1
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Álvarez P, Pittilini D, Miserocchi F, Raamamurthy S, Margiani G, Ameye O, Del Pino J, Zilberberg O, Eichler A. Biased Ising Model Using Two Coupled Kerr Parametric Oscillators with External Force. PHYSICAL REVIEW LETTERS 2024; 132:207401. [PMID: 38829099 DOI: 10.1103/physrevlett.132.207401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 04/09/2024] [Indexed: 06/05/2024]
Abstract
Networks of coupled Kerr parametric oscillators (KPOs) are a leading physical platform for analog solving of complex optimization problems. These systems are colloquially known as "Ising machines." We experimentally and theoretically study such a network under the influence of an external force. The force breaks the collective phase-parity symmetry of the system and competes with the intrinsic coupling in ordering the network configuration, similar to how a magnetic field biases an interacting spin ensemble. Specifically, we demonstrate how the force can be used to control the system, and highlight the crucial role of the phase and symmetry of the force. Our Letter thereby provides a method to create Ising machines with arbitrary bias, extending even to exotic cases that are impossible to engineer in real spin systems.
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Affiliation(s)
- Pablo Álvarez
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Davide Pittilini
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Filippo Miserocchi
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | | | - Gabriel Margiani
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Orjan Ameye
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
| | - Javier Del Pino
- Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Oded Zilberberg
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
| | - Alexander Eichler
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
- Quantum Center, ETH Zürich, CH-8093 Zürich, Switzerland
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2
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Iyama D, Kamiya T, Fujii S, Mukai H, Zhou Y, Nagase T, Tomonaga A, Wang R, Xue JJ, Watabe S, Kwon S, Tsai JS. Observation and manipulation of quantum interference in a superconducting Kerr parametric oscillator. Nat Commun 2024; 15:86. [PMID: 38167480 PMCID: PMC10762009 DOI: 10.1038/s41467-023-44496-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 12/15/2023] [Indexed: 01/05/2024] Open
Abstract
Quantum tunneling is the phenomenon that makes superconducting circuits "quantum". Recently, there has been a renewed interest in using quantum tunneling in phase space of a Kerr parametric oscillator as a resource for quantum information processing. Here, we report a direct observation of quantum interference induced by such tunneling and its dynamics in a planar superconducting circuit through Wigner tomography. We experimentally elucidate all essential properties of this quantum interference, such as mapping from Fock states to cat states, a temporal oscillation due to the pump detuning, as well as its characteristic Rabi oscillations and Ramsey fringes. Finally, we perform gate operations as manipulations of the observed quantum interference. Our findings lay the groundwork for further studies on quantum properties of superconducting Kerr parametric oscillators and their use in quantum information technologies.
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Affiliation(s)
- Daisuke Iyama
- Department of Physics, Graduate School of Science, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
| | - Takahiko Kamiya
- Department of Physics, Graduate School of Science, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
| | - Shiori Fujii
- Department of Physics, Graduate School of Science, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
| | - Hiroto Mukai
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
- Research Institute for Science and Technology, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
| | - Yu Zhou
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
| | - Toshiaki Nagase
- Department of Physics, Graduate School of Science, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
| | - Akiyoshi Tomonaga
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
- Research Institute for Science and Technology, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
| | - Rui Wang
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
- Research Institute for Science and Technology, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
| | - Jiao-Jiao Xue
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
- Institute of Theoretical Physics, School of Physics, Xi'an Jiaotong University, Xi'an, People's Republic of China
| | - Shohei Watabe
- College of Engineering, Department of Computer Science and Engineering, Shibaura Institute of Technology, Koto-ku, Tokyo, Japan
| | - Sangil Kwon
- Research Institute for Science and Technology, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan.
