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Deterministic Entanglement Swapping with Hybrid Discrete- and Continuous-Variable Systems. PHOTONICS 2022. [DOI: 10.3390/photonics9060368] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The study of entanglement between discrete and continuous variables is an important theoretical and experimental topic in quantum information processing, for which entanglement swapping is one of the interesting elements. Entanglement swapping allows two particles without interacting with each other in any way, to form an entangled state by the action of another pair of entangled particles. In this paper, we propose an experimentally feasible scheme to realize deterministic entanglement swapping in the hybrid system with discrete and continuous variables. The process is achieved by preparing two pairs of entangled states, each is formed by a qubit and two quasi-orthogonal coherent state elements of a cavity, performing a Bell-state analysis through nonlocal operations on the continuous variable states of the two cavities, and projecting the two qubits into a maximally entangled state. The present scheme may be applied to other physical systems sustaining such hybrid discrete and continuous forms, providing a typical paradigm for entanglement manipulation through deterministic swapping operations.
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2
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Huang HL, Narożniak M, Liang F, Zhao Y, Castellano AD, Gong M, Wu Y, Wang S, Lin J, Xu Y, Deng H, Rong H, Dowling JP, Peng CZ, Byrnes T, Zhu X, Pan JW. Emulating Quantum Teleportation of a Majorana Zero Mode Qubit. PHYSICAL REVIEW LETTERS 2021; 126:090502. [PMID: 33750174 DOI: 10.1103/physrevlett.126.090502] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2020] [Revised: 11/30/2020] [Accepted: 01/14/2021] [Indexed: 05/06/2023]
Abstract
Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version and realizing the ground states in a superconducting quantum processor. The teleportation transfers the quantum state encoded in the spin-mapped version of the Majorana zero mode states between two Kitaev chains. The teleportation circuit is realized using only braiding operations and can be achieved despite being restricted to Clifford gates for the Ising anyons. The Majorana encoding is a quantum error detecting code for phase-flip errors, which is used to improve the average fidelity of the teleportation for six distinct states from 70.76±0.35% to 84.60±0.11%, well beyond the classical bound in either case.
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Affiliation(s)
- He-Liang Huang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- Henan Key Laboratory of Quantum Information and Cryptography, Zhengzhou, Henan 450000, China
| | - Marek Narożniak
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China
- Department of Physics, New York University, New York, New York 10003, USA
| | - Futian Liang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Youwei Zhao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Anthony D Castellano
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Ming Gong
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yulin Wu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Shiyu Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jin Lin
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yu Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Hui Deng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Hao Rong
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jonathan P Dowling
- Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
| | - Cheng-Zhi Peng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Tim Byrnes
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China
- Department of Physics, New York University, New York, New York 10003, USA
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
| | - Xiaobo Zhu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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3
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Ning W, Huang XJ, Han PR, Li H, Deng H, Yang ZB, Zhong ZR, Xia Y, Xu K, Zheng D, Zheng SB. Deterministic Entanglement Swapping in a Superconducting Circuit. PHYSICAL REVIEW LETTERS 2019; 123:060502. [PMID: 31491139 DOI: 10.1103/physrevlett.123.060502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Indexed: 06/10/2023]
Abstract
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is deterministically transferred to another qubit that has never interacted with it. We further realize delayed-choice entanglement swapping, showing whether two qubits previously behaved as in an entangled state or as in a separable state is determined by a later choice of the type of measurement on their partners. This is the first demonstration of entanglement-separability duality in a deterministic way.
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Affiliation(s)
- Wen Ning
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Xin-Jie Huang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Pei-Rong Han
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Hekang Li
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hui Deng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhen-Biao Yang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Zhi-Rong Zhong
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Yan Xia
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Kai Xu
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Dongning Zheng
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
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4
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Wang J, Scholz VB, Renner R. Confidence Polytopes in Quantum State Tomography. PHYSICAL REVIEW LETTERS 2019; 122:190401. [PMID: 31144942 DOI: 10.1103/physrevlett.122.190401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Indexed: 06/09/2023]
Abstract
Quantum state tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be specified in terms of confidence regions, i.e., subsets of the state space which contain the system's state with high probability. Here, building upon a quantum generalization of Clopper-Pearson confidence intervals-a notion known from classical statistics-we present a simple and reliable scheme for generating confidence regions. These have the shape of a polytope and can be computed efficiently. We provide several examples to demonstrate the practical usability of the scheme in experiments.
