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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.03801">arXiv:2408.03801</a> <span> [<a href="https://arxiv.org/pdf/2408.03801">pdf</a>, <a href="https://arxiv.org/format/2408.03801">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Hamiltonian learning for 300 trapped ion qubits with long-range couplings </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Guo%2C+S+-">S. -A. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Ye%2C+J">J. Ye</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+L">L. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Lian%2C+W+-">W. -Q. Lian</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+R">R. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y+-">Y. -L. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+C">C. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y+-">Y. -Z. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Hou%2C+P+-">P. -Y. Hou</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.03801v1-abstract-short" style="display: inline;"> Quantum simulators with hundreds of qubits and engineerable Hamiltonians have the potential to explore quantum many-body models that are intractable for classical computers. However, learning the simulated Hamiltonian, a prerequisite for any applications of a quantum simulator, remains an outstanding challenge due to the fast increasing time cost with the qubit number and the lack of high-fidelity… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03801v1-abstract-full').style.display = 'inline'; document.getElementById('2408.03801v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.03801v1-abstract-full" style="display: none;"> Quantum simulators with hundreds of qubits and engineerable Hamiltonians have the potential to explore quantum many-body models that are intractable for classical computers. However, learning the simulated Hamiltonian, a prerequisite for any applications of a quantum simulator, remains an outstanding challenge due to the fast increasing time cost with the qubit number and the lack of high-fidelity universal gate operations in the noisy intermediate-scale quantum era. Here we demonstrate the Hamiltonian learning of a two-dimensional ion trap quantum simulator with 300 qubits. We employ global manipulations and single-qubit-resolved state detection to efficiently learn the all-to-all-coupled Ising model Hamiltonian, with the required quantum resources scaling at most linearly with the qubit number. Our work paves the way for wide applications of large-scale ion trap quantum simulators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03801v1-abstract-full').style.display = 'none'; document.getElementById('2408.03801v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.13999">arXiv:2406.13999</a> <span> [<a href="https://arxiv.org/pdf/2406.13999">pdf</a>, <a href="https://arxiv.org/format/2406.13999">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Individually Addressed Entangling Gates in a Two-Dimensional Ion Crystal </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Hou%2C+Y+-">Y. -H. Hou</a>, <a href="/search/quant-ph?searchtype=author&query=Yi%2C+Y+-">Y. -J. Yi</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Y+-">Y. -Y. Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+L">L. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y+-">Y. -L. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+C">C. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Yang%2C+H+-">H. -X. Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Ma%2C+J+-">J. -Y. Ma</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+S+-">S. -A. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Ye%2C+J">J. Ye</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Hou%2C+P+-">P. -Y. Hou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.13999v1-abstract-short" style="display: inline;"> Two-dimensional (2D) ion crystals have become a promising way to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. He… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.13999v1-abstract-full').style.display = 'inline'; document.getElementById('2406.13999v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.13999v1-abstract-full" style="display: none;"> Two-dimensional (2D) ion crystals have become a promising way to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates between any ion pairs in a 2D crystal of four ions. We use symmetrically placed crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve an addressing crosstalk error below 0.1%. We design and demonstrate a gate sequence by alternatingly addressing two target ions, making it compatible with any single-ion addressing techniques without crosstalk from multiple addressing beams. We further examine the gate performance versus the micromotion amplitude of the ions and show that its effect can be compensated by a recalibration of the laser intensity without degrading the gate fidelity. Our work paves the way for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion crystal. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.13999v1-abstract-full').style.display = 'none'; document.getElementById('2406.13999v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.13369">arXiv:2405.13369</a> <span> [<a href="https://arxiv.org/pdf/2405.13369">pdf</a>, <a href="https://arxiv.org/format/2405.13369">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Realization of a crosstalk-free multi-ion node for long-distance quantum networking </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lai%2C+P+-">P. -C. Lai</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Shi%2C+J+-">J. -X. Shi</a>, <a href="/search/quant-ph?searchtype=author&query=Cui%2C+Z+-">Z. -B. Cui</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Z+-">Z. -Q. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+S">S. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+P+-">P. -Y. Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Tian%2C+Z+-">Z. -C. Tian</a>, <a href="/search/quant-ph?searchtype=author&query=Sun%2C+Y+-">Y. -D. Sun</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+X+-">X. -Y. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+Y+-">Y. -Y. Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y">Y. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Pu%2C+Y+-">Y. -F. Pu</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.13369v1-abstract-short" style="display: inline;"> Trapped atomic ions constitute one of the leading physical platforms for building the quantum repeater nodes to realize large-scale quantum networks. In a long-distance trapped-ion quantum network, it is essential to have crosstalk-free dual-type qubits: one type, called the communication qubit, to establish entangling interface with telecom photons; and the other type, called the memory qubit, to… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.13369v1-abstract-full').style.display = 'inline'; document.getElementById('2405.13369v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.13369v1-abstract-full" style="display: none;"> Trapped atomic ions constitute one of the leading physical platforms for building the quantum repeater nodes to realize large-scale quantum networks. In a long-distance trapped-ion quantum network, it is essential to have crosstalk-free dual-type qubits: one type, called the communication qubit, to establish entangling interface with telecom photons; and the other type, called the memory qubit, to store quantum information immune from photon scattering under entangling attempts. Here, we report the first experimental implementation of a telecom-compatible and crosstalk-free quantum network node based on two trapped $^{40}$Ca$^{+}$ ions. The memory qubit is encoded on a long-lived metastable level to avoid crosstalk with the communication qubit encoded in another subspace of the same ion species, and a quantum wavelength conversion module is employed to generate ion-photon entanglement over a $12\,$km fiber in a heralded style. Our work therefore constitutes an important step towards the realization of quantum repeaters and long-distance quantum networks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.13369v1-abstract-full').style.display = 'none'; document.getElementById('2405.13369v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 12 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2402.07461">arXiv:2402.07461</a> <span> [<a href="https://arxiv.org/pdf/2402.07461">pdf</a>, <a href="https://arxiv.org/format/2402.07461">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Simulating the spin-boson model with a controllable reservoir in an ion trap </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Wang%2C+G+-">G. -X. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+R">R. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Lian%2C+W+-">W. -Q. Lian</a>, <a href="/search/quant-ph?searchtype=author&query=Cheng%2C+Z+-">Z. -J. Cheng</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y+-">Y. -L. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+C">C. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+Y">Y. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y+-">Y. -Z. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Hou%2C+P+-">P. -Y. Hou</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2402.07461v1-abstract-short" style="display: inline;"> The spin-boson model is a prototypical model for open quantum dynamics. Here we simulate the spin-boson model using a chain of trapped ions where a spin is coupled to a structured reservoir of bosonic modes. We engineer the spectral density of the reservoir by adjusting the ion number, the target ion location, the laser detuning to the phonon sidebands, and the number of frequency components in th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.07461v1-abstract-full').style.display = 'inline'; document.getElementById('2402.07461v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2402.07461v1-abstract-full" style="display: none;"> The spin-boson model is a prototypical model for open quantum dynamics. Here we simulate the spin-boson model using a chain of trapped ions where a spin is coupled to a structured reservoir of bosonic modes. We engineer the spectral density of the reservoir by adjusting the ion number, the target ion location, the laser detuning to the phonon sidebands, and the number of frequency components in the laser, and we observe their effects on the collapse and revival of the initially encoded information. Our work demonstrates the ion trap as a powerful platform for simulating open quantum dynamics with complicated reservoir structures. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.07461v1-abstract-full').style.display = 'none'; document.getElementById('2402.07461v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.17163">arXiv:2311.17163</a> <span> [<a href="https://arxiv.org/pdf/2311.17163">pdf</a>, <a href="https://arxiv.org/format/2311.17163">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> A Site-Resolved 2D Quantum Simulator with Hundreds of Trapped Ions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Guo%2C+S+-">S. -A. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Ye%2C+J">J. Ye</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+L">L. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Lian%2C+W+-">W. -Q. Lian</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+R">R. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Yan%2C+R+-">R. -Y. Yan</a>, <a href="/search/quant-ph?searchtype=author&query=Yi%2C+Y+-">Y. -J. Yi</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y+-">Y. -L. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+B+-">B. -W. Li</a>, <a href="/search/quant-ph?searchtype=author&query=Hou%2C+Y+-">Y. -H. Hou</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y+-">Y. -Z. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+W+-">W. -X. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+C">C. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2311.17163v2-abstract-short" style="display: inline;"> A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation. As one of the leading physical platforms for quantum information processing, the ion trap has achieved quantum simulation of tens of ions with site-resolved readout in 1D Paul trap, and that of hundreds of ions with global observables in 2D Penning trap. Howeve… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.17163v2-abstract-full').style.display = 'inline'; document.getElementById('2311.17163v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.17163v2-abstract-full" style="display: none;"> A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation. As one of the leading physical platforms for quantum information processing, the ion trap has achieved quantum simulation of tens of ions with site-resolved readout in 1D Paul trap, and that of hundreds of ions with global observables in 2D Penning trap. 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 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 NISQ algorithms using 2D ion trap quantum simulators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.17163v2-abstract-full').style.display = 'none'; document.getElementById('2311.17163v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.14405">arXiv:2306.14405</a> <span> [<a href="https://arxiv.org/pdf/2306.14405">pdf</a>, <a href="https://arxiv.org/format/2306.14405">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Realization of a crosstalk-avoided quantum network node with dual-type qubits by the same ion species </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Feng%2C+L">L. Feng</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+Y+-">Y. -Y Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+W+-">W. -X. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Ma%2C+J+-">J. -Y. Ma</a>, <a href="/search/quant-ph?searchtype=author&query=Yang%2C+H+-">H. -X. Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+L">L. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+C+-">C. -X. Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+C">C. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Pu%2C+Y+-">Y. -F. Pu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.14405v2-abstract-short" style="display: inline;"> Generating ion-photon entanglement is a crucial step for scalable trapped-ion quantum networks. To avoid the crosstalk on memory qubits carrying quantum information, it is common to use a different ion species for ion-photon entanglement generation such that the scattered photons are far off-resonant for the memory qubits. However, such a dual-species scheme requires elaborate control of the porti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14405v2-abstract-full').style.display = 'inline'; document.getElementById('2306.14405v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.14405v2-abstract-full" style="display: none;"> Generating ion-photon entanglement is a crucial step for scalable trapped-ion quantum networks. To avoid the crosstalk on memory qubits carrying quantum information, it is common to use a different ion species for ion-photon entanglement generation such that the scattered photons are far off-resonant for the memory qubits. However, such a dual-species scheme requires elaborate control of the portion and the location of different ion species, and can be subject to inefficient sympathetic cooling. Here we demonstrate a trapped-ion quantum network node in the dual-type qubit scheme where two types of qubits are encoded in the $S$ and $F$ hyperfine structure levels of ${}^{171}\mathrm{Yb}^+$ ions. We generate ion photon entanglement for the $S$-qubit in a typical timescale of hundreds of milliseconds, and verify its small crosstalk on a nearby $F$-qubit with coherence time above seconds. Our work demonstrates an enabling function of the dual-type qubit scheme for scalable quantum networks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14405v2-abstract-full').style.display = 'none'; document.getElementById('2306.14405v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.15459">arXiv:2209.15459</a> <span> [<a href="https://arxiv.org/pdf/2209.15459">pdf</a>, <a href="https://arxiv.org/format/2209.15459">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.106.062617">10.1103/PhysRevA.106.062617 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Experimental realization of a 218-ion multi-qubit quantum memory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Yao%2C+R">R. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Lian%2C+W+-">W. -Q. Lian</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+G+-">G. -X. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+B+-">B. -W. Li</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.15459v1-abstract-short" style="display: inline;"> Storage lifetime and capacity are two important factors to characterize the performance of a quantum memory. Here we report the stable trapping of above 200 ions in a cryogenic setup, and demonstrate the combination of the multi-qubit capacity and long storage lifetime by measuring the coherence time of randomly chosen ions to be on the order of hundreds of milliseconds. We apply composite microwa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.15459v1-abstract-full').style.display = 'inline'; document.getElementById('2209.15459v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.15459v1-abstract-full" style="display: none;"> Storage lifetime and capacity are two important factors to characterize the performance of a quantum memory. Here we report the stable trapping of above 200 ions in a cryogenic setup, and demonstrate the combination of the multi-qubit capacity and long storage lifetime by measuring the coherence time of randomly chosen ions to be on the order of hundreds of milliseconds. We apply composite microwave pulses to manipulate qubit states globally for efficient characterization of different storage units simultaneously, and we compare the performance of the quantum memory with and without the sympathetic cooling laser, thus unambiguously show the necessity of sympathetic cooling for the long-time storage of multiple ionic qubits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.15459v1-abstract-full').style.display = 'none'; document.getElementById('2209.15459v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.03060">arXiv:2208.03060</a> <span> [<a href="https://arxiv.org/pdf/2208.03060">pdf</a>, <a href="https://arxiv.org/format/2208.03060">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Probing critical behavior of long-range transverse-field Ising model through quantum Kibble-Zurek mechanism </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Li%2C+B+-">B. -W. Li</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+R">R. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Lian%2C+W+-">W. -Q. Lian</a>, <a href="/search/quant-ph?searchtype=author&query=Cai%2C+M+-">M. -L. Cai</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.03060v2-abstract-short" style="display: inline;"> The trapped ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions. In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena such as quantum phase transition, localization, thermalization and information propagation. For near-term practical usage, a c… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.03060v2-abstract-full').style.display = 'inline'; document.getElementById('2208.03060v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.03060v2-abstract-full" style="display: none;"> The trapped ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions. In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena such as quantum phase transition, localization, thermalization and information propagation. For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters. Here we report the quantum simulation of a long-range transverse-field Ising model using up to 61 ions and probe the critical behavior of its quantum phase transition through the Kibble-Zurek mechanism. By calibrating and verifying the coupling coefficients, we realize the same model for increasing ion numbers, so as to extract a critical exponent free of the finite size effect. For ferromagnetic interaction, our experimental result agrees well with the previous numerical predictions. As for the anti-ferromagnetic case, signals are too weak to fit a critical exponent due to the frustration in the interaction, but still consistent with the theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.03060v2-abstract-full').style.display = 'none'; document.getElementById('2208.03060v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.15529">arXiv:2205.15529</a> <span> [<a href="https://arxiv.org/pdf/2205.15529">pdf</a>, <a href="https://arxiv.org/format/2205.15529">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.129.140501">10.1103/PhysRevLett.129.140501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observation of Non-Markovian Spin Dynamics in a Jaynes-Cummings-Hubbard Model using a Trapped-Ion Quantum Simulator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Li%2C+B+-">B. -W. Li</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Cai%2C+M+-">M. -L. Cai</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.15529v1-abstract-short" style="display: inline;"> Jaynes-Cummings-Hubbard (JCH) model is a fundamental many-body model for light-matter interaction. As a leading platform for quantum simulation, the trapped ion system has realized the JCH model for two to three ions. Here we report the quantum simulation of the JCH model using up to 32 ions. We verify the simulation results even for large ion numbers by engineering low excitations and thus low ef… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.15529v1-abstract-full').style.display = 'inline'; document.getElementById('2205.15529v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.15529v1-abstract-full" style="display: none;"> Jaynes-Cummings-Hubbard (JCH) model is a fundamental many-body model for light-matter interaction. As a leading platform for quantum simulation, the trapped ion system has realized the JCH model for two to three ions. Here we report the quantum simulation of the JCH model using up to 32 ions. We verify the simulation results even for large ion numbers by engineering