Full reconstruction of a 14-qubit state within four hours

TL;DR

This paper demonstrates a highly efficient method for full quantum state tomography of a 14-qubit system, reducing computational time from years to hours using optimized algorithms and GPU acceleration.

Contribution

It introduces a scalable, fast approach for reconstructing large quantum states with reduced computational complexity and practical runtime.

Findings

Reconstructed a 14-qubit state in 3.35 hours

Reduced LRE algorithm complexity from 10^19 to 10^15

Achieved efficient parallel processing with GPU

Abstract

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 $O(10^{19})$ to $O(10^{15})$ 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 can play an important role in quantum information technologies with large quantum systems.