| | - Jaw-Shen Tsai
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama, Japan
- Research Institute for Science and Technology, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
- Graduate School of Science, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
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3
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Downing CA, Vidiella-Barranco A. Parametrically driving a quantum oscillator into exceptionality. Sci Rep 2023; 13:11004. [PMID: 37419917 PMCID: PMC10329046 DOI: 10.1038/s41598-023-37964-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 06/30/2023] [Indexed: 07/09/2023] Open
Abstract
The mathematical objects employed in physical theories do not always behave well. Einstein's theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase and polarization singularities pervade wave physics. Within dissipative systems governed by matrices, singularities occur at the exceptional points in parameter space whereby some eigenvalues and eigenvectors coalesce simultaneously. However, the nature of exceptional points arising in quantum systems described within an open quantum systems approach has been much less studied. Here we consider a quantum oscillator driven parametrically and subject to loss. This squeezed system exhibits an exceptional point in the dynamical equations describing its first and second moments, which acts as a borderland between two phases with distinctive physical consequences. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. We also remark upon the presence of a dissipative phase transition at a critical point, which is associated with the closing of the Liouvillian gap. Our results invite the experimental probing of quantum resonators under two-photon driving, and perhaps a reappraisal of exceptional and critical points within dissipative quantum systems more generally.
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Affiliation(s)
- C A Downing
- Department of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK.
| | - A Vidiella-Barranco
- Gleb Wataghin Institute of Physics, University of Campinas - UNICAMP, Campinas, SP, 13083-859, Brazil
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4
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Suzuki Y, Watabe S, Kawabata S, Masuda S. Measurement-based preparation of stable coherent states of a Kerr parametric oscillator. Sci Rep 2023; 13:1606. [PMID: 36709379 PMCID: PMC9884232 DOI: 10.1038/s41598-023-28682-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 01/23/2023] [Indexed: 01/30/2023] Open
Abstract
Kerr parametric oscillators (KPOs) have attracted increasing attention in terms of their application to quantum information processing and quantum simulations. The state preparation and measurement of KPOs are typical requirements when used as qubits. The methods previously proposed for state preparations of KPOs utilize modulation of external fields such as a pump and drive fields. We study the stochastic state preparation of stable coherent states of a KPO with homodyne detection, which does not require modulation of external fields, and thus can reduce experimental efforts and exclude unwanted effects of possible imperfection in control of external fields. We quantitatively show that the detection data, if averaged over an optimal averaging time to decrease the effect of measurement noise, has a strong correlation with the state of the KPO, and therefore can be used to estimate the state (stochastic state preparation). We examine the success probability of the state estimation taking into account the measurement noise and bit flips. Moreover, the proper range of the averaging time to realize a high success probability is obtained by developing a binomial-coherent-state model, which describes the stochastic dynamics of the KPO under homodyne detection.
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Affiliation(s)
- Yuta Suzuki
- grid.143643.70000 0001 0660 6861Department of Physics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 Japan ,grid.208504.b0000 0001 2230 7538Research Center for Emerging Computing Technologies (RCECT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 Japan
| | - Shohei Watabe
- grid.143643.70000 0001 0660 6861Department of Physics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 Japan ,grid.419152.a0000 0001 0166 4675Department of Computer Science and Engineering, College of Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548 Japan
| | - Shiro Kawabata
- grid.208504.b0000 0001 2230 7538Research Center for Emerging Computing Technologies (RCECT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 Japan ,grid.208504.b0000 0001 2230 7538NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568 Japan
| | - Shumpei Masuda
- grid.208504.b0000 0001 2230 7538Research Center for Emerging Computing Technologies (RCECT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 Japan ,grid.208504.b0000 0001 2230 7538NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568 Japan
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5
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Xu B, Zhang P, Zhu J, Liu Z, Eichler A, Zheng XQ, Lee J, Dash A, More S, Wu S, Wang Y, Jia H, Naik A, Bachtold A, Yang R, Feng PXL, Wang Z. Nanomechanical Resonators: Toward Atomic Scale. ACS NANO 2022; 16:15545-15585. [PMID: 36054880 PMCID: PMC9620412 DOI: 10.1021/acsnano.2c01673] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2022] [Accepted: 08/12/2022] [Indexed: 06/15/2023]
Abstract
The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.
