Full reconstruction of a 14-qubit state within four hours

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 ∼10 19 to ∼10 15 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.

Simple preparation of Bell and Greenberger-Horne-Zeilinger states using ultrastrong-coupling circuit QED

“…New systems and methods for preparing * e-mail:anton.frisk.kockum@gmail.com and measuring such entangled states has therefore been sought intensively for a long time , and remains a very active field of research. In recent years, entanglement of ten or more qubits has been demonstrated in various experimental setups [45][46][47][48][49].…”

Tomography from collective measurements

“…If we look at the example of N qubits, which will be our thread in this paper, one has to make at least 2 N + 1 measurements in different bases before to determine the state of a priori unknown system [3][4][5][6]. With such an exponential scaling, it is clear that only few-qubit states can be reconstructed in a reasonable time [7,8].…”

Optimal design of measurement settings for quantum-state-tomography experiments

“…To give another example, in Ref. [14] it was shown that, in reconstructing a 14-qubit state, using both smart choice of the state representation and parallel graphic processing unit programming can speed up the post-processing by a factor of 10 4 . Besides of these technical improvements, there also exist various theoretical approaches that are devoted to enhance the capability of quantum state tomography [15][16][17].…”