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Affiliation(s)
- Jinzhao Wang
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Volkher B Scholz
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Renato Renner
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
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5
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Matsuzaki Y, Benjamin S, Nakayama S, Saito S, Munro WJ. Quantum Metrology beyond the Classical Limit under the Effect of Dephasing. PHYSICAL REVIEW LETTERS 2018; 120:140501. [PMID: 29694131 DOI: 10.1103/physrevlett.120.140501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Indexed: 06/08/2023]
Abstract
Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields scales inversely with the square root of the measurement time T. On the other hand, by using quantum resources, we can reduce this scaling of the uncertainty with time to 1/T. However, as quantum states are susceptible to dephasing, it has not been clear whether we can achieve sensitivities with a scaling of 1/T for a measurement time longer than the coherence time. Here, we propose a scheme that estimates the amplitude of globally applied fields with the uncertainty of 1/T for an arbitrary time scale under the effect of dephasing. We use one-way quantum-computing-based teleportation between qubits to prevent any increase in the correlation between the quantum state and its local environment from building up and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our method has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensor.
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Affiliation(s)
- Yuichiro Matsuzaki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
- NTT Theoretical Quantum Physics Center, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Simon Benjamin
- Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
| | - Shojun Nakayama
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
| | - Shiro Saito
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - William J Munro
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
- NTT Theoretical Quantum Physics Center, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
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6
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Wendin G. Quantum information processing with superconducting circuits: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:106001. [PMID: 28682303 DOI: 10.1088/1361-6633/aa7e1a] [Citation(s) in RCA: 107] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.
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Affiliation(s)
- G Wendin
- Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
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7
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Transferring arbitrary d-dimensional quantum states of a superconducting transmon qudit in circuit QED. Sci Rep 2017; 7:7039. [PMID: 28765631 PMCID: PMC5539217 DOI: 10.1038/s41598-017-07225-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Accepted: 06/26/2017] [Indexed: 11/08/2022] Open
Abstract
A qudit (d-level quantum system) has a large Hilbert space and thus can be used to achieve many quantum information and communication tasks. Here, we propose a method to transfer arbitrary d-dimensional quantum states (known or unknown) between two superconducting transmon qudits coupled to a single cavity. The state transfer can be performed by employing resonant interactions only. In addition, quantum states can be deterministically transferred without measurement. Numerical simulations show that high-fidelity transfer of quantum states between two superconducting transmon qudits (d ≤ 5) is feasible with current circuit QED technology. This proposal is quite general and can be applied to accomplish the same task with natural or artificial atoms of a ladder-type level structure coupled to a cavity or resonator.
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Xin T, Lu D, Klassen J, Yu N, Ji Z, Chen J, Ma X, Long G, Zeng B, Laflamme R. Quantum State Tomography via Reduced Density Matrices. PHYSICAL REVIEW LETTERS 2017; 118:020401. [PMID: 28128623 DOI: 10.1103/physrevlett.118.020401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2016] [Indexed: 06/06/2023]
Abstract
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.
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Affiliation(s)
- Tao Xin
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Dawei Lu
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Joel Klassen
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada
| | - Nengkun Yu
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia
- Department of Mathematics and Statistics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada
| | - Zhengfeng Ji
- Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia
- State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, 100190 Beijing, China
| | - Jianxin Chen
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland, USA
| | - Xian Ma
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Guilu Long
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Bei Zeng
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Mathematics and Statistics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada
- Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada
| | - Raymond Laflamme
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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9
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Liu T, Su QP, Xiong SJ, Liu JM, Yang CP, Nori F. Generation of a macroscopic entangled coherent state using quantum memories in circuit QED. Sci Rep 2016; 6:32004. [PMID: 27562055 PMCID: PMC4999958 DOI: 10.1038/srep32004] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Accepted: 08/01/2016] [Indexed: 11/13/2022] Open
Abstract
W-type entangled states can be used as quantum channels for, e.g., quantum teleportation, quantum dense coding, and quantum key distribution. In this work, we propose a way to generate a macroscopic W-type entangled coherent state using quantum memories in circuit QED. The memories considered here are nitrogen-vacancy center ensembles (NVEs), each located in a different cavity. This proposal does not require initially preparing each NVE in a coherent state instead of a ground state, which should significantly reduce its experimental difficulty. For most of the operation time, each cavity remains in a vacuum state, thus decoherence caused by the cavity decay and the unwanted inter-cavity crosstalk are greatly suppressed. Moreover, only one external-cavity coupler qubit is needed, which simplifies the circuit.
