1
|
Guo SA, Wu YK, Ye J, Zhang L, Lian WQ, Yao R, Wang Y, Yan RY, Yi YJ, Xu YL, Li BW, Hou YH, Xu YZ, Guo WX, Zhang C, Qi BX, Zhou ZC, He L, Duan LM. A site-resolved two-dimensional quantum simulator with hundreds of trapped ions. Nature 2024; 630:613-618. [PMID: 38811737 DOI: 10.1038/s41586-024-07459-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 04/24/2024] [Indexed: 05/31/2024]
Abstract
A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation1. As one of the leading physical platforms for quantum information processing, the ion trap has achieved a quantum simulation of tens of ions with site-resolved readout in a one-dimensional Paul trap2-4 and of hundreds of ions with global observables in a two-dimensional (2D) Penning trap5,6. However, integrating these two features into a single system is still very challenging. Here we report the stable trapping of 512 ions in a 2D Wigner crystal and the sideband cooling of their transverse motion. We demonstrate the quantum simulation of long-range quantum Ising models with tunable coupling strengths and patterns, with or without frustration, using 300 ions. Enabled by the site resolution in the single-shot measurement, we observe rich spatial correlation patterns in the quasi-adiabatically prepared ground states, which allows us to verify quantum simulation results by comparing the measured two-spin correlations with the calculated collective phonon modes and with classical simulated annealing. We further probe the quench dynamics of the Ising model in a transverse field to demonstrate quantum sampling tasks. Our work paves the way for simulating classically intractable quantum dynamics and for running noisy intermediate-scale quantum algorithms7,8 using 2D ion trap quantum simulators.
Collapse
Affiliation(s)
- S-A Guo
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - Y-K Wu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
- Hefei National Laboratory, Hefei, P.R. China
| | - J Ye
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - L Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - W-Q Lian
- HYQ Co., Ltd, Beijing, P.R. China
| | - R Yao
- HYQ Co., Ltd, Beijing, P.R. China
| | - Y Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
- HYQ Co., Ltd, Beijing, P.R. China
| | - R-Y Yan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - Y-J Yi
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - Y-L Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - B-W Li
- HYQ Co., Ltd, Beijing, P.R. China
| | - Y-H Hou
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - Y-Z Xu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - W-X Guo
- HYQ Co., Ltd, Beijing, P.R. China
| | - C Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - B-X Qi
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
| | - Z-C Zhou
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
- Hefei National Laboratory, Hefei, P.R. China
| | - L He
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China
- Hefei National Laboratory, Hefei, P.R. China
| | - L-M Duan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P.R. China.
- Hefei National Laboratory, Hefei, P.R. China.
- New Cornerstone Science Laboratory, Beijing, P.R. China.
| |
Collapse
|
2
|
Adelhardt P, Koziol JA, Langheld A, Schmidt KP. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. ENTROPY (BASEL, SWITZERLAND) 2024; 26:401. [PMID: 38785650 PMCID: PMC11120707 DOI: 10.3390/e26050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 04/17/2024] [Accepted: 04/19/2024] [Indexed: 05/25/2024]
Abstract
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.
Collapse
Affiliation(s)
| | | | | | - Kai P. Schmidt
- Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany; (P.A.); (J.A.K.); (A.L.)
| |
Collapse
|
3
|
Feng L, Katz O, Haack C, Maghrebi M, Gorshkov AV, Gong Z, Cetina M, Monroe C. Continuous symmetry breaking in a trapped-ion spin chain. Nature 2023; 623:713-717. [PMID: 37968402 DOI: 10.1038/s41586-023-06656-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 09/20/2023] [Indexed: 11/17/2023]
Abstract
One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions1. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter2,3. Our preparation relies on simultaneous control over an array of tightly focused individual addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.
Collapse
Affiliation(s)
- Lei Feng
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Or Katz
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Casey Haack
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Mohammad Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansings, MI, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD, USA
| | - Zhexuan Gong
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Marko Cetina
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Christopher Monroe
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
- IonQ, Inc., College Park, MD, USA.
| |
Collapse
|
4
|
Yamaguchi YY, Barré J. Discontinuous codimension-two bifurcation in a Vlasov equation. Phys Rev E 2023; 107:054203. [PMID: 37328987 DOI: 10.1103/physreve.107.054203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Accepted: 04/01/2023] [Indexed: 06/18/2023]
Abstract
In a Vlasov equation, the destabilization of a homogeneous stationary state is typically described by a continuous bifurcation characterized by strong resonances between the unstable mode and the continuous spectrum. However, when the reference stationary state has a flat top, it is known that resonances drastically weaken and the bifurcation becomes discontinuous. In this article we analyze one-dimensional spatially periodic Vlasov systems, using a combination of analytical tools and precise numerical simulations to demonstrate that this behavior is related to a codimension-two bifurcation, which we study in detail.
Collapse
Affiliation(s)
| | - Julien Barré
- Institut Denis Poisson, Université d'Orléans, Université de Tours and CNRS, 45067 Orléans, France
| |
Collapse
|
5
|
Sugimoto S, Hamazaki R, Ueda M. Eigenstate Thermalization in Long-Range Interacting Systems. PHYSICAL REVIEW LETTERS 2022; 129:030602. [PMID: 35905337 DOI: 10.1103/physrevlett.129.030602] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Revised: 03/27/2022] [Accepted: 06/16/2022] [Indexed: 05/16/2023]
Abstract
Motivated by recent ion experiments on tunable long-range interacting quantum systems [Neyenhuis et al., Sci. Adv. 3, e1700672 (2017)SACDAF2375-254810.1126/sciadv.1700672], we test the strong eigenstate thermalization hypothesis for systems with power-law interactions ∼1/r^{α}. We numerically demonstrate that the strong eigenstate thermalization hypothesis typically holds, at least for systems with α≥0.6, which include Coulomb, monopole-dipole, and dipole-dipole interactions. Compared with short-range interacting systems, the eigenstate expectation value of a generic local observable is shown to deviate significantly from its microcanonical ensemble average for long-range interacting systems. We find that Srednicki's ansatz breaks down for α≲1.0, at least for relatively large system sizes.
Collapse
Affiliation(s)
- Shoki Sugimoto
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Ryusuke Hamazaki
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
| | - Masahito Ueda
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| |
Collapse
|
6
|
Laha P, Slodička L, Moore DW, Filip R. Thermally induced entanglement of atomic oscillators. OPTICS EXPRESS 2022; 30:8814-8828. [PMID: 35299326 DOI: 10.1364/oe.449811] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2021] [Accepted: 02/14/2022] [Indexed: 06/14/2023]
Abstract
Laser cooled ions trapped in a linear Paul trap are long-standing ideal candidates for realizing quantum simulation, especially of many-body systems. The properties that contribute to this also provide the opportunity to demonstrate unexpected quantum phenomena in few-body systems. A pair of ions interacting in such traps exchange vibrational quanta through the Coulomb interaction. This linear interaction can be anharmonically modulated by an elementary coupling to the internal two-level structure of one of the ions. Driven by thermal energy in the passively coupled oscillators, which are themselves coupled to the internal ground states of the ions, the nonlinear interaction autonomously and unconditionally generates entanglement between the mechanical modes of the ions. We examine this counter-intuitive thermally induced entanglement for several experimentally feasible model systems and propose parameter regimes where state-of-the-art trapped ion systems can produce such phenomena. In addition, we demonstrate a multiqubit enhancement of such thermally induced entanglements.