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Affiliation(s)
- Bo Xu
- Institute
of Fundamental and Frontier Sciences, University
of Electronic Science and Technology of China, Chengdu610054, China
| | - Pengcheng Zhang
- University
of Michigan−Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai200240, China
| | - Jiankai Zhu
- Institute
of Fundamental and Frontier Sciences, University
of Electronic Science and Technology of China, Chengdu610054, China
| | - Zuheng Liu
- University
of Michigan−Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai200240, China
| | | | - Xu-Qian Zheng
- Department
of Electrical and Computer Engineering, Herbert Wertheim College of
Engineering, University of Florida, Gainesville, Florida32611, United States
- College
of Integrated Circuit Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing210023, China
| | - Jaesung Lee
- Department
of Electrical and Computer Engineering, Herbert Wertheim College of
Engineering, University of Florida, Gainesville, Florida32611, United States
- Department
of Electrical and Computer Engineering, University of Texas at El Paso, El Paso, Texas79968, United States
| | - Aneesh Dash
- Centre
for
Nano Science and Engineering, Indian Institute
of Science, Bangalore560012, Karnataka, India
| | - Swapnil More
- Centre
for
Nano Science and Engineering, Indian Institute
of Science, Bangalore560012, Karnataka, India
| | - Song Wu
- Institute
of Fundamental and Frontier Sciences, University
of Electronic Science and Technology of China, Chengdu610054, China
| | - Yanan Wang
- Department
of Electrical and Computer Engineering, Herbert Wertheim College of
Engineering, University of Florida, Gainesville, Florida32611, United States
- Department
of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska68588, United States
| | - Hao Jia
- Shanghai
Institute of Microsystem and Information Technology, Chinese Academy
of Sciences, Shanghai200050, China
| | - Akshay Naik
- Centre
for
Nano Science and Engineering, Indian Institute
of Science, Bangalore560012, Karnataka, India
| | - Adrian Bachtold
- ICFO-Institut
de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, Castelldefels, Barcelona08860, Spain
| | - Rui Yang
- University
of Michigan−Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai200240, China
- School of
Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai200240, China
| | - Philip X.-L. Feng
- Department
of Electrical and Computer Engineering, Herbert Wertheim College of
Engineering, University of Florida, Gainesville, Florida32611, United States
| | - Zenghui Wang
- Institute
of Fundamental and Frontier Sciences, University
of Electronic Science and Technology of China, Chengdu610054, China
- State
Key Laboratory of Electronic Thin Films and Integrated Devices, University
of Electronic Science and Technology of China, Chengdu610054, China
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6
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Candeloro A, Razzoli L, Bordone P, Paris MGA. Role of topology in determining the precision of a finite thermometer. Phys Rev E 2021; 104:014136. [PMID: 34412220 DOI: 10.1103/physreve.104.014136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2021] [Accepted: 07/07/2021] [Indexed: 12/17/2022]
Abstract
Temperature fluctuations of a finite system follow the Landau bound δT^{2}=T^{2}/C(T) where C(T) is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modeling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.
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Affiliation(s)
- Alessandro Candeloro
- Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, I-20133 Milan, Italy
| | - Luca Razzoli
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, I-41125 Modena, Italy
| | - Paolo Bordone
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, I-41125 Modena, Italy.,Centro S3, CNR-Istituto di Nanoscienze, I-41125 Modena, Italy
| | - Matteo G A Paris
- Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, I-20133 Milan, Italy.,INFN, Sezione di Milano, I-20133 Milan, Italy
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7
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Controls of a superconducting quantum parametron under a strong pump field. Sci Rep 2021; 11:11459. [PMID: 34075132 PMCID: PMC8169783 DOI: 10.1038/s41598-021-90874-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Accepted: 05/17/2021] [Indexed: 11/08/2022] Open
Abstract
Pumped at approximately twice the natural frequency, a Josephson parametric oscillator called parametron or Kerr parametric oscillator shows self-oscillation. Quantum annealing and universal quantum computation using self-oscillating parametrons as qubits were proposed. However, controls of parametrons under the pump field are degraded by unwanted rapidly oscillating terms in the Hamiltonian, which we call non-resonant rapidly oscillating terms (NROTs) coming from the violation of the rotating wave approximation. Therefore, the pump field can be an intrinsic origin of the imperfection of controls of parametrons. Here, we theoretically study the influence of the NROTs on the accuracy of controls of a parametron: a cat-state creation and a single-qubit gate. It is shown that there is a trade-off relationship between the suppression of the nonadiabatic transitions and the validity of the rotating wave approximation in a conventional approach. We also show that the tailored time dependence of the detuning of the pump field can suppress both of the nonadiabatic transitions and the disturbance of the state of the parametron due to the NROTs.