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Affiliation(s)
- Tong Liu
- Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
| | - Qi-Ping Su
- Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
| | - Shao-Jie Xiong
- Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
| | - Jin-Ming Liu
- State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, China
| | - Chui-Ping Yang
- Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
| | - Franco Nori
- CEMS, RIKEN, Saitama 351-0198, Japan
- Department of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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10
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Faist P, Renner R. Practical and Reliable Error Bars in Quantum Tomography. PHYSICAL REVIEW LETTERS 2016; 117:010404. [PMID: 27419548 DOI: 10.1103/physrevlett.117.010404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Indexed: 06/06/2023]
Abstract
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis. Promising recent methods based on confidence regions are difficult to apply in practice or yield error bars which are unnecessarily large. Here, we propose a practical yet robust method for obtaining error bars. We do so by introducing a novel representation of the output of the tomography procedure, the quantum error bars. This representation is (i) concise, being given in terms of few parameters, (ii) intuitive, providing a fair idea of the "spread" of the error, and (iii) useful, containing the necessary information for constructing confidence regions. The statements resulting from our method are formulated in terms of a figure of merit, such as the fidelity to a reference state. We present an algorithm for computing this representation and provide ready-to-use software. Our procedure is applied to actual experimental data obtained from two superconducting qubits in an entangled state, demonstrating the applicability of our method.
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Affiliation(s)
- Philippe Faist
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Renato Renner
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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11
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Liu T, Xiong SJ, Cao XZ, Su QP, Yang CP. Efficient transfer of an arbitrary qutrit state in circuit quantum electrodynamics. OPTICS LETTERS 2015; 40:5602-5605. [PMID: 26625061 DOI: 10.1364/ol.40.005602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Compared with a qubit, a qutrit (i.e., three-level quantum system) has a larger Hilbert space and thus can be used to encode more information in quantum information processing and communication. Here, we propose a method to transfer an arbitrary quantum state between two flux qutrits coupled to two resonators. This scheme is simple because it only requires two basic operations. The state-transfer operation can be performed fast because only resonant interactions are used. Numerical simulations show that the high-fidelity transfer of quantum states between the two qutrits is feasible with current circuit-QED technology. This scheme is quite general and can be applied to accomplish the same task for other solid-state qutrits coupled to resonators.
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12
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Graham TM, Bernstein HJ, Wei TC, Junge M, Kwiat PG. Superdense teleportation using hyperentangled photons. Nat Commun 2015; 6:7185. [PMID: 26018201 PMCID: PMC4458874 DOI: 10.1038/ncomms8185] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2014] [Accepted: 04/10/2015] [Indexed: 12/02/2022] Open
Abstract
Transmitting quantum information between two remote parties is a requirement for many quantum applications; however, direct transmission of states is often impossible because of noise and loss in the communication channel. Entanglement-enhanced state communication can be used to avoid this issue, but current techniques require extensive experimental resources to transmit large quantum states deterministically. To reduce these resource requirements, we use photon pairs hyperentangled in polarization and orbital angular momentum to implement superdense teleportation, which can communicate a specific class of single-photon ququarts. We achieve an average fidelity of 87.0(1)%, almost twice the classical limit of 44% with reduced experimental resources than traditional techniques. We conclude by discussing the information content of this constrained set of states and demonstrate that this set has an exponentially larger state space volume than the lower-dimensional general states with the same number of state parameters. Implementations of known quantum teleportation techniques suffer from a number of technical limitations, most notably the scaling of the required classical resources. Here, the authors implement a new protocol, superdense teleportation, which requires fewer resources than the conventional approaches.
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Affiliation(s)
- Trent M Graham
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Herbert J Bernstein
- Institute for Science &Interdisciplinary Studies &School of Natural Sciences, Hampshire College, Amherst, Massachusetts 01002, USA
| | - Tzu-Chieh Wei
- C.N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794, USA
| | - Marius Junge
- Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801, USA
| | - Paul G Kwiat
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
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13
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Abstract
Quantum electromagnetic fluctuations induce forces between neutral particles, known as the van der Waals and Casimir interactions. These fundamental forces, mediated by virtual photons from the vacuum, play an important role in basic physics and chemistry and in emerging technologies involving, e.g., microelectromechanical systems or quantum information processing. Here we show that these interactions can be enhanced by many orders of magnitude upon changing the character of the mediating vacuum modes. By considering two polarizable particles in the vicinity of any standard electric transmission line, along which photons can propagate in one dimension, we find a much stronger and longer-range interaction than in free space. This enhancement may have profound implications on many-particle and bulk systems and impact the quantum technologies mentioned above. The predicted giant vacuum force is estimated to be measurable in a coplanar waveguide line.