Collapse
|
7
|
Quantum Computing With Trapped Ions: An Overview. IEEE NANOTECHNOLOGY MAGAZINE 2022. [DOI: 10.1109/mnano.2022.3175384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
|
8
|
Mazzanti M, Schüssler RX, Arias Espinoza JD, Wu Z, Gerritsma R, Safavi-Naini A. Trapped Ion Quantum Computing Using Optical Tweezers and Electric Fields. PHYSICAL REVIEW LETTERS 2021; 127:260502. [PMID: 35029474 DOI: 10.1103/physrevlett.127.260502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 11/09/2021] [Indexed: 06/14/2023]
Abstract
We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground-state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglement, and discuss the prospects of implementing the state-dependent tweezers in the laboratory.
Collapse
Affiliation(s)
- M Mazzanti
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands
| | - R X Schüssler
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands
| | - J D Arias Espinoza
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands
| | - Z Wu
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands
| | - R Gerritsma
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands
- QuSoft, Science Park 123, 1098 XG Amsterdam, Netherlands
| | - A Safavi-Naini
- QuSoft, Science Park 123, 1098 XG Amsterdam, Netherlands
- Institute for Theoretical Physics, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| |
Collapse
|
9
|
Tran QH, Nakajima K. Learning Temporal Quantum Tomography. PHYSICAL REVIEW LETTERS 2021; 127:260401. [PMID: 35029475 DOI: 10.1103/physrevlett.127.260401] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Revised: 10/11/2021] [Accepted: 11/30/2021] [Indexed: 05/26/2023]
Abstract
Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which requires a vast number of resources. However, tomography for a quantum device with temporal processing, which is fundamentally different from standard tomography, has not been formulated. We develop a practical and approximate tomography method using a recurrent machine learning framework for this intriguing situation. The method is based on repeated quantum interactions between a system called quantum reservoir with a stream of quantum states. Measurement data from the reservoir are connected to a linear readout to train a recurrent relation between quantum channels applied to the input stream. We demonstrate our algorithms for representative quantum learning tasks, followed by the proposal of a quantum memory capacity to evaluate the temporal processing ability of near-term quantum devices.
Collapse
Affiliation(s)
- Quoc Hoan Tran
- Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Kohei Nakajima
- Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
- Next Generation Artificial Intelligence Research Center, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
10
|
Lewis D, Benhemou A, Feinstein N, Banchi L, Bose S. Optimal Quantum Spatial Search with One-Dimensional Long-Range Interactions. PHYSICAL REVIEW LETTERS 2021; 126:240502. [PMID: 34213945 DOI: 10.1103/physrevlett.126.240502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Revised: 04/09/2021] [Accepted: 05/07/2021] [Indexed: 06/13/2023]
Abstract
Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in O(sqrt[n]) time for n entries. However, the capability of models found in nature is largely unexplored-e.g., in one dimension only nearest-neighbor Hamiltonians have been considered so far, for which the quadratic speedup does not exist. Here, we prove that optimal spatial search, namely with O(sqrt[n]) run time and high fidelity, is possible in one-dimensional spin chains with long-range interactions that decay as 1/r^{α} with distance r. In particular, near unit fidelity is achieved for α≈1 and, in the limit n→∞, we find a continuous transition from a region where optimal spatial search does exist (α<1.5) to where it does not (α>1.5). Numerically, we show that spatial search is robust to dephasing noise and that, for reasonable chain lengths, α≲1.2 should be sufficient to demonstrate optimal spatial search experimentally with near unit fidelity.
Collapse
Affiliation(s)
- Dylan Lewis
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Asmae Benhemou
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Natasha Feinstein
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Leonardo Banchi
- Department of Physics and Astronomy, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino (Florence), Italy
- INFN Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Florence), Italy
| | - Sougato Bose
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| |
Collapse
|
11
|
Kyprianidis A, Machado F, Morong W, Becker P, Collins KS, Else DV, Feng L, Hess PW, Nayak C, Pagano G, Yao NY, Monroe C. Observation of a prethermal discrete time crystal. Science 2021; 372:1192-1196. [PMID: 34112691 DOI: 10.1126/science.abg8102] [Citation(s) in RCA: 46] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2021] [Accepted: 04/30/2021] [Indexed: 11/02/2022]
Abstract
Extending the framework of statistical physics to the nonequilibrium setting has led to the discovery of previously unidentified phases of matter, often catalyzed by periodic driving. However, preventing the runaway heating that is associated with driving a strongly interacting quantum system remains a challenge in the investigation of these newly discovered phases. In this work, we utilize a trapped-ion quantum simulator to observe the signatures of a nonequilibrium driven phase without disorder-the prethermal discrete time crystal. Here, the heating problem is circumvented not by disorder-induced many-body localization, but rather by high-frequency driving, which leads to an expansive time window where nonequilibrium phases can emerge. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing, and studying intrinsically out-of-equilibrium phases of matter.
Collapse
Affiliation(s)
- A Kyprianidis
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.
| | - F Machado
- Department of Physics, University of California, Berkeley, CA 94720, USA.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - W Morong
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - P Becker
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - K S Collins
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - D V Else
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - L Feng
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - P W Hess
- Department of Physics, Middlebury College, Middlebury, VT 05753, USA
| | - C Nayak
- Microsoft Quantum, Station Q, Santa Barbara, CA 93106, USA.,Department of Physics, University of California, Santa Barbara, CA 93106, USA
| | - G Pagano
- Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA
| | - N Y Yao
- Department of Physics, University of California, Berkeley, CA 94720, USA.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - C Monroe
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| |
Collapse
|
12
|
Lewis-Swan RJ, Muleady SR, Rey AM. Detecting Out-of-Time-Order Correlations via Quasiadiabatic Echoes as a Tool to Reveal Quantum Coherence in Equilibrium Quantum Phase Transitions. PHYSICAL REVIEW LETTERS 2020; 125:240605. [PMID: 33412057 DOI: 10.1103/physrevlett.125.240605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 09/09/2020] [Accepted: 10/26/2020] [Indexed: 06/12/2023]
Abstract
We propose a new dynamical method to connect equilibrium quantum phase transitions and quantum coherence using out-of-time-order correlations (OTOCs). Adopting the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as illustrative examples, we show that an abrupt change in coherence and entanglement of the ground state across a quantum phase transition is observable in the spectrum of multiple quantum coherence intensities, which are a special type of OTOC. We also develop a robust protocol to obtain the relevant OTOCs using quasi-adiabatic quenches through the ground state phase diagram. Our scheme allows for the detection of OTOCs without time reversal of coherent dynamics, making it applicable and important for a broad range of current experiments where time reversal cannot be achieved by inverting the sign of the underlying Hamiltonian.
Collapse
Affiliation(s)
- R J Lewis-Swan
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - S R Muleady
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - A M Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| |
Collapse
|
13
|
Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator. Proc Natl Acad Sci U S A 2020; 117:25396-25401. [PMID: 33024018 PMCID: PMC7568299 DOI: 10.1073/pnas.2006373117] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Variational quantum algorithms combine quantum resources with classical optimization methods, providing a promising approach to solve both quantum many-body and classical optimization problems. A crucial question is how variational algorithms perform as a function of qubit number. Here, we address this question by applying a variational quantum algorithm (QAOA) to approximate the ground-state energy of a long-range Ising model, both quantum and classical, and investigating the algorithm performance on a trapped-ion quantum simulator with up to 40 qubits. A negligible performance degradation and almost constant runtime scaling is observed as a function of the number of qubits. By modeling the error sources, we explain the experimental performance, marking a stepping stone toward more general realizations of hybrid quantum–classical algorithms. Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.
