1
|
Tang F, Zhang D, Chen L. Nontrivial evolution and geometric phase for an orbital angular momentum qutrit. OPTICS EXPRESS 2024; 32:21200-21215. [PMID: 38859480 DOI: 10.1364/oe.525024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Accepted: 05/12/2024] [Indexed: 06/12/2024]
Abstract
Photonic orbital angular momentum (OAM) offers a promising platform for high-dimensional quantum information processing. While geometric phase (GP) is the crucial tool in enabling intrinsically fault-tolerant quantum computation, the measurement of GP using linear optics remains relatively unexplored in the OAM state space. Here, we propose an experimental scheme to detect GP shifts resulting from the cyclic evolution of OAM qutrit states. Distinguished with the conventional evolution along cyclic path on the Poincaré sphere (PS), the nontrivial evolution in our theoretical scheme is along a cyclic path residing within the SU(3)/U(2) parameter space. By employing a combination of X-gates, dove prisms, and double cylindrical lenses, we achieve the cyclic evolution and analyse the resultant GP through our designed Sagnac interferometer. Our theoretical study may find potential in high-dimensional quantum computation using twisted photons and in exploring the geometric structure of such optical systems.
Collapse
|
2
|
Viotti L, Lombardo FC, Villar PI. Geometric Phase of a Transmon in a Dissipative Quantum Circuit. ENTROPY (BASEL, SWITZERLAND) 2024; 26:89. [PMID: 38275497 PMCID: PMC10814483 DOI: 10.3390/e26010089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2023] [Revised: 01/15/2024] [Accepted: 01/16/2024] [Indexed: 01/27/2024]
Abstract
Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.
Collapse
Affiliation(s)
- Ludmila Viotti
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Fernando C. Lombardo
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires 1428, Argentina
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires 1428, Argentina
| | - Paula I. Villar
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires 1428, Argentina
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires 1428, Argentina
| |
Collapse
|
3
|
Zheng RH, Ning W, Chen YH, Lü JH, Shen LT, Xu K, Zhang YR, Xu D, Li H, Xia Y, Wu F, Yang ZB, Miranowicz A, Lambert N, Zheng D, Fan H, Nori F, Zheng SB. Observation of a Superradiant Phase Transition with Emergent Cat States. PHYSICAL REVIEW LETTERS 2023; 131:113601. [PMID: 37774281 DOI: 10.1103/physrevlett.131.113601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 05/29/2023] [Accepted: 08/10/2023] [Indexed: 10/01/2023]
Abstract
Superradiant phase transitions (SPTs) are important for understanding light-matter interactions at the quantum level, and play a central role in criticality-enhanced quantum sensing. So far, SPTs have been observed in driven-dissipative systems, but the emergent light fields did not show any nonclassical characteristic due to the presence of strong dissipation. Here we report an experimental demonstration of the SPT featuring the emergence of a highly nonclassical photonic field, realized with a resonator coupled to a superconducting qubit, implementing the quantum Rabi model. We fully characterize the light-matter state by Wigner matrix tomography. The measured matrix elements exhibit quantum interference intrinsic of a photonic mesoscopic superposition, and reveal light-matter entanglement.
Collapse
Affiliation(s)
- Ri-Hua Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Wen Ning
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Ye-Hong Chen
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Quantum Information Physics Theory Research Team, RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
| | - Jia-Hao Lü
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Li-Tuo Shen
- 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
| | - Yu-Ran Zhang
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Quantum Information Physics Theory Research Team, RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Da Xu
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou 310027, China
| | - Hekang Li
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Yan Xia
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Fan Wu
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, 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
| | - Adam Miranowicz
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
| | - Neill Lambert
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - 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
| | - Heng Fan
- 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
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Quantum Information Physics Theory Research Team, RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| |
Collapse
|
4
|
High-fidelity qutrit entangling gates for superconducting circuits. Nat Commun 2022; 13:7481. [PMID: 36470858 PMCID: PMC9722686 DOI: 10.1038/s41467-022-34851-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 11/08/2022] [Indexed: 12/12/2022] Open
Abstract
Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the ZZ interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ† and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device.
