Quantum process tomography is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this paper, we propose a two-stage solution for both trace-preserving and non-trace-preserving quantum process tomography. Utilizing a tensor structure, our algorithm exhibits a computational complexity of$O(MLd^{2})$where d is the dimension of the quantum system and$M, L~(M\geq d^{2}, L\geq d^{2})$represent the numbers of different input states and measurement operators, respectively. We establish an analytical error upper bound and then design the optimal input states and the optimal measurement operators, which are both based on minimizing the error upper bound and maximizing the robustness characterized by the condition number. Numerical examples and testing on IBM quantum devices are presented to demonstrate the performance and efficiency of our algorithm.

Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, a novel quantum detector tomography method is proposed. First, a series of different probe states are used to generate measurement data. Then, using constrained linear regression estimation, a stage-1 estimation of the detector is obtained. Finally, the positive semidefinite requirement is added to guarantee a physical stage-2 estimation. This Two-stage Estimation (TSE) method has computational complexity O(nd2M), where n is the number of d-dimensional detector matrices and M is the number of different probe states. An error upper bound is established, and optimization on the coherent probe states is investigated. We perform simulation and a quantum optical experiment to testify the effectiveness of the TSE method.

This paper proposes a recursively adaptive tomography protocol to improve the precision of quantum process estimation for finite dimensional systems. The problem of quantum process tomography is firstly formulated as a parameter estimation problem which can then be solved by the linear regression estimation method. An adaptive algorithm is proposed for the selection of subsequent input states given the previous estimation results. Numerical results show that the proposed adaptive process tomography protocol can achieve an improved level of estimation performance.

In this paper, we consider the modeling of dynamical spin network systems. The system Hamiltonian governs the evolution of the network system and shows the structure of how the element systems are coupled. Probes are employed to measure a set of spins of the network. For a variety of applications, the state space model is a useful way to describe the system dynamics. One important task in establishing a state space model is to obtain an accessible set containing all the operators coupled to the measurement operators. We provide analytic results on simplifying the process of generating accessible sets. An example is provided to demonstrate the generation of an accessible set under a certain measurement scheme.