基于ADMM的压缩量子态层析算法
A Robust Compressive Quantum State Tomography Algorithm Using ADMM
摘要：
可能的状态空间维度相对于量子比特的数量呈指数增长。这一特性使得量子态层析成像技术对于识别仅仅几个量子比特的状态来说昂贵且不切实际。最近开发的方法，压缩传感，给了我们一个替代估计量子态与较少的测量。证明了该估计可以转化为一个带量子力学约束的凸优化问题。本文提出了一种求解量子凸优化问题的交替增广拉格朗日方法，目的是在给定观测量和观测期望值的情况下，恢复被稀疏噪声破坏的纯或近纯量子态。该算法速度快，对离群噪声（甚至对某些条目非常大）具有鲁棒性，并且可以分布式地解决重建问题。仿真结果验证了该算法的优越性，并与传统的最小二乘和压缩量子层析成像方法进行了比较。
英文摘要：
The possible state space dimension increases exponentially with respect to the number of qubits. This feature makes the quantum state tomography expensive and impractical for identifying the state of merely several qubits. The recent developed approach, compressed sensing, gives us an alternative to estimate the quantum state with fewer measurements. It is proved that the estimation then can be converted to a convex optimization problem with quantum mechanics constraints. In this paper we present an alternating augmented Lagrangian method for quantum convex optimization problem aiming for recovering pure or near pure quantum states corrupted by sparse noise given observables and the expectation values of the measurements. The proposed algorithm is much faster, robust to outlier noises (even very large for some entries) and can solve the reconstruction problem distributively. The simulations verify the superiority of the proposed algorithm and compare it to the conventional least square and compressive quantum tomography using Dantzig method.
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