Collapse
|
5
|
Park KH, Yap YS, Tan YP, Hufnagel C, Nguyen LH, Lau KH, Bore P, Efthymiou S, Carrazza S, Budoyo RP, Dumke R. ICARUS-Q: Integrated control and readout unit for scalable quantum processors. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:104704. [PMID: 36319343 DOI: 10.1063/5.0081232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 08/30/2022] [Indexed: 06/16/2023]
Abstract
We present a control and measurement setup for superconducting qubits based on the Xilinx 16-channel radio-frequency system-on-chip (RFSoC) device. The proposed setup consists of four parts: multiple RFSoC boards, a setup to synchronize every digital to analog converter (DAC) and analog to digital converter (ADC) channel across multiple boards, a low-noise direct current supply for tuning the qubit frequency, and cloud access for remotely performing experiments. We also designed the setup to be free of physical mixers. The RFSoC boards directly generate microwave pulses using sixteen DAC channels up to the third Nyquist zone, which are directly sampled by its eight ADC channels between the fifth and the ninth zones.
Collapse
Affiliation(s)
- Kun Hee Park
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Yung Szen Yap
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Yuanzheng Paul Tan
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Christoph Hufnagel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Long Hoang Nguyen
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Karn Hwa Lau
- Advinno Technologies Pte., Ltd., 22, Sin Ming Lane, No. 05-75, Midview City 573969, Singapore
| | - Patrick Bore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Stavros Efthymiou
- Quantum Research Centre, Technology Innovation Institute, Accelerator 2 Building, on Plot M12, P.O. Box 9639, Masdar City, Abu Dhabi, United Arab Emirates
| | - Stefano Carrazza
- Quantum Research Centre, Technology Innovation Institute, Accelerator 2 Building, on Plot M12, P.O. Box 9639, Masdar City, Abu Dhabi, United Arab Emirates
| | - Rangga P Budoyo
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Rainer Dumke
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| |
Collapse
|
6
|
Verification of Information Thermodynamics in a Trapped Ion System. ENTROPY 2022; 24:e24060813. [PMID: 35741534 PMCID: PMC9222944 DOI: 10.3390/e24060813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Revised: 06/07/2022] [Accepted: 06/08/2022] [Indexed: 02/05/2023]
Abstract
Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.
Collapse
|
7
|
Zhang K, Li H, Zhang P, Yuan J, Chen J, Ren W, Wang Z, Song C, Wang DW, Wang H, Zhu S, Agarwal GS, Scully MO. Synthesizing Five-Body Interaction in a Superconducting Quantum Circuit. PHYSICAL REVIEW LETTERS 2022; 128:190502. [PMID: 35622028 DOI: 10.1103/physrevlett.128.190502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 04/26/2022] [Indexed: 06/15/2023]
Abstract
Synthesizing many-body interaction Hamiltonians is a central task in quantum simulation. However, it is challenging to synthesize Hamiltonians that have more than two spins in a single term. Here we synthesize m-body spin-exchange Hamiltonians with m up to 5 in a superconducting quantum circuit by simultaneously exciting multiple independent qubits with time-energy correlated photons generated from a qudit. The dynamic evolution of the m-body interaction is governed by the Rabi oscillation between two m-spin states, in which the states of each spin are different. We demonstrate the scalability of our approach by comparing the influence of noises on the three-, four- and five-body interaction and building a many-body Mach-Zehnder interferometer which potentially has a Heisenberg-limit sensitivity. This study paves a way for quantum simulation involving many-body interaction Hamiltonians such as lattice gauge theories in quantum circuits.
Collapse
Affiliation(s)
- Ke Zhang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Hekang Li
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Pengfei Zhang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jiale Yuan
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jinyan Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Wenhui Ren
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Zhen Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Chao Song
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Da-Wei Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
- CAS Center of Excellence in Topological Quantum Computation, Beijing 100190, China
| | - H Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
- Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 311215, China
| | - Shiyao Zhu
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
- Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 311215, China
| | - Girish S Agarwal
- Institute of Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA
| | - Marlan O Scully
- Institute of Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA
| |
Collapse
|
8
|
Ryeol Choi J. Effects of light-wave nonstaticity on accompanying geometric-phase evolutions. OPTICS EXPRESS 2021; 29:35712-35724. [PMID: 34809000 DOI: 10.1364/oe.440512] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 09/20/2021] [Indexed: 06/13/2023]
Abstract
Quantum mechanics allows the emergence of nonstatic quantum light waves in the Fock state even in a transparent medium of which electromagnetic parameters do not vary over time. Such wave packets become broad and narrow in turn periodically in the quadrature space. We investigate the effects of wave nonstaticity arisen in a static environment on the behavior of accompanying geometric phases in the Fock states. In this case, the geometric phases appear only when the measure of nonstaticity is not zero and their time behavior is deeply related to the measure of nonstaticity. While the dynamical phases undergo linear decrease over time, the geometric phases exhibit somewhat oscillatory behavior where the center of oscillation increases linearly. In particular, if the measure of nonstaticity is sufficiently high, the geometric phases abruptly change whenever the waves become narrow in the quadrature space. The understanding for the phase evolution of nonstatic light waves is necessary in their technological applications regarding wave modulations.
