the measurement as it is done in the circuit model. Finally, we demonstrate the utility of our technique on two examples of high practical relevance—the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver (VQE) for the ground-state energy estimation of the water molecule. For the VQE, we find a reduction of the depth by a factor of 4 to 5 using measurement patterns vs. the standard circuit model. At the same time, since we incorporate the simultaneous measurements, our patterns allow us to save shots by a factor of at least 3.5 compared to measuring Pauli strings individually in the circuit model.

中文翻译：

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基于图状态将量子电路映射到浅层深度测量模式


基于测量的量子计算 （MBQC） 的范式从高度纠缠的资源状态开始，在该状态上通过自适应测量和校正执行幺正操作，确保确定性。这与更常见的量子电路模型形成鲜明对比，在量子电路模型中，幺正运算在最终测量之前直接通过量子门实现。在这项工作中，我们将 MBQC 的概念整合到电路模型中，以创建一种混合仿真技术，使我们能够将任何量子电路拆分为经典高效的可模拟 Clifford 部分和由稳定器状态和局部（自适应）测量指令组成的第二部分——所谓的标准形式——在量子计算机上执行。我们进一步使用图态形式处理稳定器状态，从而能够显着降低某些应用的电路深度。我们表明，在我们的协议中使用完全并行（即非自适应）测量来实现相互交换运算符组。此外，我们还讨论了如何通过调整资源状态来模拟测量相互交换的可观察对象组，而不是像在电路模型中那样在测量之前执行昂贵的基变换。最后，我们在两个具有高度实际相关性的例子上展示了我们的技术的实用性——量子近似优化算法和变分量子特征求解器 （VQE），用于水分子的基态能量估计。对于 VQE，我们发现与标准电路模型相比，使用测量模式的深度减少了 4 到 5 倍。 同时，由于我们结合了同步测量，与在电路模型中单独测量 Pauli 琴弦相比，我们的模式使我们能够节省至少 3.5 倍的镜头。