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8
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Karabayir I, Akbilgic O, Tas N. A Novel Learning Algorithm to Optimize Deep Neural Networks: Evolved Gradient Direction Optimizer (EVGO). IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:685-694. [PMID: 32481228 DOI: 10.1109/tnnls.2020.2979121] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Gradient-based algorithms have been widely used in optimizing parameters of deep neural networks' (DNNs) architectures. However, the vanishing gradient remains as one of the common issues in the parameter optimization of such networks. To cope with the vanishing gradient problem, in this article, we propose a novel algorithm, evolved gradient direction optimizer (EVGO), updating the weights of DNNs based on the first-order gradient and a novel hyperplane we introduce. We compare the EVGO algorithm with other gradient-based algorithms, such as gradient descent, RMSProp, Adagrad, momentum, and Adam on the well-known Modified National Institute of Standards and Technology (MNIST) data set for handwritten digit recognition by implementing deep convolutional neural networks. Furthermore, we present empirical evaluations of EVGO on the CIFAR-10 and CIFAR-100 data sets by using the well-known AlexNet and ResNet architectures. Finally, we implement an empirical analysis for EVGO and other algorithms to investigate the behavior of the loss functions. The results show that EVGO outperforms all the algorithms in comparison for all experiments. We conclude that EVGO can be used effectively in the optimization of DNNs, and also, the proposed hyperplane may provide a basis for future optimization algorithms.
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9
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Heugel TL, Biondi M, Zilberberg O, Chitra R. Quantum Transducer Using a Parametric Driven-Dissipative Phase Transition. PHYSICAL REVIEW LETTERS 2019; 123:173601. [PMID: 31702226 DOI: 10.1103/physrevlett.123.173601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2018] [Indexed: 06/10/2023]
Abstract
We study a dissipative Kerr resonator subject to both single- and two-photon detuned drives. Beyond a critical detuning threshold, the Kerr resonator exhibits a semiclassical first-order dissipative phase transition between two different steady states that are characterized by a π phase switch of the cavity field. This transition is shown to persist deep into the quantum limit of low photon numbers. Remarkably, the detuning frequency at which this transition occurs depends almost linearly on the amplitude of the single-photon drive. Based on this phase-switching feature, we devise a sensitive quantum transducer that translates the observed frequency of the parametric quantum phase transition to the detected single-photon amplitude signal. The effects of noise and temperature on the corresponding sensing protocol are addressed, and a realistic circuit-QED implementation is discussed.
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Affiliation(s)
- Toni L Heugel
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Matteo Biondi
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Oded Zilberberg
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - R Chitra
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
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10
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Chou J, Bramhavar S, Ghosh S, Herzog W. Analog Coupled Oscillator Based Weighted Ising Machine. Sci Rep 2019; 9:14786. [PMID: 31615999 PMCID: PMC6794317 DOI: 10.1038/s41598-019-49699-5] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Accepted: 08/27/2019] [Indexed: 11/08/2022] Open
Abstract
We report on an analog computing system with coupled non-linear oscillators which is capable of solving complex combinatorial optimization problems using the weighted Ising model. The circuit is composed of a fully-connected 4-node LC oscillator network with low-cost electronic components and compatible with traditional integrated circuit technologies. We present the theoretical modeling, experimental characterization, and statistical analysis our system, demonstrating single-run ground state accuracies of 98% on randomized MAX-CUT problem sets with binary weights and 84% with 5-bit weight resolutions. Solutions are obtained within 5 oscillator cycles, and the time-to-solution has been demonstrated to scale directly with oscillator frequency. We present scaling analysis which suggests that large coupled oscillator networks may be used to solve computationally intensive problems faster and more efficiently than conventional algorithms. The proof-of-concept system presented here provides the foundation for realizing such larger scale systems using existing hardware technologies and could pave the way towards an entirely novel computing paradigm.
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Affiliation(s)
- Jeffrey Chou
- Massachusetts Institute of Technology Lincoln Laboratory, Lexington, Massachusetts, USA
| | - Suraj Bramhavar
- Massachusetts Institute of Technology Lincoln Laboratory, Lexington, Massachusetts, USA
| | - Siddhartha Ghosh
- Massachusetts Institute of Technology Lincoln Laboratory, Lexington, Massachusetts, USA
| | - William Herzog
- Massachusetts Institute of Technology Lincoln Laboratory, Lexington, Massachusetts, USA.