Collapse
|
9
|
Zhang JW, Yan LL, Li JC, Ding GY, Bu JT, Chen L, Su SL, Zhou F, Feng M. Single-Atom Verification of the Noise-Resilient and Fast Characteristics of Universal Nonadiabatic Noncyclic Geometric Quantum Gates. PHYSICAL REVIEW LETTERS 2021; 127:030502. [PMID: 34328774 DOI: 10.1103/physrevlett.127.030502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Accepted: 06/16/2021] [Indexed: 06/13/2023]
Abstract
Quantum gates induced by geometric phases are intrinsically robust against noise due to the global properties of their evolution paths. Compared to conventional nonadiabatic geometric quantum computation, the recently proposed nonadiabatic noncyclic geometric quantum computation (NNGQC) works in a faster fashion while still remaining the robust feature of the geometric operations. Here, we experimentally implement the NNGQC in a single trapped ultracold ^{40}Ca^{+} ion to verify the noise-resilient and fast feature. By performing unitary operations under imperfect conditions, we witness the advantages of the NNGQC with measured fidelities by quantum process tomography in comparison to other two quantum gates by conventional nonadiabatic geometric quantum computation and by straightforward dynamical evolution. Our results provide the first evidence confirming the possibility of accelerated quantum information processing with limited systematic errors even in an imperfect situation.
Collapse
Affiliation(s)
- J W Zhang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - L-L Yan
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - J C Li
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - G Y Ding
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - J T Bu
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - L Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - S-L Su
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - F Zhou
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - M Feng
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
- Research Center for Quantum Precision Measurement, Institute of Industry Technology, Guangzhou and Chinese Academy of Sciences, Guangzhou 511458, China
| |
Collapse
|
10
|
Milne AR, Hempel C, Li L, Edmunds CL, Slatyer HJ, Ball H, Hush MR, Biercuk MJ. Quantum Oscillator Noise Spectroscopy via Displaced Cat States. PHYSICAL REVIEW LETTERS 2021; 126:250506. [PMID: 34241523 DOI: 10.1103/physrevlett.126.250506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 04/21/2021] [Indexed: 06/13/2023]
Abstract
Quantum harmonic oscillators are central to many modern quantum technologies. We introduce a method to determine the frequency noise spectrum of oscillator modes through coupling them to a qubit with continuously driven qubit-state-dependent displacements. We reconstruct the noise spectrum using a series of different drive phase and amplitude modulation patterns in conjunction with a data-fusion routine based on convex optimization. We apply the technique to the identification of intrinsic noise in the motional frequency of a single trapped ion with sensitivity to fluctuations at the sub-Hz level in a spectral range from quasi-dc up to 50 kHz.
