[论文解读] State Preparation on Quantum Computers via Quantum Steering

Daniel Volya, Prabhat Mishra|arXiv (Cornell University)|Feb 27, 2023

Quantum Computing Algorithms and Architecture参考文献 67被引用 5

一句话总结

本文提出了一种基于测量的量子导引协议，用于在近期超导量子计算机上制备任意量子态。通过反复将系统量子比特与辅助量子比特 entangle，测量辅助量子比特，并主动将其重置为 |0⟩，系统态被导引至目标态——该方法在量子比特和量子三重态上均得到验证，收敛速度呈指数级，且通过测量结果的实时经典反馈得以加速。

ABSTRACT

One of the major components for realizing quantum computers is the ability to initialize the computer to a known fiducial state, also known as state preparation. We demonstrate a state preparation method via measurement-induced steering on contemporary, digital quantum computers. By delegating ancilla qubits and systems qubits, the system state is prepared by repeatedly performing the following steps: (1) executing a designated system-ancilla entangling circuit, (2) measuring the ancilla qubits, and (3) re-initializing ancilla qubits to known states through active reset. While the ancilla qubits are measured and reinitialized to known states, the system qubits are steered from arbitrary initial states to desired final states. We show results of the method by preparing arbitrary qubit states and qutrit (three-level) states. We also demonstrate that the state convergence can be accelerated by utilizing the readouts of the ancilla qubits to guide the protocol in an active manner. This protocol serves as a nontrivial example that incorporates and characterizes essential operations such as qubit reuse (qubit reset), entangling circuits, and measurement. These operations are not only vital for near-term noisy intermediate-scale quantum (NISQ) applications but are also crucial for realizing future error-correcting codes.

研究动机与目标

• 为解决在长相干时间下被动热化变得不切实际时，将量子计算机初始化为任意非基准态的挑战。
• 开发一种可扩展的、非门基的态制备方法，避免对精确门校准和大量误差缓解的需求。
• 通过态保真度表征关键NISQ操作（纠缠门、中间电路测量和量子比特重置）的整体性能。
• 在真实的IBM量子硬件上，展示对量子比特和更高维量子系统（量子三重态）态制备的可行性。
• 探索基于反馈的导引机制，通过实时利用辅助量子比特的测量结果，加速收敛过程。

提出的方法

• 协议利用系统量子比特与辅助量子比特之间的参数化耦合强度 $ J $ 的酉纠缠相互作用 $ U(J) $，在系统上诱导反作用。
• 每次纠缠操作后，使用IBM处理器支持的中间电路测量和量子重置操作，对辅助量子比特进行测量并主动重置为 |0⟩。
• 系统量子比特在重复应用纠缠酉操作和测量引起的坍缩作用下演化，无论初始条件如何，均被导引至目标态。
• 对于主动导引，经典反馈利用辅助量子比特的测量结果，自适应调整协议参数，从而加速收敛。
• 通过Qiskit Pulse的脉冲级控制实现量子三重态态制备，校准Rabi振荡和频率扫描以实现 $ \pi_{1\to2} $ 跃迁。
• 使用Gell-Mann矩阵进行量子态层析，重构系统量子比特或量子三重态的密度矩阵，并对测量读出结果应用误差缓解。

Figure 1: The measurement-induced steering protocol conceptually consists of (a) passively steering a system (qubit or qutrit) to an arbitrary state via coupling to an ancilla qubit that is exposed to an environment for measurement and simple state reset (i.e., to $\ket{0}$ ). A specifically chosen

实验结果

研究问题

• RQ1 测量诱导的量子导引是否能在不依赖门基态制备的前提下，实现在当前数字量子计算机上任意态的制备？
• RQ2 系统态向目标态的收敛速率如何依赖于迭代次数和耦合强度 $ J $？
• RQ3 辅助量子比特测量结果的经典反馈在多大程度上能加速导引协议的收敛？
• RQ4 在真实硬件上使用主动重置和测量反馈时，量子比特和量子三重态的态制备保真度如何？
• RQ5 中间电路测量和主动重置的性能特性对整体态制备保真度有何影响？

主要发现

• 系统态随迭代次数 $ n $ 增加，独立于初始条件，按理论模型预测呈指数收敛至目标态 $ \ket{+} $。
• 当 $ J = \pi/2 $ 时收敛速度最快，在理想情况下单步即可实现完全收敛。
• 在IBM的 ibm_perth 处理器上，该协议成功制备了任意量子比特态，最终态在Bloch球上聚集于目标 $ \ket{+} $ 态附近。
• 通过校准的 $ \pi_{1\to2} $ 脉冲实现了量子三重态态制备，误差缓解后测量判别器准确率达到0.917。
• 多次连续重置显著提升了主动重置保真度，实测 $ \ket{0} $ 制备保真度在测试设备上超过90%。
• 基于反馈的导引显著加速了收敛，减少了达到高保真度目标态所需的迭代次数。

(a) Starting from an unknown initial state $\rho_{S}$ , the system qubit $S$ is steered via a repeated application of an ancilla-system entanglement operation $U_{A-S}$ , followed by measurements and active resets of the ancilla qubit $A$ . After $N$ applications, the system qubit arrives to a targe