Yuanlong Wang

Full reconstruction of a 14-qubit state within four hours

Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum system without \emph{a priori} knowledge or assumptions. Unfortunately, since FQST requires informationally (over)complete measurements, both the number of measurement bases and the computational complexity of data processing suffer an exponential growth with the size of the quantum system. A 14-qubit entangled state has already been experimentally prepared in an ion trap, and the data processing capability for FQST of a 14-qubit state seems to be far away from practical applications. In this paper, the computational capability of FQST is pushed forward to reconstruct a 14-qubit state with a run time of only 3.35 hours using the linear regression estimation (LRE) algorithm, even when informationally overcomplete Pauli measurements are employed. The computational complexity of the LRE algorithm is first reduced from

Adaptive quantum state tomography via linear regression estimation: Theory and two-qubit experiment

O(10^{19})

Closed-loop and robust control of quantum systems.

to

Further results on sampled-data design for robust control of a single qubit

O(10^{15})

Notes on Sampled-Data Design for Robust Control of a Single Qubit

for a 14-qubit state, by dropping all the zero elements, and its computational efficiency is further sped up by fully exploiting the parallelism of the LRE algorithm with parallel Graphic Processing Unit (GPU) programming. Our result can play an important role in quantum information technologies with large quantum systems.

An iterative algorithm for Hamiltonian identification of quantum systems

Bo Qi, 2, ∗ Zhibo Hou, 4, ∗ Yuanlong Wang, Daoyi Dong, Han-Sen Zhong, 4 Li Li, Guo-Yong Xiang, 4, † Howard M. Wiseman, Chuan-Feng Li, 4 and Guang-Can Guo 4 Key Laboratory of Systems and Control, ISS, and National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, CAS, Beijing 100190, P. R. China Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, People’s Republic of China Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia (Dated: December 8, 2015)

Sampled-data design for robust control of open two-level quantum systems with operator errors

For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H ∞ control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.

A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

This paper presents further results on the robust control method for qubit systems in Dong et al. (2013). Based on the properties of an antisymmetric system, an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints.

State Tomography of Qubit Systems Using Linear Regression Estimation and Adaptive Measurements * *This work was supported by the Australian Research Council’s Discovery Projects funding scheme under Project DP130101658 and the National Natural Science Foundation of China under Grants (Nos. 61222504, 11574291, 61374092, 61621003 and 61227902).

Abstract This paper presents several notes on the robust control method proposed in [Dong et al (2013), Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, in press] and furthermore improves the original sampling periods so that this control method can be better and more easily realized. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for both of the above two cases under the same assumption as that in [Dong et al (2013), Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, in press].

Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond

Identifying parameters in the system Hamiltonian is a vitally important task in the development of quantum technology. This paper investigates the problem of Hamiltonian identification for closed quantum systems and develops a new algorithm to achieve the task of identifying the Hamiltonian. Under the framework of standard quantum process tomography and without prior assumptions, we first convert the problem of Hamiltonian identification into an optimization problem and then design an iterative algorithm to numerically solve this problem. Numerical results for a two-qubit system are presented to show the effectiveness of the proposed algorithm through analyzing the mean squared error.