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Pereira L, García-Ripoll JJ, Ramos T. Complete Physical Characterization of Quantum Nondemolition Measurements via Tomography. PHYSICAL REVIEW LETTERS 2022; 129:010402. [PMID: 35841584 DOI: 10.1103/physrevlett.129.010402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 06/03/2022] [Indexed: 06/15/2023]
Abstract
We introduce a self-consistent tomography for arbitrary quantum nondemolition (QND) detectors. Based on this, we build a complete physical characterization of the detector, including the measurement processes and a quantification of the fidelity, ideality, and backaction of the measurement. This framework is a diagnostic tool for the dynamics of QND detectors, allowing us to identify errors, and to improve their calibration and design. We illustrate this on a realistic Jaynes-Cummings simulation of a superconducting qubit readout. We characterize nondispersive errors, quantify the backaction introduced by the readout cavity, and calibrate the optimal measurement point.
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Affiliation(s)
- L Pereira
- Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
| | - J J García-Ripoll
- Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
| | - T Ramos
- Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
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2
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Gao X, Erhard M, Zeilinger A, Krenn M. Computer-Inspired Concept for High-Dimensional Multipartite Quantum Gates. PHYSICAL REVIEW LETTERS 2020. [PMID: 32794870 DOI: 10.1038/s42254-020-0230-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multiphotonic quantum systems. The proposals rely on two new ideas: (i) a novel high-dimensional quantum nondemolition measurement, (ii) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world and thereby we identify important pathways for experimental research in the near future. The concepts have been found using the computer algorithm melvin for designing computer-inspired quantum experiments. As opposed to the field of machine learning, here the human learns new scientific concepts by interpreting and analyzing the results presented by the machine. This demonstrates that computer algorithms can inspire new ideas in science, which has a widely unexplored potential that goes far beyond experimental quantum information science.
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Affiliation(s)
- Xiaoqin Gao
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
- National Mobile Communications Research Laboratory and Quantum Information Research Center, Southeast University, Nanjing, 210096, China
| | - Manuel Erhard
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
| | - Anton Zeilinger
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
| | - Mario Krenn
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
- Department of Chemistry and Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada
- Vector Institute for Artificial Intelligence, Toronto, Ontario M5G 1M1, Canada
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3
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Estimation of pure quantum states in high dimension at the limit of quantum accuracy through complex optimization and statistical inference. Sci Rep 2020; 10:12781. [PMID: 32728142 PMCID: PMC7391742 DOI: 10.1038/s41598-020-69646-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2020] [Accepted: 07/15/2020] [Indexed: 11/29/2022] Open
Abstract
Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices. This drives the search for tomographic methods that achieve greater accuracy. In the case of mixed states of a single 2-dimensional quantum system adaptive methods have been recently introduced that achieve the theoretical accuracy limit deduced by Hayashi and Gill and Massar. However, accurate estimation of higher-dimensional quantum states remains poorly understood. This is mainly due to the existence of incompatible observables, which makes multiparameter estimation difficult. Here we present an adaptive tomographic method and show through numerical simulations that, after a few iterations, it is asymptotically approaching the fundamental Gill–Massar lower bound for the estimation accuracy of pure quantum states in high dimension. The method is based on a combination of stochastic optimization on the field of the complex numbers and statistical inference, exceeds the accuracy of any mixed-state tomographic method, and can be demonstrated with current experimental capabilities. The proposed method may lead to new developments in quantum metrology.
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Kim Y, Teo YS, Ahn D, Im DG, Cho YW, Leuchs G, Sánchez-Soto LL, Jeong H, Kim YH. Universal Compressive Characterization of Quantum Dynamics. PHYSICAL REVIEW LETTERS 2020; 124:210401. [PMID: 32530676 DOI: 10.1103/physrevlett.124.210401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 04/27/2020] [Indexed: 06/11/2023]
Abstract
Recent quantum technologies utilize complex multidimensional processes that govern the dynamics of quantum systems. We develop an adaptive diagonal-element-probing compression technique that feasibly characterizes any unknown quantum processes using much fewer measurements compared to conventional methods. This technique utilizes compressive projective measurements that are generalizable to an arbitrary number of subsystems. Both numerical analysis and experimental results with unitary gates demonstrate low measurement costs, of order O(d^{2}) for d-dimensional systems, and robustness against statistical noise. Our work potentially paves the way for a reliable and highly compressive characterization of general quantum devices.