Collapse
|
14
|
Gambetta FM, Zhang C, Hennrich M, Lesanovsky I, Li W. Long-Range Multibody Interactions and Three-Body Antiblockade in a Trapped Rydberg Ion Chain. PHYSICAL REVIEW LETTERS 2020; 125:133602. [PMID: 33034467 DOI: 10.1103/physrevlett.125.133602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Accepted: 08/27/2020] [Indexed: 06/11/2023]
Abstract
Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing that combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range and multibody interactions consisting of two, three, and four-body terms. Their shape, strength, and range can be controlled via the ion trap parameters and strongly depends on both the equilibrium configuration and vibrational modes of the ion crystal. By focusing on an experimentally feasible quasi one-dimensional setup of ^{88}Sr^{+} Rydberg ions, we demonstrate that multibody interactions are enhanced by the emergence of soft modes associated with, e.g., a structural phase transition. This has a striking impact on many-body electronic states and results-for example-in a three-body antiblockade effect that can be employed as a sensitive probe to detect structural phase transitions in Rydberg ion chains. Our study unveils the possibilities offered by trapped Rydberg ions for studying exotic phases of matter and quantum dynamics driven by enhanced multibody interactions.
Collapse
Affiliation(s)
- Filippo M Gambetta
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Chi Zhang
- Department of Physics, Stockholm University, 10691 Stockholm, Sweden
| | - Markus Hennrich
- Department of Physics, Stockholm University, 10691 Stockholm, Sweden
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Institut für Theoretische Physik, University of Tübingen, 72076 Tübingen, Germany
| | - Weibin Li
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
15
|
Kaplan HB, Guo L, Tan WL, De A, Marquardt F, Pagano G, Monroe C. Many-Body Dephasing in a Trapped-Ion Quantum Simulator. PHYSICAL REVIEW LETTERS 2020; 125:120605. [PMID: 33016720 DOI: 10.1103/physrevlett.125.120605] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Accepted: 08/20/2020] [Indexed: 06/11/2023]
Abstract
How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.
Collapse
Affiliation(s)
- Harvey B Kaplan
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Lingzhen Guo
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
| | - Wen Lin Tan
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Arinjoy De
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Florian Marquardt
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
- Physics Department, University of Erlangen-Nuremberg, Staudtstrasse 5, 91058 Erlangen, Germany
| | - Guido Pagano
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, Texas 77005, USA
| | - Christopher Monroe
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|
16
|
Puebla R, Smirne A, Huelga SF, Plenio MB. Universal Anti-Kibble-Zurek Scaling in Fully Connected Systems. PHYSICAL REVIEW LETTERS 2020; 124:230602. [PMID: 32603162 DOI: 10.1103/physrevlett.124.230602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Accepted: 05/21/2020] [Indexed: 06/11/2023]
Abstract
We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws break down and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus nonadiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of nonlinear ramps and finite-size systems.
Collapse
Affiliation(s)
- Ricardo Puebla
- Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Andrea Smirne
- Institute of Theoretical Physics and IQST, Albert-Einstein Allee 11, Universität Ulm, 89069 Ulm, Germany
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, e Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milan, Italy
| | - Susana F Huelga
- Institute of Theoretical Physics and IQST, Albert-Einstein Allee 11, Universität Ulm, 89069 Ulm, Germany
| | - Martin B Plenio
- Institute of Theoretical Physics and IQST, Albert-Einstein Allee 11, Universität Ulm, 89069 Ulm, Germany
| |
Collapse
|
17
|
Ivanov PA, Vitanov NV. Two-qubit quantum gate and entanglement protected by circulant symmetry. Sci Rep 2020; 10:5030. [PMID: 32193404 PMCID: PMC7081313 DOI: 10.1038/s41598-020-61766-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Accepted: 02/25/2020] [Indexed: 11/23/2022] Open
Abstract
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not depend on the magnitude of the Hamiltonian elements as long as the circulant symmetry is preserved. The QFT implementation relies on the adiabatic transition from each of the spin product states to the respective quantum Fourier superposition states. We show that in ion traps one can obtain a Hamiltonian with the circulant symmetry by tuning the spin-spin interaction between the trapped ions. We present numerical results which demonstrate that very high fidelity can be obtained with realistic experimental resources. We also describe how the gate can be accelerated by using a "shortcut-to-adiabaticity" field.
Collapse
Affiliation(s)
- Peter A Ivanov
- Department of Physics, St. Kliment Ohridski University of Sofia, James Bourchier 5 blvd, 1164, Sofia, Bulgaria.
| | - Nikolay V Vitanov
- Department of Physics, St. Kliment Ohridski University of Sofia, James Bourchier 5 blvd, 1164, Sofia, Bulgaria
| |
Collapse
|
18
|
Raghunandan M, Wolf F, Ospelkaus C, Schmidt PO, Weimer H. Initialization of quantum simulators by sympathetic cooling. SCIENCE ADVANCES 2020; 6:eaaw9268. [PMID: 32181335 PMCID: PMC7060053 DOI: 10.1126/sciadv.aaw9268] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/06/2019] [Accepted: 12/11/2019] [Indexed: 06/10/2023]
Abstract
Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.
Collapse
Affiliation(s)
- Meghana Raghunandan
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraβe 2, 30167 Hannover, Germany
| | - Fabian Wolf
- QUEST Institut, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Christian Ospelkaus
- QUEST Institut, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
| | - Piet O. Schmidt
- QUEST Institut, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraβe 2, 30167 Hannover, Germany
| |
Collapse
|
19
|
Plestid R, Lambert J. Quantum fluctuations inhibit symmetry breaking in the Hamiltonian mean-field model. Phys Rev E 2020; 101:012136. [PMID: 32069647 DOI: 10.1103/physreve.101.012136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2019] [Indexed: 11/07/2022]
Abstract
It is widely believed that mean-field theory is exact for a wide range of classical long-range interacting systems. Is this also true once quantum fluctuations have been accounted for? As a test case we study the Hamiltonian mean-field (HMF) model for a system of bosons which is predicted (according to mean-field theory) to undergo a second-order quantum phase transition at zero temperature. The ordered phase is characterized by a spontaneously broken O(2) symmetry, which, despite occurring in a one-dimensional model, is not ruled out by the Mermin-Wagner theorem due to the presence of long-range interactions. Nevertheless, a spontaneously broken symmetry implies gapless Goldstone modes whose large fluctuations can restore broken symmetries. In this work we study the influence of quantum fluctuations by projecting the Hamiltonian onto the continuous subspace of symmetry-breaking mean-field states. We find that the energetic cost of gradients in the center-of-mass wave function inhibits the breaking of the O(2) symmetry, but that the energetic cost is very small, scaling as O(1/N^{2}). Nevertheless, for any finite N, no matter how large, this implies that the ground state has a restored O(2) symmetry. Implications for the finite-temperature phases, as well as the classical limit, of the HMF model are discussed.
