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 a priori knowledge or assumptions. Unfortunately, since FQST requires informationally (over)complete measurements, both the number of measurement bases and the computational complexity...

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Published in:New journal of physics Vol. 18; no. 8; pp. 83036 - 83043
Main Authors: Hou, Zhibo, Zhong, Han-Sen, Tian, Ye, Dong, Daoyi, Qi, Bo, Li, Li, Wang, Yuanlong, Nori, Franco, Xiang, Guo-Yong, Li, Chuan-Feng, Guo, Guang-Can
Format: Journal Article
Language:English
Published: Bristol IOP Publishing 18.08.2016
Subjects:
14-qubit
Algorithms
Complexity
Data processing
Entangled states
full tomography
Graphics processing units
LRE
parallel GPU programming
Parallel processing
Physics
Quantum computing
Quantum phenomena
Quantum theory
Qubits (quantum computing)
ISSN:1367-2630, 1367-2630
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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.
AbstractList 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.
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.
Author Li, Li
Xiang, Guo-Yong
Nori, Franco
Guo, Guang-Can
Zhong, Han-Sen
Hou, Zhibo
Li, Chuan-Feng
Tian, Ye
Dong, Daoyi
Qi, Bo
Wang, Yuanlong
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  organization: University of Michigan Physics Department, Ann Arbor, Michigan 48109-1040, USA
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  organization: University of Science and Technology of China Synergetic Innovation Center of Quantum Information and Quantum Physics, Hefei, Anhui 230026, People's Republic of China
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Snippet 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....
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SubjectTerms 14-qubit
Algorithms
Complexity
Data processing
Entangled states
full tomography
Graphics processing units
LRE
parallel GPU programming
Parallel processing
Physics
Quantum computing
Quantum phenomena
Quantum theory
Qubits (quantum computing)
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Title Full reconstruction of a 14-qubit state within four hours
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Volume 18
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