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Steffen L, Salathe Y, Oppliger M, Kurpiers P, Baur M, Lang C, Eichler C, Puebla-Hellmann G, Fedorov A, Wallraff A. Deterministic quantum teleportation with feed-forward in a solid state system. Nature 2013; 500:319-22. [PMID: 23955231 DOI: 10.1038/nature12422] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2013] [Accepted: 06/28/2013] [Indexed: 11/09/2022]
Abstract
Engineered macroscopic quantum systems based on superconducting electronic circuits are attractive for experimentally exploring diverse questions in quantum information science. At the current state of the art, quantum bits (qubits) are fabricated, initialized, controlled, read out and coupled to each other in simple circuits. This enables the realization of basic logic gates, the creation of complex entangled states and the demonstration of algorithms or error correction. Using different variants of low-noise parametric amplifiers, dispersive quantum non-demolition single-shot readout of single-qubit states with high fidelity has enabled continuous and discrete feedback control of single qubits. Here we realize full deterministic quantum teleportation with feed-forward in a chip-based superconducting circuit architecture. We use a set of two parametric amplifiers for both joint two-qubit and individual qubit single-shot readout, combined with flexible real-time digital electronics. Our device uses a crossed quantum bus technology that allows us to create complex networks with arbitrary connecting topology in a planar architecture. The deterministic teleportation process succeeds with order unit probability for any input state, as we prepare maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two-qubit measurement with high efficiency and high fidelity. We teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 10(4) s(-1), exceeding other reported implementations. The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.
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Affiliation(s)
- L Steffen
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland.
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Ristè D, Bultink CC, Lehnert KW, DiCarlo L. Feedback control of a solid-state qubit using high-fidelity projective measurement. PHYSICAL REVIEW LETTERS 2012; 109:240502. [PMID: 23368293 DOI: 10.1103/physrevlett.109.240502] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate feedback control of a superconducting transmon qubit using discrete, projective measurement and conditional coherent driving. Feedback realizes a fast and deterministic qubit reset to a target state with 2.4% error averaged over input superposition states, and allows concatenating experiments more than 10 times faster than by passive initialization. This closed-loop qubit control is necessary for measurement-based protocols such as quantum error correction and teleportation.
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Affiliation(s)
- D Ristè
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands
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Sabín C, Peropadre B, del Rey M, Martín-Martínez E. Extracting past-future vacuum correlations using circuit QED. PHYSICAL REVIEW LETTERS 2012; 109:033602. [PMID: 22861847 DOI: 10.1103/physrevlett.109.033602] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2012] [Revised: 05/25/2012] [Indexed: 06/01/2023]
Abstract
We propose a realistic circuit QED experiment to test the extraction of past-future vacuum entanglement to a pair of superconducting qubits. The qubit P interacts with the quantum field along an open transmission line for an interval T(on) and then, after a time-lapse T(off), the qubit F starts interacting for a time T(on) in a symmetric fashion. After that, past-future quantum correlations will have transferred to the qubits, even if the qubits do not coexist at the same time. We show that this experiment can be realized with current technology and discuss its utility as a possible implementation of a quantum memory.
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Affiliation(s)
- Carlos Sabín
- Instituto de Física Fundamental, CSIC, Serrano 113-B, 28006 Madrid, Spain.
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17
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Steffen L, da Silva MP, Fedorov A, Baur M, Wallraff A. Experimental Monte Carlo quantum process certification. PHYSICAL REVIEW LETTERS 2012; 108:260506. [PMID: 23004949 DOI: 10.1103/physrevlett.108.260506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2012] [Indexed: 06/01/2023]
Abstract
Experimental implementations of quantum information processing have now reached a level of sophistication where quantum process tomography is impractical. The number of experimental settings as well as the computational cost of the data postprocessing now translates to days of effort to characterize even experiments with as few as 8 qubits. Recently a more practical approach to determine the fidelity of an experimental quantum process has been proposed, where the experimental data are compared directly with an ideal process using Monte Carlo sampling. Here, we present an experimental implementation of this scheme in a circuit quantum electrodynamics setup to determine the fidelity of 2-qubit gates, such as the CPHASE and the CNOT gate, and 3-qubit gates, such as the Toffoli gate and two sequential CPHASE gates.
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Affiliation(s)
- L Steffen
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
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