Collapse
Affiliation(s)
- Alistair R Milne
- ARC Centre of Excellence for Engineered Quantum Systems, The University of Sydney, School of Physics, New South Wales 2006, Australia
| | - Cornelius Hempel
- ARC Centre of Excellence for Engineered Quantum Systems, The University of Sydney, School of Physics, New South Wales 2006, Australia
| | - Li Li
- Q-CTRL Pty Ltd, Sydney, New South Wales 2006, Australia
| | - Claire L Edmunds
- ARC Centre of Excellence for Engineered Quantum Systems, The University of Sydney, School of Physics, New South Wales 2006, Australia
| | | | - Harrison Ball
- Q-CTRL Pty Ltd, Sydney, New South Wales 2006, Australia
| | | | - Michael J Biercuk
- ARC Centre of Excellence for Engineered Quantum Systems, The University of Sydney, School of Physics, New South Wales 2006, Australia
- Q-CTRL Pty Ltd, Sydney, New South Wales 2006, Australia
| |
Collapse
|
11
|
Morvan A, Ramasesh VV, Blok MS, Kreikebaum JM, O'Brien K, Chen L, Mitchell BK, Naik RK, Santiago DI, Siddiqi I. Qutrit Randomized Benchmarking. PHYSICAL REVIEW LETTERS 2021; 126:210504. [PMID: 34114846 DOI: 10.1103/physrevlett.126.210504] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Accepted: 04/27/2021] [Indexed: 05/02/2023]
Abstract
Ternary quantum processors offer significant potential computational advantages over conventional qubit technologies, leveraging the encoding and processing of quantum information in qutrits (three-level systems). To evaluate and compare the performance of such emerging quantum hardware it is essential to have robust benchmarking methods suitable for a higher-dimensional Hilbert space. We demonstrate extensions of industry standard randomized benchmarking (RB) protocols, developed and used extensively for qubits, suitable for ternary quantum logic. Using a superconducting five-qutrit processor, we find an average single-qutrit process infidelity of 3.8×10^{-3}. Through interleaved RB, we characterize a few relevant gates, and employ simultaneous RB to fully characterize crosstalk errors. Finally, we apply cycle benchmarking to a two-qutrit CSUM gate and obtain a two-qutrit process fidelity of 0.85. Our results present and demonstrate RB-based tools to characterize the performance of a qutrit processor, and a general approach to diagnose control errors in future qudit hardware.
Collapse
Affiliation(s)
- A Morvan
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| | - V V Ramasesh
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - M S Blok
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - J M Kreikebaum
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| | - K O'Brien
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - L Chen
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - B K Mitchell
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - R K Naik
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - D I Santiago
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| | - I Siddiqi
- Quantum Nanoelectronics Laboratory, Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| |
Collapse
|
12
|
Yun M, Guo FQ, Li M, Yan LL, Feng M, Li YX, Su SL. Distributed geometric quantum computation based on the optimized-control-technique in a cavity-atom system via exchanging virtual photons. OPTICS EXPRESS 2021; 29:8737-8750. [PMID: 33820315 DOI: 10.1364/oe.418626] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2020] [Accepted: 02/25/2021] [Indexed: 06/12/2023]
Abstract
We propose a scheme for quantum geometric computation on a fiber-cavity-fiber system, in which two atoms are located in two single-mode cavities, respectively, connected with each other by optical fiber. This scheme not only has the feature of virtual excitation of photons in the cavity quantum electrodynamics (CQED) that can reduce the effect of decay effectively but also has the advantage of geometric phase to withstand noises due to its built-in noise-resilience feature and robust merit. Specifically, our proposal combined with optimized-control-technology (OCT) can reduce gate operation error by adjusting the time-dependent amplitude and phase of the resonant field which further enhances the robustness of the quantum operation. The robustness against decoherence is demonstrated numerically and the scheme may be applied in the remote quantum information processing tasks and quantum computation.
Collapse
|
13
|
Xu Y, Hua Z, Chen T, Pan X, Li X, Han J, Cai W, Ma Y, Wang H, Song YP, Xue ZY, Sun L. Experimental Implementation of Universal Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit. PHYSICAL REVIEW LETTERS 2020; 124:230503. [PMID: 32603172 DOI: 10.1103/physrevlett.124.230503] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2019] [Accepted: 05/18/2020] [Indexed: 06/11/2023]
Abstract
Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.
Collapse
Affiliation(s)
- Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Z Hua
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Tao Chen
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - X Pan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Li
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Zheng-Yuan Xue
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| |
Collapse
|
14
|
Xu Y, Ma Y, Cai W, Mu X, Dai W, Wang W, Hu L, Li X, Han J, Wang H, Song YP, Yang ZB, Zheng SB, Sun L. Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits. PHYSICAL REVIEW LETTERS 2020; 124:120501. [PMID: 32281851 DOI: 10.1103/physrevlett.124.120501] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Revised: 10/09/2019] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.