Collapse
Affiliation(s)
- Ryan Plestid
- Department of Physics & Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1.,Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5
| | - James Lambert
- Department of Physics & Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1
| |
Collapse
|
20
|
Zhang S, Lu Y, Zhang K, Chen W, Li Y, Zhang JN, Kim K. Error-mitigated quantum gates exceeding physical fidelities in a trapped-ion system. Nat Commun 2020; 11:587. [PMID: 32001680 PMCID: PMC6992797 DOI: 10.1038/s41467-020-14376-z] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2019] [Accepted: 12/13/2019] [Indexed: 11/22/2022] Open
Abstract
Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from being affordable for near-term technologies. To alleviate the detrimental effects of errors on the estimation of expectation values, quantum error mitigation techniques have been proposed, which require no additional qubit resources. Here we benchmark the performance of a quantum error mitigation technique based on probabilistic error cancellation in a trapped-ion system. Our results clearly show that effective gate fidelities exceed physical fidelities, i.e., we surpass the break-even point of eliminating gate errors, by programming quantum circuits. The error rates are effectively reduced from (1.10 ± 0.12) × 10−3 to (1.44 ± 5.28) × 10−5 and from (0.99 ± 0.06) × 10−2 to (0.96 ± 0.10) × 10−3 for single- and two-qubit gates, respectively. Our demonstration opens up the possibility of implementing high-fidelity computations on a near-term noisy quantum device. Quantum error mitigation promises to improve expectation values’ estimation without the resource overhead of quantum error correction. Here, the authors test probabilistic error cancellation using trapped ions, decreasing single- and two-qubit gates’ error rates by two and one order of magnitude respectively.
Collapse
Affiliation(s)
- Shuaining Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Yao Lu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Kuan Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.,MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Wentao Chen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Ying Li
- Graduate School of China Academy of Engineering Physics, Beijing, 100193, China.
| | - Jing-Ning Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China. .,Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
| | - Kihwan Kim
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.
| |
Collapse
|
21
|
Palmero M, Simón MÁ, Poletti D. Towards Generation of Cat States in Trapped Ions Set-Ups via FAQUAD Protocols and Dynamical Decoupling. ENTROPY 2019. [PMCID: PMC7514552 DOI: 10.3390/e21121207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The high fidelity generation of strongly entangled states of many particles, such as cat states, is a particularly demanding challenge. One approach is to drive the system, within a certain final time, as adiabatically as possible, in order to avoid the generation of unwanted excitations. However, excitations can also be generated by the presence of dissipative effects such as dephasing. Here we compare the effectiveness of Local Adiabatic and the FAst QUasi ADiabatic protocols in achieving a high fidelity for a target superposition state both with and without dephasing. In particular, we consider trapped ions set-ups in which each spin interacts with all the others with the uniform coupling strength or with a power-law coupling. In order to mitigate the effects of dephasing, we complement the adiabatic protocols with dynamical decoupling and we test its effectiveness. The protocols we study could be readily implemented with state-of-the-art techniques.
Collapse
Affiliation(s)
- Mikel Palmero
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
- Correspondence: (M.P.); (D.P.)
| | - Miguel Ángel Simón
- Departamento de Química-Física, Universidad del País Vasco UPV-EHU, B. Sarriena s/n, 48940 Leioa, Spain;
| | - Dario Poletti
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
- Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
- Correspondence: (M.P.); (D.P.)
| |
Collapse
|
22
|
Lu Y, Zhang S, Zhang K, Chen W, Shen Y, Zhang J, Zhang JN, Kim K. Global entangling gates on arbitrary ion qubits. Nature 2019; 572:363-367. [PMID: 31341282 DOI: 10.1038/s41586-019-1428-4] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2019] [Accepted: 05/10/2019] [Indexed: 11/09/2022]
Abstract
Quantum computers can efficiently solve classically intractable problems, such as the factorization of a large number1 and the simulation of quantum many-body systems2,3. Universal quantum computation can be simplified by decomposing circuits into single- and two-qubit entangling gates4, but such decomposition is not necessarily efficient. It has been suggested that polynomial or exponential speedups can be obtained with global N-qubit (N greater than two) entangling gates5-9. Such global gates involve all-to-all connectivity, which emerges among trapped-ion qubits when using laser-driven collective motional modes10-14, and have been implemented for a single motional mode15,16. However, the single-mode approach is difficult to scale up because isolating single modes becomes challenging as the number of ions increases in a single crystal, and multi-mode schemes are scalable17,18 but limited to pairwise gates19-23. Here we propose and implement a scalable scheme for realizing global entangling gates on multiple 171Yb+ ion qubits by coupling to multiple motional modes through modulated laser fields. Because such global gates require decoupling multiple modes and balancing all pairwise coupling strengths during the gate, we develop a system with fully independent control capability on each ion14. To demonstrate the usefulness and flexibility of these global gates, we generate a Greenberger-Horne-Zeilinger state with up to four qubits using a single global operation. Our approach realizes global entangling gates as scalable building blocks for universal quantum computation, motivating future research in scalable global methods for quantum information processing.
Collapse
Affiliation(s)
- Yao Lu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China.
| | - Shuaining Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
| | - Kuan Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China.,MOE Key Laboratory of Fundamental Physical Quantities Measurement & Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan, China
| | - Wentao Chen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
| | - Yangchao Shen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
| | - Jialiang Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
| | - Jing-Ning Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
| | - Kihwan Kim
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China.
| |
Collapse
|
23
|
Guo Y, Kroeze RM, Vaidya VD, Keeling J, Lev BL. Sign-Changing Photon-Mediated Atom Interactions in Multimode Cavity Quantum Electrodynamics. PHYSICAL REVIEW LETTERS 2019; 122:193601. [PMID: 31144918 DOI: 10.1103/physrevlett.122.193601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2018] [Indexed: 06/09/2023]
Abstract
Sign-changing interactions constitute a crucial ingredient in the creation of frustrated many-body systems such as spin glasses. We present here the demonstration of a photon-mediated sign-changing interaction between Bose-Einstein-condensed atoms in a confocal cavity. The interaction between two atoms is of an unusual, nonlocal form proportional to the cosine of the inner product of the atoms' position vectors. This interaction arises from the differing Gouy phase shifts of the cavity's degenerate modes. The interaction drives a nonequilibrium Dicke-type phase transition in the system leading to atomic checkerboard density-wave order. Because of the Gouy phase anomalies, the checkerboard pattern can assume either a sinelike or cosinelike character. This state is detected via the holographic imaging of the cavity's superradiant emission. Together with a companion paper [Y. Guo, V. D. Vaidya, R. M. Kroeze, R. A. Lunney, B. L. Lev, and J. Keeling, Emergent and broken symmetries of atomic self-organization arising from Gouy phases in multimode cavity QED, Phys. Rev. A 99, 053818 (2019)PLRAAN2469-992610.1103/PhysRevA.99.053818], we explore this interaction's influence on superradiant phase transitions in multimode cavities. Employing this interaction in cavity QED spin systems may enable the creation of artificial spin glasses and quantum neural networks.
Collapse
Affiliation(s)
- Yudan Guo
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Ronen M Kroeze
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Varun D Vaidya
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Jonathan Keeling
- SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS United Kingdom
| | - Benjamin L Lev
- Department of Physics, Stanford University, Stanford, California 94305, USA
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| |
Collapse
|
24
|
Kokail C, Maier C, van Bijnen R, Brydges T, Joshi MK, Jurcevic P, Muschik CA, Silvi P, Blatt R, Roos CF, Zoller P. Self-verifying variational quantum simulation of lattice models. Nature 2019; 569:355-360. [DOI: 10.1038/s41586-019-1177-4] [Citation(s) in RCA: 264] [Impact Index Per Article: 52.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2018] [Accepted: 03/21/2019] [Indexed: 11/09/2022]
|
25
|
Ge W, Sawyer BC, Britton JW, Jacobs K, Bollinger JJ, Foss-Feig M. Trapped Ion Quantum Information Processing with Squeezed Phonons. PHYSICAL REVIEW LETTERS 2019; 122:030501. [PMID: 30735427 DOI: 10.1103/physrevlett.122.030501] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2018] [Indexed: 06/09/2023]
Abstract
Trapped ions offer a pristine platform for quantum computation and simulation, but improving their coherence remains a crucial challenge. Here, we propose and analyze a new strategy to enhance the coherent interactions in trapped ion systems via parametric amplification of the ions' motion-by squeezing the collective motional modes (phonons), the spin-spin interactions they mediate can be significantly enhanced. We illustrate the power of this approach by showing how it can enhance collective spin states useful for quantum metrology, and how it can improve the speed and fidelity of two-qubit gates in multi-ion systems, important ingredients for scalable trapped ion quantum computation. Our results are also directly relevant to numerous other physical platforms in which spin interactions are mediated by bosons.