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Affiliation(s)
- Yosep Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), 37673 Pohang, Korea
| | - Yong Siah Teo
- Department of Physics and Astronomy, Seoul National University, 08826 Seoul, Korea
| | - Daekun Ahn
- Department of Physics and Astronomy, Seoul National University, 08826 Seoul, Korea
| | - Dong-Gil Im
- Department of Physics, Pohang University of Science and Technology (POSTECH), 37673 Pohang, Korea
| | - Young-Wook Cho
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), 02792 Seoul, Korea
| | - Gerd Leuchs
- Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany
- Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
| | - Luis L Sánchez-Soto
- Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany
- Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
| | - Hyunseok Jeong
- Department of Physics and Astronomy, Seoul National University, 08826 Seoul, Korea
| | - Yoon-Ho Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), 37673 Pohang, Korea
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5
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Utreras-Alarcón A, Rivera-Tapia M, Niklitschek S, Delgado A. Stochastic optimization on complex variables and pure-state quantum tomography. Sci Rep 2019; 9:16143. [PMID: 31695070 PMCID: PMC6834649 DOI: 10.1038/s41598-019-52289-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2019] [Accepted: 10/14/2019] [Indexed: 12/04/2022] Open
Abstract
Real-valued functions of complex arguments violate the Cauchy-Riemann conditions and, consequently, do not have Taylor series expansion. Therefore, optimization methods based on derivatives cannot be directly applied to this class of functions. This is circumvented by mapping the problem to the field of the real numbers by considering real and imaginary parts of the complex arguments as the new independent variables. We introduce a stochastic optimization method that works within the field of the complex numbers. This has two advantages: Equations on complex arguments are simpler and easy to analyze and the use of the complex structure leads to performance improvements. The method produces a sequence of estimates that converges asymptotically in mean to the optimizer. Each estimate is generated by evaluating the target function at two different randomly chosen points. Thereby, the method allows the optimization of functions with unknown parameters. Furthermore, the method exhibits a large performance enhancement. This is demonstrated by comparing its performance with other algorithms in the case of quantum tomography of pure states. The method provides solutions which can be two orders of magnitude closer to the true minima or achieve similar results as other methods but with three orders of magnitude less resources.
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Affiliation(s)
- A Utreras-Alarcón
- Instituto Milenio de Investigación en Óptica, Universidad de Concepción, Concepción, Chile.,Facultad de Ciencias Físicas y Matemáticas, Departamento de Física, Universidad de Concepción, Concepción, Chile
| | - M Rivera-Tapia
- Instituto Milenio de Investigación en Óptica, Universidad de Concepción, Concepción, Chile.,Facultad de Ciencias Físicas y Matemáticas, Departamento de Física, Universidad de Concepción, Concepción, Chile
| | - S Niklitschek
- Instituto Milenio de Investigación en Óptica, Universidad de Concepción, Concepción, Chile.,Facultad de Ciencias Físicas y Matemáticas, Departamento de Estadística, Universidad de Concepción, Concepción, Chile
| | - A Delgado
- Instituto Milenio de Investigación en Óptica, Universidad de Concepción, Concepción, Chile. .,Facultad de Ciencias Físicas y Matemáticas, Departamento de Física, Universidad de Concepción, Concepción, Chile.
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Métillon V, Gerlich S, Brune M, Raimond JM, Rouchon P, Dotsenko I. Benchmarking Maximum-Likelihood State Estimation with an Entangled Two-Cavity State. PHYSICAL REVIEW LETTERS 2019; 123:060404. [PMID: 31491182 DOI: 10.1103/physrevlett.123.060404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Indexed: 06/10/2023]
Abstract
The efficient quantum state reconstruction algorithm described by Six et al. [Phys. Rev. A 93, 012109 (2016)PLRAAN2469-992610.1103/PhysRevA.93.012109] is experimentally implemented on the nonlocal state of two microwave cavities entangled by a circular Rydberg atom. We use information provided by long sequences of measurements performed by resonant and dispersive probe atoms over timescales involving the system decoherence. Moreover, we benefit from the consolidation, in the same reconstruction, of different measurement protocols providing complementary information. Finally, we obtain realistic error bars for the matrix elements of the reconstructed density operator. These results demonstrate the pertinence and precision of the method, directly applicable to any complex quantum system.
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Affiliation(s)
- V Métillon
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 place Marcelin Berthelot, F-75231 Paris, France
| | - S Gerlich
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 place Marcelin Berthelot, F-75231 Paris, France
| | - M Brune
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 place Marcelin Berthelot, F-75231 Paris, France
| | - J M Raimond
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 place Marcelin Berthelot, F-75231 Paris, France
| | - P Rouchon
- Centre Automatique et Systèmes, Mines-ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75006 Paris, France
- INRIA Paris, 2 rue Simone Iff, 75012 Paris, France
| | - I Dotsenko
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 place Marcelin Berthelot, F-75231 Paris, France
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