Collapse
Affiliation(s)
- Y Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Mu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Dai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - W Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - L Hu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - X Li
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - J Han
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - H Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y P Song
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, 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
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - L Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| |
Collapse
|
15
|
Zhang ZY, Liu JM, Hu Z, Wang Y. Optical control of entanglement and coherence for polar molecules in pendular states. OPTICS EXPRESS 2019; 27:26588-26599. [PMID: 31674537 DOI: 10.1364/oe.27.026588] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 08/15/2019] [Indexed: 06/10/2023]
Abstract
Quantum entanglement and coherence are both essential physical resources in quantum theory. Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus have been suggested as a platform for quantum information processing. In this paper, we employ the pendular states of the polar molecules trapped in static electric fields as the qubits, and put forward several theoretical schemes to generate the entanglement and coherence for two coupled dipoles by using optimal control theory. Through the designs of appropriate laser pulses, the transitions from the ground state to the Bell state and maximally coherent state can be realized with high fidelities 0.9906 and 0.9943 in the two-dipole system, respectively. Meanwhile, we show that the degrees of entanglement and coherence between the two pendular qubits are effectively enhanced with the help of optimized control fields. Furthermore, our schemes are generalized to the preparation of the Hardy state and even to the creation of arbitrary two-qubit states. Our findings can shed some light on the implementation of quantum information tasks with the molecular pendular states.
Collapse
|
16
|
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.
Collapse
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
| |
Collapse
|
17
|
Choi JR, Ju S. Properties of the Geometric Phase in Electromechanical Oscillations of Carbon-Nanotube-Based Nanowire Resonators. NANOSCALE RESEARCH LETTERS 2019; 14:44. [PMID: 30721358 PMCID: PMC6363811 DOI: 10.1186/s11671-019-2855-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Accepted: 01/03/2019] [Indexed: 06/09/2023]
Abstract
The geometric phase is an extra phase evolution in the wave function of vibrations that is potentially applicable in a broad range of science and technology. The characteristics of the geometric phase in the squeezed state for a carbon-nanotube-based nanowire resonator have been investigated by means of the invariant operator method. The introduction of a linear invariant operator, which is useful for treating a complicated time-dependent Hamiltonian system, enabled us to derive the analytical formula of the geometric phase. By making use of this, we have analyzed the time behavior of the geometric phase based on relevant illustrations. The influence of squeezing parameters on the evolution of the geometric phase has been investigated. The geometric phase, in large, oscillates, and the envelope of such oscillation increases over time. The rate of the increase of the geometric phase is large when the parameters, such as the classical amplitude of the oscillation, the damping factor, and the amplitude of the driving force, are large. We have confirmed a very sharp increase of the geometric phase over time in the case that the angular frequency of the system reaches near the resonance angular frequency. Our development regarding the characteristics of the geometric phase is crucial for understanding the topological features in nanowire oscillations.
Collapse
Affiliation(s)
- Jeong Ryeol Choi
- Department of Physics, Kyonggi University, Gwanggyosan-ro, Yeongtong-gu, Suwon, Gyeonggi-do, 16227 Republic of Korea
| | - Sanghyun Ju
- Department of Physics, Kyonggi University, Gwanggyosan-ro, Yeongtong-gu, Suwon, Gyeonggi-do, 16227 Republic of Korea
| |
Collapse
|
18
|
Song C, Xu D, Zhang P, Wang J, Guo Q, Liu W, Xu K, Deng H, Huang K, Zheng D, Zheng SB, Wang H, Zhu X, Lu CY, Pan JW. Demonstration of Topological Robustness of Anyonic Braiding Statistics with a Superconducting Quantum Circuit. PHYSICAL REVIEW LETTERS 2018; 121:030502. [PMID: 30085793 DOI: 10.1103/physrevlett.121.030502] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Indexed: 05/06/2023]
Abstract
Anyons are quasiparticles occurring in two dimensions, whose topological properties are believed to be robust against local perturbations and may hold promise for fault tolerant quantum computing. Here we present an experiment of demonstrating the path independent nature of anyonic braiding statistics with a superconducting quantum circuit, which represents a 7-qubit version of the toric code model. We dynamically create the ground state of the model, achieving a state fidelity of 0.688±0.015 as verified by quantum state tomography. Anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations. The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct, but topologically equivalent paths: Both reveal the nontrivial π-phase shift, the hallmark of Abelian 1/2 anyons, with a phase accuracy of ∼99% in the Ramsey-type interference measurement.
Collapse
Affiliation(s)
- Chao Song
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- CAS Center for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Da Xu
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Pengfei Zhang
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Jianwen Wang
- CAS Center for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qiujiang Guo
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Wuxin Liu
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Kai Xu
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Hui Deng
- CAS Center for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Keqiang Huang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350116, China
| | - H Wang
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- CAS Center for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiaobo Zhu
- CAS Center for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China
| | - Chao-Yang Lu
- CAS Center for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China
| | - Jian-Wei Pan
- CAS Center for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China
| |
Collapse
|