Collapse
Affiliation(s)
- Wenchao Ge
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- The Institute for Research in Electronics and Applied Physics (IREAP), College Park, Maryland 20740, USA
| | - Brian C Sawyer
- Georgia Tech Research Institute, Atlanta, Georgia 30332, USA
| | - Joseph W Britton
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - Kurt Jacobs
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA
- Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - John J Bollinger
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Michael Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|
26
|
Lang J, Frank B, Halimeh JC. Dynamical Quantum Phase Transitions: A Geometric Picture. PHYSICAL REVIEW LETTERS 2018; 121:130603. [PMID: 30312040 DOI: 10.1103/physrevlett.121.130603] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2018] [Revised: 08/01/2018] [Indexed: 06/08/2023]
Abstract
The Loschmidt echo is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model as an example, we show that this indeed is not the case and that a simple semiclassical approximation to systems well described by mean-field theory is, in fact, in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the postquench dynamics provided in Supplemental Material visualize this new point of view.
Collapse
Affiliation(s)
- Johannes Lang
- Physik Department, Technische Universität München, 85747 Garching, Germany
| | - Bernhard Frank
- Physik Department, Technische Universität München, 85747 Garching, Germany
| | - Jad C Halimeh
- Physik Department, Technische Universität München, 85747 Garching, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| |
Collapse
|
27
|
Yamaguchi YY, Kaneko K. Collective 1/f fluctuation by pseudo-Casimir-invariants. Phys Rev E 2018; 98:020201. [PMID: 30253593 DOI: 10.1103/physreve.98.020201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Indexed: 11/07/2022]
Abstract
In this study, we propose a universal scenario explaining the 1/f fluctuation, including pink noises, in Hamiltonian dynamical systems with many degrees of freedom under long-range interaction. In the thermodynamic limit, the dynamics of such systems can be described by the Vlasov equation, which has an infinite number of Casimir invariants. In a finite system, they become pseudoinvariants, which yield quasistationary states. The dynamics then exhibit slow motion over them, up to the timescale where the pseudo-Casimir-invariants are effective. Such long-time correlation leads to 1/f fluctuations of collective variables, as is confirmed by direct numerical simulations. The universality of this collective 1/f fluctuation is demonstrated by taking a variety of Hamiltonians and changing the range of interaction and number of particles.
Collapse
Affiliation(s)
- Yoshiyuki Y Yamaguchi
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - Kunihiko Kaneko
- Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| |
Collapse
|
28
|
Safavi-Naini A, Lewis-Swan RJ, Bohnet JG, Gärttner M, Gilmore KA, Jordan JE, Cohn J, Freericks JK, Rey AM, Bollinger JJ. Verification of a Many-Ion Simulator of the Dicke Model Through Slow Quenches across a Phase Transition. PHYSICAL REVIEW LETTERS 2018; 121:040503. [PMID: 30095931 DOI: 10.1103/physrevlett.121.040503] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2018] [Revised: 06/26/2018] [Indexed: 06/08/2023]
Abstract
We use a self-assembled two-dimensional Coulomb crystal of ∼70 ions in the presence of an external transverse field to engineer a simulator of the Dicke Hamiltonian, an iconic model in quantum optics which features a quantum phase transition between a superradiant (ferromagnetic) and a normal (paramagnetic) phase. We experimentally implement slow quenches across the quantum critical point and benchmark the dynamics and the performance of the simulator through extensive theory-experiment comparisons which show excellent agreement. The implementation of the Dicke model in fully controllable trapped ion arrays can open a path for the generation of highly entangled states useful for enhanced metrology and the observation of scrambling and quantum chaos in a many-body system.
Collapse
Affiliation(s)
- A Safavi-Naini
- JILA, NIST and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - R J Lewis-Swan
- JILA, NIST and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | | | - M Gärttner
- JILA, NIST and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | | | | | - J Cohn
- Department of Physics, Georgetown University, Washington, DC 20057, USA
| | - J K Freericks
- Department of Physics, Georgetown University, Washington, DC 20057, USA
| | - A M Rey
- JILA, NIST and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | | |
Collapse
|
29
|
Bayat A, Alkurtass B, Sodano P, Johannesson H, Bose S. Measurement Quench in Many-Body Systems. PHYSICAL REVIEW LETTERS 2018; 121:030601. [PMID: 30085809 DOI: 10.1103/physrevlett.121.030601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Revised: 05/09/2018] [Indexed: 06/08/2023]
Abstract
Measurement is one of the key concepts which discriminates classical and quantum physics. Unlike classical systems, a measurement on a quantum system typically alters it drastically as a result of wave function collapse. Here we suggest that this feature can be exploited for inducing quench dynamics in a many-body system while leaving its Hamiltonian unchanged. Importantly, by doing away with dedicated macroscopic devices for inducing a quench-using instead the indispensable measurement apparatus only-the protocol is expected to be easier to implement and more resilient against decoherence. By way of various case studies, we show that our scheme also has decisive advantages beyond reducing decoherence-for spectroscopy purposes and probing nonequilibrium scaling of critical and quantum impurity many-body systems.
Collapse
Affiliation(s)
- Abolfazl Bayat
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Bedoor Alkurtass
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
- Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia
| | - Pasquale Sodano
- International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal-RN, Brazil
| | - Henrik Johannesson
- Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden
- Beijing Computational Science Research Center, Beijing 100094, China
| | - Sougato Bose
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| |
Collapse
|
30
|
Yamaguchi YY, Doi Y. Low-frequency discrete breathers in long-range systems without on-site potential. Phys Rev E 2018; 97:062218. [PMID: 30011521 DOI: 10.1103/physreve.97.062218] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Indexed: 11/07/2022]
Abstract
A mechanism of long-range couplings is proposed to realize low-frequency discrete breathers without on-site potentials. The realization of such discrete breathers requires a gap below the band of linear eigenfrequencies. Under the periodic boundary condition of a one-dimensional lattice and the limit of large population, we show theoretically that the long-range couplings universally open the gap below the band irrespective of the coupling functions, while the short-range couplings cannot. The existence of the low-frequency discrete breathers, spatial localization, and stability are numerically analyzed from long range to short range.