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11
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Heugel TL, Oscity M, Eichler A, Zilberberg O, Chitra R. Classical Many-Body Time Crystals. PHYSICAL REVIEW LETTERS 2019; 123:124301. [PMID: 31633949 DOI: 10.1103/physrevlett.123.124301] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2019] [Indexed: 06/10/2023]
Abstract
Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a many-body state, alongside several experimental realizations. In this work, we provide a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators. In our analysis, we use classical period-doubling bifurcation theory and present a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition. We experimentally demonstrate this paradigm using coupled mechanical oscillators, thus providing a clear route for time crystal realizations in real materials.
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Affiliation(s)
- Toni L Heugel
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Matthias Oscity
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
- Institute for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Alexander Eichler
- Institute for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Oded Zilberberg
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - R Chitra
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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12
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Goto H, Tatsumura K, Dixon AR. Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems. SCIENCE ADVANCES 2019; 5:eaav2372. [PMID: 31016238 PMCID: PMC6474767 DOI: 10.1126/sciadv.aav2372] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Accepted: 02/27/2019] [Indexed: 05/20/2023]
Abstract
Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.
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13
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Rota R, Minganti F, Ciuti C, Savona V. Quantum Critical Regime in a Quadratically Driven Nonlinear Photonic Lattice. PHYSICAL REVIEW LETTERS 2019; 122:110405. [PMID: 30951358 DOI: 10.1103/physrevlett.122.110405] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Indexed: 06/09/2023]
Abstract
We study an array of coupled optical cavities in the presence of two-photon driving and dissipation. The system displays a critical behavior similar to that of a quantum Ising model at finite temperature. Using the corner-space renormalization method, we compute the steady-state properties of finite lattices of varying size, both in one and two dimensions. From a finite-size scaling of the average of the photon number parity, we highlight the emergence of a critical point in regimes of small dissipations, belonging to the quantum Ising universality class. For increasing photon loss rates, a departure from this universal behavior signals the onset of a quantum critical regime, where classical fluctuations induced by losses compete with long-range quantum correlations.
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Affiliation(s)
- Riccardo Rota
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Fabrizio Minganti
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS-UMR 7162, 75013 Paris, France
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Cristiano Ciuti
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS-UMR 7162, 75013 Paris, France
| | - Vincenzo Savona
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Li F, Chernyak VY, Sinitsyn NA. Quantum Annealing and Thermalization: Insights from Integrability. PHYSICAL REVIEW LETTERS 2018; 121:190601. [PMID: 30468584 DOI: 10.1103/physrevlett.121.190601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2018] [Revised: 06/05/2018] [Indexed: 06/09/2023]
Abstract
We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap during the whole evolution, and a programmable computational problem that is encoded by parameters of the Ising part of the spin Hamiltonian. Our solution enables exact nonperturbative characterization of final nonadiabatic excitations, including a scaling of their number with the annealing rate and the system size. We prove that quantum correlations can accelerate computations and, at the end of the annealing protocol, lead to the perfect Gibbs distribution of all microstates.
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Affiliation(s)
- Fuxiang Li
- School of Physics and Electronics, Hunan University, Changsha 410082, China, Theoretical Division, Los Alamos National Laboratory, B213, Los Alamos, New Mexico 87545, USA and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Vladimir Y Chernyak
- Department of Chemistry and Department of Mathematics, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
| | - Nikolai A Sinitsyn
- Theoretical Division, Los Alamos National Laboratory, B213, Los Alamos, New Mexico 87545, USA
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Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators. Sci Rep 2018; 8:7154. [PMID: 29740061 PMCID: PMC5940910 DOI: 10.1038/s41598-018-25492-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Accepted: 04/20/2018] [Indexed: 11/28/2022] Open
Abstract
A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.
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Puri S, Andersen CK, Grimsmo AL, Blais A. Quantum annealing with all-to-all connected nonlinear oscillators. Nat Commun 2017; 8:15785. [PMID: 28593952 PMCID: PMC5472748 DOI: 10.1038/ncomms15785] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Accepted: 04/28/2017] [Indexed: 11/09/2022] Open
Abstract
Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine.
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Affiliation(s)
- Shruti Puri
- Institut quantique and Départment de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
| | | | - Arne L. Grimsmo
- Institut quantique and Départment de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
| | - Alexandre Blais
- Institut quantique and Départment de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
- Canadian Institute for Advanced Research, Toronto MG5 1N1, Canada
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