Full reconstruction of a 14-qubit state within four hours

Zhibo Hou,Guo-Yong Xiang,Han-Sen Zhong,Ye Tian,Daoyi Dong,Yuanlong Wang,Guang-Can Guo,Bo Qi,Li Li,Chuan-Feng Li,Franco Nori

doi:10.1088/1367-2630/18/8/083036

Abstract

Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum system without 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 ∼1019 to ∼1015 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 demonstrates the effectiveness of using parallel computation to speed up the postprocessing for FQST, and can play an important role in quantum information technologies with large quantum systems.

Highlights

Quantum state tomography [1,2,3], characterizing the state of a quantum system via quantum measurements and data processing, is a starting point and the standard for verification and benchmarking of various quantum information processing tasks, such as quantum computation [4], cryptography [5], and metrology [6,7,8,9,10].To reconstruct quantum states wherein we have no a priori information, we can resort to informationallycomplete measurements
We push the data processing capability of full quantum state tomography (FQST) to a 14-qubit state using the informationally overcomplete Pauli measurements by optimizing the linear regression estimation (LRE) algorithm in [39] and employing parallel programming with graphics processing unit (GPU)
In order to show the relationship between the amount of speed up and the number of parallel threads in GPU programming, the reciprocal of the run time in step (i) for a maximally-mixed 12-qubit state is plotted with respect to m in figure 1, where m is the number of streaming multiprocessors (SMs)