Collapse
Affiliation(s)
- Yoshiyuki Y Yamaguchi
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - Yusuke Doi
- Department of Adaptive Machine Systems, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan
| |
Collapse
|
31
|
Plestid R, Mahon P, O'Dell DHJ. Violent relaxation in quantum fluids with long-range interactions. Phys Rev E 2018; 98:012112. [PMID: 30110820 DOI: 10.1103/physreve.98.012112] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Indexed: 06/08/2023]
Abstract
Violent relaxation is a process that occurs in systems with long-range interactions. It has the peculiar feature of dramatically amplifying small perturbations, and rather than driving the system to equilibrium, it instead leads to slowly evolving configurations known as quasistationary states that fall outside the standard paradigm of statistical mechanics. Violent relaxation was originally identified in gravity-driven stellar dynamics; here, we extend the theory into the quantum regime by developing a quantum version of the Hamiltonian mean field (HMF) model which exemplifies many of the generic properties of long-range interacting systems. The HMF model can either be viewed as describing particles interacting via a cosine potential, or equivalently as the kinetic XY model with infinite-range interactions, and its quantum fluid dynamics can be obtained from a generalized Gross-Pitaevskii equation. We show that singular caustics that form during violent relaxation are regulated by interference effects in a universal way described by Thom's catastrophe theory applied to waves and this leads to emergent length scales and timescales not present in the classical problem. In the deep quantum regime we find that violent relaxation is suppressed altogether by quantum zero-point motion. Our results are relevant to laboratory studies of self-organization in cold atomic gases with long-range interactions.
Collapse
Affiliation(s)
- Ryan Plestid
- Department of Physics and Astronomy, McMaster University, 1280 Main St. W. Hamilton, Ontario, Canada L8S 4M1
- Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario, Canada N2L 2Y5
| | - Perry Mahon
- Department of Physics and Astronomy, McMaster University, 1280 Main St. W. Hamilton, Ontario, Canada L8S 4M1
- Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7
| | - D H J O'Dell
- Department of Physics and Astronomy, McMaster University, 1280 Main St. W. Hamilton, Ontario, Canada L8S 4M1
| |
Collapse
|
32
|
Płodzień M, Sowiński T, Kokkelmans S. Simulating polaron biophysics with Rydberg atoms. Sci Rep 2018; 8:9247. [PMID: 29915263 PMCID: PMC6006159 DOI: 10.1038/s41598-018-27232-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Accepted: 05/23/2018] [Indexed: 11/17/2022] Open
Abstract
Transport of excitations along proteins can be formulated in a quantum physics context, based on the periodicity and vibrational modes of the structures. Numerically exact solutions of the corresponding equations are very challenging to obtain on classical computers. Approximate solutions based on the Davydov ansatz have demonstrated the possibility of stabilized solitonic excitations along the protein, however, experimentally these solutions have never been directly observed. Here we propose an alternative study of biophysical transport phenomena based on a quantum simulator composed of a chain of ultracold dressed Rydberg atoms, which allows for a direct observation of the Davydov phenomena. We show that there is an experimentally accessible range of parameters where the system directly mimics the Davydov equations and their solutions. Moreover, we show that such a quantum simulator has access to the regime in between the small and large polaron regimes, which cannot be described perturbatively.
Collapse
Affiliation(s)
- Marcin Płodzień
- Department of Applied Physics, Eindhoven University of Technology, PO Box 513, Eindhoven, 5600 MB, The Netherlands. .,Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Warsaw, PL-02668, Poland.
| | - Tomasz Sowiński
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Warsaw, PL-02668, Poland
| | - Servaas Kokkelmans
- Department of Applied Physics, Eindhoven University of Technology, PO Box 513, Eindhoven, 5600 MB, The Netherlands
| |
Collapse
|
33
|
Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 2018; 551:601-604. [PMID: 29189781 DOI: 10.1038/nature24654] [Citation(s) in RCA: 197] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Accepted: 10/20/2017] [Indexed: 12/23/2022]
Abstract
A quantum simulator is a type of quantum computer that controls the interactions between quantum bits (or qubits) in a way that can be mapped to certain quantum many-body problems. As it becomes possible to exert more control over larger numbers of qubits, such simulators will be able to tackle a wider range of problems, such as materials design and molecular modelling, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. Here we use a quantum simulator composed of up to 53 qubits to study non-equilibrium dynamics in the transverse-field Ising model with long-range interactions. We observe a dynamical phase transition after a sudden change of the Hamiltonian, in a regime in which conventional statistical mechanics does not apply. The qubits are represented by the spins of trapped ions, which can be prepared in various initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with an efficiency of nearly 99 per cent. Such high efficiency means that arbitrary many-body correlations between qubits can be measured in a single shot, enabling the dynamical phase transition to be probed directly and revealing computationally intractable features that rely on the long-range interactions and high connectivity between qubits.
Collapse
|
34
|
Zhang C, Luo Q, Cheng S, Bu Y. Unusual Indirect Nuclear Spin-Spin Exchange Coupling through Solvated Electron. J Phys Chem Lett 2018; 9:689-695. [PMID: 29369635 DOI: 10.1021/acs.jpclett.7b03249] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Solvated electrons have been found to exist in various media which also exhibit more intriguing properties such as superconductivity, nonlinear optical response, and so on. However, how they affect the nuclear spin properties has not been proven. In this work, we present the first detailed study on solvated-electron-triggered indirect nuclear spin-spin J-coupling using density functional theory calculations. Taking 19F as a probe, we verify the presence of unusual J couplings between two distant F atoms in HF-containing anionic clusters. These couplings occur "through solvated electron", rather than through conventional covalent bonds or space. Solvated electron can serve as an additional channel to efficiently realize long-range J-coupling between far separated nuclei because of its dispersivity and Rydberg character. The coupling magnitude strongly depends on the unique distribution of solvated electron and its second-order interaction with solvating HF units. This work provides novel insights into the mediating roles of electrons, possibly opening up potential applications based on weakly bound electrons.
Collapse
Affiliation(s)
- Changzhe Zhang
- School of Chemistry and Chemical Engineering, Shandong University , Jinan, 250100, People's Republic of China
| | - Qi Luo
- School of Chemistry and Chemical Engineering, Shandong University , Jinan, 250100, People's Republic of China
| | - Shibo Cheng
- School of Chemistry and Chemical Engineering, Shandong University , Jinan, 250100, People's Republic of China
| | - Yuxiang Bu
- School of Chemistry and Chemical Engineering, Shandong University , Jinan, 250100, People's Republic of China
| |
Collapse
|
35
|
Zhang X, Zhang K, Shen Y, Zhang S, Zhang JN, Yung MH, Casanova J, Pedernales JS, Lamata L, Solano E, Kim K. Experimental quantum simulation of fermion-antifermion scattering via boson exchange in a trapped ion. Nat Commun 2018; 9:195. [PMID: 29335446 PMCID: PMC5768889 DOI: 10.1038/s41467-017-02507-y] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2017] [Accepted: 12/06/2017] [Indexed: 11/09/2022] Open
Abstract
Quantum field theories describe a variety of fundamental phenomena in physics. However, their study often involves cumbersome numerical simulations. Quantum simulators, on the other hand, may outperform classical computational capacities due to their potential scalability. Here we report an experimental realization of a quantum simulation of fermion-antifermion scattering mediated by bosonic modes, using a multilevel trapped ion, which is a simplified model of fermion scattering in both perturbative and non-perturbative quantum electrodynamics. The simulated model exhibits prototypical features in quantum field theory including particle pair creation and annihilation, as well as self-energy interactions. These are experimentally observed by manipulating four internal levels of a 171Yb+ trapped ion, where we encode the fermionic modes, and two motional degrees of freedom that simulate the bosonic modes. Our experiment establishes an avenue towards the efficient implementation of field modes, which may prove useful in studies of quantum field theories including non-perturbative regimes.
