基于凸优化的量子态与量子过程的真实实验重构
True experimental reconstruction of quantum states and processes via convex optimization
AI总结：
针对传统量子态与过程层析的线性反演易产生非物理矩阵的问题，提出基于半定规划求解的约束凸优化方法，在两比特NMR系统中实现了更高保真度的物理有效量子态、过程及噪声表征。
摘要：
我们采用约束凸优化（constrained convex optimization, CCO）方法，在两比特核磁共振（NMR）量子信息处理器上对任意量子态和未知量子过程进行实验表征。传统的量子态与量子过程层析标准协议基于线性反演，往往会得到非物理的密度矩阵，进而得到无效的过程矩阵。而CCO方法能够生成符合物理有效性的密度矩阵与过程矩阵，相较于标准方法保真度显著提升。该约束优化问题通过半定规划（semi-definite programming, SDP）协议求解。我们利用CCO方法估计Kraus算子，并在存在退相干误差的情况下表征量子门。随后我们假设系统具有马尔可夫动力学，将Lindblad主方程与CCO方法结合，完整表征了NMR量子比特中存在的噪声过程。
英文摘要：
We use a constrained convex optimization (CCO) method to experimentally characterize arbitrary quantum states and unknown quantum processes on a two-qubit NMR quantum information processor. Standard protocols for quantum state and quantum process tomography are based on linear inversion, which often result in an unphysical density matrix and hence an invalid process matrix. The CCO method on the other hand, produces physically valid density matrices and process matrices, with significantly improved fidelity as compared to the standard methods. The constrainedoptimization problem is solved with the help of a semi-definite programming (SDP) protocol. We use the CCO method to estimate the Kraus operators and characterize gates in the presence of errors due to decoherence. We then assume Markovian system dynamics and use a Lindblad master equation in conjunction with the CCO method to completely characterize the noise processes present in the NMR qubits.
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