Fast Quantum State Reconstruction via Accelerated Non-Convex Programming
We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (MiFGD), extends the applicability of quantum tomography for larger systems. Despite...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/10/2/116 |
| _version_ | 1797618696332509184 |
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| author | Junhyung Lyle Kim George Kollias Amir Kalev Ken X. Wei Anastasios Kyrillidis |
| author_facet | Junhyung Lyle Kim George Kollias Amir Kalev Ken X. Wei Anastasios Kyrillidis |
| author_sort | Junhyung Lyle Kim |
| collection | DOAJ |
| description | We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (MiFGD), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, MiFGD converges provably close to the true density matrix at an accelerated linear rate asymptotically in the absence of experimental and statistical noise, under common assumptions. With this manuscript, we present the method, prove its convergence property and provide the Frobenius norm bound guarantees with respect to the true density matrix. From a practical point of view, we benchmark the algorithm performance with respect to other existing methods, in both synthetic and real (noisy) experiments, performed on the IBM’s quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than the state-of-the-art approaches, with similar or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite the presence of experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems. |
| first_indexed | 2024-03-11T08:16:01Z |
| format | Article |
| id | doaj.art-9caa9fe17f314739aa658cf04a391ded |
| institution | Directory Open Access Journal |
| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-11T08:16:01Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Photonics |
| spelling | doaj.art-9caa9fe17f314739aa658cf04a391ded2023-11-16T22:44:35ZengMDPI AGPhotonics2304-67322023-01-0110211610.3390/photonics10020116Fast Quantum State Reconstruction via Accelerated Non-Convex ProgrammingJunhyung Lyle Kim0George Kollias1Amir Kalev2Ken X. Wei3Anastasios Kyrillidis4Computer Science Department, Rice University, Houston, TX 77005, USAIBM Research, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USAInformation Sciences Institute, University of Southern California, Marina del Rey, CA 90292, USAIBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USAComputer Science Department, Rice University, Houston, TX 77005, USAWe propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (MiFGD), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, MiFGD converges provably close to the true density matrix at an accelerated linear rate asymptotically in the absence of experimental and statistical noise, under common assumptions. With this manuscript, we present the method, prove its convergence property and provide the Frobenius norm bound guarantees with respect to the true density matrix. From a practical point of view, we benchmark the algorithm performance with respect to other existing methods, in both synthetic and real (noisy) experiments, performed on the IBM’s quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than the state-of-the-art approaches, with similar or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite the presence of experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems.https://www.mdpi.com/2304-6732/10/2/116quantum state tomographynon-convex optimizationmatrix factorizationacceleration |
| spellingShingle | Junhyung Lyle Kim George Kollias Amir Kalev Ken X. Wei Anastasios Kyrillidis Fast Quantum State Reconstruction via Accelerated Non-Convex Programming Photonics quantum state tomography non-convex optimization matrix factorization acceleration |
| title | Fast Quantum State Reconstruction via Accelerated Non-Convex Programming |
| title_full | Fast Quantum State Reconstruction via Accelerated Non-Convex Programming |
| title_fullStr | Fast Quantum State Reconstruction via Accelerated Non-Convex Programming |
| title_full_unstemmed | Fast Quantum State Reconstruction via Accelerated Non-Convex Programming |
| title_short | Fast Quantum State Reconstruction via Accelerated Non-Convex Programming |
| title_sort | fast quantum state reconstruction via accelerated non convex programming |
| topic | quantum state tomography non-convex optimization matrix factorization acceleration |
| url | https://www.mdpi.com/2304-6732/10/2/116 |
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