Collapse
Affiliation(s)
- Xiang Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.,Department of Physics, Renmin University of China, Beijing, 100872, China
| | - Kuan Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Yangchao Shen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Shuaining Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Jing-Ning Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.
| | - Man-Hong Yung
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.,Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology of China, Shenzhen, 518055, China.,Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, 518055, China
| | - Jorge Casanova
- Institut für Theoretische Physik and IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany
| | - Julen S Pedernales
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain
| | - Lucas Lamata
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain
| | - Enrique Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain.,IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao, Spain.,Department of Physics, Shanghai University, 200444, Shanghai, China
| | - Kihwan Kim
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.
| |
Collapse
|
36
|
Leung PH, Landsman KA, Figgatt C, Linke NM, Monroe C, Brown KR. Robust 2-Qubit Gates in a Linear Ion Crystal Using a Frequency-Modulated Driving Force. PHYSICAL REVIEW LETTERS 2018; 120:020501. [PMID: 29376710 DOI: 10.1103/physrevlett.120.020501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Revised: 10/30/2017] [Indexed: 06/07/2023]
Abstract
In an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multiqubit logical gates. Any residual entanglement between the internal and motional states of the ions results in loss of fidelity, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated driving force to minimize such errors. In simulation, we obtained an optimized frequency-modulated 2-qubit gate that can suppress errors to less than 0.01% and is robust against frequency drifts over ±1 kHz. Experimentally, we have obtained a 2-qubit gate fidelity of 98.3(4)%, a state-of-the-art result for 2-qubit gates with five ions.
Collapse
Affiliation(s)
- Pak Hong Leung
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Kevin A Landsman
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Caroline Figgatt
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Norbert M Linke
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Christopher Monroe
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
- IonQ Inc., College Park, Maryland 20742, USA
| | - Kenneth R Brown
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- Schools of Chemistry and Biochemistry and Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| |
Collapse
|
37
|
Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions. Sci Rep 2018; 8:48. [PMID: 29311605 PMCID: PMC5758581 DOI: 10.1038/s41598-017-18505-5] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Accepted: 12/13/2017] [Indexed: 11/08/2022] Open
Abstract
The exactly solvable model of two indistinguishable quantum particles (bosons or fermions) confined in a one-dimensional harmonic trap and interacting via finite-range soft-core interaction is presented and many properties of the system are examined. Particularly, it is shown that independently on the potential range, in the strong interaction limit bosonic and fermionic solutions become degenerate. For sufficiently large ranges a specific crystallization appears in the system. The results are compared to predictions of the celebrated Busch et al. model and those obtained in the Tonks-Girardeau limit. The assumed inter-particle potential is very similar to the potential between ultra-cold dressed Rydberg atoms. Therefore, the model can be examined experimentally.
Collapse
|
38
|
Hess PW, Becker P, Kaplan HB, Kyprianidis A, Lee AC, Neyenhuis B, Pagano G, Richerme P, Senko C, Smith J, Tan WL, Zhang J, Monroe C. Non-thermalization in trapped atomic ion spin chains. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2017.0107. [PMID: 29084886 PMCID: PMC5665787 DOI: 10.1098/rsta.2017.0107] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/27/2017] [Indexed: 05/27/2023]
Abstract
Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
Collapse
Affiliation(s)
- P W Hess
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - P Becker
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - H B Kaplan
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - A Kyprianidis
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - A C Lee
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - B Neyenhuis
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - G Pagano
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - P Richerme
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - C Senko
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - J Smith
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - W L Tan
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - J Zhang
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - C Monroe
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| |
Collapse
|
39
|
Cerezo M, Rossignoli R, Canosa N, Ríos E. Factorization and Criticality in Finite XXZ Systems of Arbitrary Spin. PHYSICAL REVIEW LETTERS 2017; 119:220605. [PMID: 29286784 DOI: 10.1103/physrevlett.119.220605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Indexed: 06/07/2023]
Abstract
We analyze ground state (GS) factorization in general arrays of spins s_{i} with XXZ couplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GSs can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero-bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid for d-dimensional arrays. The definite magnetization-projected GSs at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization-compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.
Collapse
Affiliation(s)
- M Cerezo
- Instituto de Física de La Plata, CONICET, and Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata 1900, Argentina
| | - R Rossignoli
- Instituto de Física de La Plata, CONICET, and Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata 1900, Argentina
- Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CIC), La Plata 1900, Argentina
| | - N Canosa
- Instituto de Física de La Plata, CONICET, and Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata 1900, Argentina
| | - E Ríos
- Departamento de Ingeniería Química, Universidad Tecnológica Nacional, Facultad Regional Avellaneda, C.C. 1874, Argentina
| |
Collapse
|
40
|
Manovitz T, Rotem A, Shaniv R, Cohen I, Shapira Y, Akerman N, Retzker A, Ozeri R. Fast Dynamical Decoupling of the Mølmer-Sørensen Entangling Gate. PHYSICAL REVIEW LETTERS 2017; 119:220505. [PMID: 29286763 DOI: 10.1103/physrevlett.119.220505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Indexed: 06/07/2023]
Abstract
Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of sqrt[N], with N being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson-mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of π/2, independently of the number of pulses applied. We experimentally demonstrate the robustness of our entangling gate with fast dynamical decoupling to σ_{z} noise using ions in a Paul trap.
Collapse
Affiliation(s)
- Tom Manovitz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Amit Rotem
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Givat Ram, Israel
| | - Ravid Shaniv
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Itsik Cohen
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Givat Ram, Israel
| | - Yotam Shapira
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Nitzan Akerman
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Alex Retzker
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Givat Ram, Israel
| | - Roee Ozeri
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| |
Collapse
|
41
|
Jurcevic P, Shen H, Hauke P, Maier C, Brydges T, Hempel C, Lanyon BP, Heyl M, Blatt R, Roos CF. Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System. PHYSICAL REVIEW LETTERS 2017; 119:080501. [PMID: 28952773 DOI: 10.1103/physrevlett.119.080501] [Citation(s) in RCA: 85] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Indexed: 05/27/2023]
Abstract
The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
Collapse
Affiliation(s)
- P Jurcevic
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - H Shen
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
| | - P Hauke
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - C Maier
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - T Brydges
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - C Hempel
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
| | - B P Lanyon
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - M Heyl
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
- Physik Department, Technische Universität München, 85747 Garching, Germany
| | - R Blatt
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - C F Roos
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| |
Collapse
|
42
|
Neyenhuis B, Zhang J, Hess PW, Smith J, Lee AC, Richerme P, Gong ZX, Gorshkov AV, Monroe C. Observation of prethermalization in long-range interacting spin chains. SCIENCE ADVANCES 2017; 3:e1700672. [PMID: 28875166 PMCID: PMC5573308 DOI: 10.1126/sciadv.1700672] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Accepted: 08/01/2017] [Indexed: 05/16/2023]
Abstract
Although statistical mechanics describes thermal equilibrium states, these states may or may not emerge dynamically for a subsystem of an isolated quantum many-body system. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale, and instead relax to quasi-stationary prethermal states that can be described by statistical mechanics, when approximately conserved quantities are included in a generalized Gibbs ensemble (GGE). We experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse-field Ising Hamiltonian following a sudden quench. For sufficiently long-range interactions, the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. However, the prethermal state in this case cannot be described by a standard GGE; it rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.
Collapse
Affiliation(s)
- Brian Neyenhuis
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
- Corresponding author.
| | - Jiehang Zhang
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
- Corresponding author.
| | - Paul W. Hess
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - Jacob Smith
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - Aaron C. Lee
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - Phil Richerme
- Department of Physics, Indiana University, Bloomington, IN 47405, USA
| | - Zhe-Xuan Gong
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - Alexey V. Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - Christopher Monroe
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, MD 20742, USA
| |
Collapse
|
43
|
Observation of a discrete time crystal. Nature 2017; 543:217-220. [DOI: 10.1038/nature21413] [Citation(s) in RCA: 634] [Impact Index Per Article: 90.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2016] [Accepted: 01/10/2017] [Indexed: 11/08/2022]
|
44
|
Carrasco JA, Finkel F, González-López A, Rodríguez MA, Tempesta P. Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions. Phys Rev E 2016; 93:062103. [PMID: 27415204 DOI: 10.1103/physreve.93.062103] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Indexed: 11/07/2022]
Abstract
We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.
