Density matrix exponentiation (DME) is a general technique for using a quantum state $\rho$ to enact the quantum operation $e^{-i\rho \theta }$ on a target system. It was first proposed in the context of quantum machine learning, but has since been shown to have broad applications in quantum metrology and computation. No experimental demonstration of DME has been performed thus far due to its demanding circuit depths and the need to efficiently generate multiple identical copies of $\rho$ during the finite lifetime of the target system. In this work, we describe the first demonstration of the DME algorithm, which we accomplish using a superconducting quantum processor. Our demonstration relies on a 99.7% fidelity controlled-phase gate implemented using two tunable superconducting transmon qubits. We achieve a fidelity surpassing 90% at circuit depths exceeding 70 when comparing the output of the circuit executed on our quantum processor to a simulation assuming perfect operations and measurements.

中文翻译：

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使用超导量子处理器演示密度矩阵求幂

密度矩阵求幂 (DME) 是一种使用量子态的通用技术 $\rho$ 制定量子操作 $e^{-\mathrm{一世}\rho \theta }$在目标系统上。它最初是在量子机器学习的背景下提出的，但后来被证明在量子计量和计算中具有广泛的应用。由于 DME 要求电路深度和需要有效地生成多个相同的$\rho$在目标系统的有限生命周期内。在这项工作中，我们描述了 DME 算法的首次演示，我们使用超导量子处理器完成了该算法。我们的演示依赖于使用两个可调谐超导传输量子比特实现的 99.7% 保真度受控相位门。将在我们的量子处理器上执行的电路的输出与假设完美操作和测量的模拟进行比较时，我们在电路深度超过 70 时实现了超过 90% 的保真度。