Collapse
Affiliation(s)
- José A Carrasco
- Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Federico Finkel
- Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Artemio González-López
- Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Miguel A Rodríguez
- Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Piergiulio Tempesta
- Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain.,Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), c/ Nicolás Cabrera 13-15, 28049 Madrid, Spain
| |
Collapse
|
45
|
Graß T, Raventós D, Juliá-Díaz B, Gogolin C, Lewenstein M. Quantum annealing for the number-partitioning problem using a tunable spin glass of ions. Nat Commun 2016; 7:11524. [PMID: 27230802 PMCID: PMC4894973 DOI: 10.1038/ncomms11524] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2015] [Accepted: 04/05/2016] [Indexed: 11/29/2022] Open
Abstract
Exploiting quantum properties to outperform classical ways of information processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in controllable quantum systems. Here we demonstrate that in a trapped ion setup, with present day technology, it is possible to realize a spin model of the Mattis-type that exhibits spin glass phases. Our method produces the glassy behaviour without the need for any disorder potential, just by controlling the detuning of the spin-phonon coupling. Applying a transverse field, the system can be used to benchmark quantum annealing strategies which aim at reaching the ground state of the spin glass starting from the paramagnetic phase. In the vicinity of a phonon resonance, the problem maps onto number partitioning, and instances which are difficult to address classically can be implemented. Spin models appear in several fields of physics and beyond, but solving many of them is a task for which no general efficient classical algorithm is known to exist. Here the authors demonstrate how a variety of spin glass models can be implemented and solved, via quantum simulation, in a system of trapped ions.
Collapse
Affiliation(s)
- Tobias Graß
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Avinguda Carl-Friedrich Gauss 2, Castelldefels 08860, Spain
| | - David Raventós
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Avinguda Carl-Friedrich Gauss 2, Castelldefels 08860, Spain
| | - Bruno Juliá-Díaz
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Avinguda Carl-Friedrich Gauss 2, Castelldefels 08860, Spain.,Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, Barcelona 08028, Spain.,Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, Barcelona 08028, Spain
| | - Christian Gogolin
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Avinguda Carl-Friedrich Gauss 2, Castelldefels 08860, Spain.,Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, Garching 85748, Germany
| | - Maciej Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Avinguda Carl-Friedrich Gauss 2, Castelldefels 08860, Spain.,ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluís Companys 23, Barcelona 08010, Spain
| |
Collapse
|
46
|
Marty O, Cramer M, Plenio MB. Practical Entanglement Estimation for Spin-System Quantum Simulators. PHYSICAL REVIEW LETTERS 2016; 116:105301. [PMID: 27015489 DOI: 10.1103/physrevlett.116.105301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Indexed: 06/05/2023]
Abstract
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focusing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and that may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the performance of routinely measured observables as quantitative entanglement witnesses. Possible applications include experimental studies of entanglement scaling in critical systems and the reliable benchmarking of quantum simulators.
Collapse
Affiliation(s)
- O Marty
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M Cramer
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M B Plenio
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| |
Collapse
|
47
|
Schmiegelow CT, Kaufmann H, Ruster T, Schulz J, Kaushal V, Hettrich M, Schmidt-Kaler F, Poschinger UG. Phase-Stable Free-Space Optical Lattices for Trapped Ions. PHYSICAL REVIEW LETTERS 2016; 116:033002. [PMID: 26849591 DOI: 10.1103/physrevlett.116.033002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Indexed: 06/05/2023]
Abstract
We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, and we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion position over the 157 μm range along the trap axis at accuracies of better than 6 nm.
Collapse
Affiliation(s)
- C T Schmiegelow
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - H Kaufmann
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - T Ruster
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - J Schulz
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - V Kaushal
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - M Hettrich
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - F Schmidt-Kaler
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - U G Poschinger
- Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| |
Collapse
|
48
|
Schulte M, Lörch N, Leroux ID, Schmidt PO, Hammerer K. Quantum Algorithmic Readout in Multi-Ion Clocks. PHYSICAL REVIEW LETTERS 2016; 116:013002. [PMID: 26799016 DOI: 10.1103/physrevlett.116.013002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2015] [Indexed: 06/05/2023]
Abstract
Optical clocks based on ensembles of trapped ions promise record frequency accuracy with good short-term stability. Most suitable ion species lack closed transitions, so the clock signal must be read out indirectly by transferring the quantum state of the clock ions to cotrapped logic ions of a different species. Existing methods of quantum logic readout require a linear overhead in either time or the number of logic ions. Here we describe a quantum algorithmic readout whose overhead scales logarithmically with the number of clock ions in both of these respects. The scheme allows a quantum nondemolition readout of the number of excited clock ions using a single multispecies gate operation which can also be used in other areas of ion trap technology such as quantum information processing, quantum simulations, metrology, and precision spectroscopy.
Collapse
Affiliation(s)
- M Schulte
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover, Callinstrasse 38, 30167 Hannover, Germany
| | - N Lörch
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover, Callinstrasse 38, 30167 Hannover, Germany
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - I D Leroux
- QUEST Institut, Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
| | - P O Schmidt
- QUEST Institut, Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
- Institute for Quantum Optics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany
| | - K Hammerer
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover, Callinstrasse 38, 30167 Hannover, Germany
| |
Collapse
|
49
|
Zhang G, Song Z. Topological Characterization of Extended Quantum Ising Models. PHYSICAL REVIEW LETTERS 2015; 115:177204. [PMID: 26551140 DOI: 10.1103/physrevlett.115.177204] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Indexed: 06/05/2023]
Abstract
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.
Collapse
Affiliation(s)
- G Zhang
- School of Physics, Nankai University, Tianjin 300071, China
| | - Z Song
- School of Physics, Nankai University, Tianjin 300071, China
| |
Collapse
|
50
|
Green TJ, Biercuk MJ. Phase-modulated decoupling and error suppression in qubit-oscillator systems. PHYSICAL REVIEW LETTERS 2015; 114:120502. [PMID: 25860726 DOI: 10.1103/physrevlett.114.120502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2014] [Indexed: 06/04/2023]
Abstract
We present a scheme designed to suppress the dominant source of infidelity in entangling gates between quantum systems coupled through intermediate bosonic oscillator modes. Such systems are particularly susceptible to residual qubit-oscillator entanglement at the conclusion of a gate period that reduces the fidelity of the target entangling operation. We demonstrate how the exclusive use of discrete shifts in the phase of the field moderating the qubit-oscillator interaction is sufficient to both ensure multiple oscillator modes are decoupled and to suppress the effects of fluctuations in the driving field. This approach is amenable to a wide variety of technical implementations including geometric phase gates in superconducting qubits and the Molmer-Sorensen gate for trapped ions. We present detailed example protocols tailored to trapped-ion experiments and demonstrate that our approach has the potential to enable multiqubit gate implementation with a significant reduction in technical complexity relative to previously demonstrated protocols.
Collapse
Affiliation(s)
- Todd J Green
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, New South Wales 2006 Australia
| | - Michael J Biercuk
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, New South Wales 2006 Australia
| |
Collapse
|