low excitations and thus low effective dimensions; then we extend to 32 excitations for an effective dimension of $2^{77}$, which is difficult for classical computers. By regarding the phonon modes as baths, we explore Markovian or non-Markovian spin dynamics in different parameter regimes of the JCH model, similar to quantum emitters in a structured photonic environment. We further examine the dependence of the non-Markovian dynamics on the effective Hilbert space dimension. Our work demonstrates the trapped ion system as a powerful quantum simulator for many-body physics and open quantum systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.15529v1-abstract-full').style.display = 'none'; document.getElementById('2205.15529v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 129, 140501 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.14860">arXiv:2205.14860</a> <span> [<a href="https://arxiv.org/pdf/2205.14860">pdf</a>, <a href="https://arxiv.org/format/2205.14860">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41467-022-31058-0">10.1038/s41467-022-31058-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observation of Supersymmetry and its Spontaneous Breaking in a Trapped Ion Quantum Simulator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cai%2C+M+-">M. -L. Cai</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Zhao%2C+W+-">W. -D. Zhao</a>, <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+Y">Y. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.14860v1-abstract-short" style="display: inline;"> Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.14860v1-abstract-full').style.display = 'inline'; document.getElementById('2205.14860v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.14860v1-abstract-full" style="display: none;"> Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.14860v1-abstract-full').style.display = 'none'; document.getElementById('2205.14860v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature Communications volume 13, Article number: 3412 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.14038">arXiv:2205.14038</a> <span> [<a href="https://arxiv.org/pdf/2205.14038">pdf</a>, <a href="https://arxiv.org/format/2205.14038">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.128.200502">10.1103/PhysRevLett.128.200502 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Simulation of the Two-Dimensional Weyl Equation in a Magnetic Field </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+Y">Y. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Cai%2C+M+-">M. -L. Cai</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Zhao%2C+W+-">W. -D. Zhao</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+X+-">X. -Y. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.14038v1-abstract-short" style="display: inline;"> Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain unexplored. Here we simulate the dynamics of a 2D Weyl particle. We show the linear dispersion relation of the free particle and the discrete Landau levels in a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.14038v1-abstract-full').style.display = 'inline'; document.getElementById('2205.14038v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.14038v1-abstract-full" style="display: none;"> Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain unexplored. Here we simulate the dynamics of a 2D Weyl particle. We show the linear dispersion relation of the free particle and the discrete Landau levels in a magnetic field, and we explicitly measure the spatial and spin dynamics from which the conservation of helicity and properties of antiparticles can be verified. Our work extends the application of an ion trap quantum simulator in particle physics with the additional spatial and spin degrees of freedom. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.14038v1-abstract-full').style.display = 'none'; document.getElementById('2205.14038v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review Letters 128, 200502 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2202.03690">arXiv:2202.03690</a> <span> [<a href="https://arxiv.org/pdf/2202.03690">pdf</a>, <a href="https://arxiv.org/format/2202.03690">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0256-307X/39/2/020502">10.1088/0256-307X/39/2/020502 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Probing a dissipative phase transition with a trapped ion through reservoir engineering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cai%2C+M+-">M. -L. Cai</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+Z+-">Z. -D. Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+Y">Y. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Zhao%2C+W+-">W. -D. Zhao</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+X">X. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2202.03690v1-abstract-short" style="display: inline;"> Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources both in quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the io… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03690v1-abstract-full').style.display = 'inline'; document.getElementById('2202.03690v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2202.03690v1-abstract-full" style="display: none;"> Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources both in quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion's spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average phonon number of the oscillation mode is used as the order parameter to provide evidence for the DPT. Our work highlights the suitability of trapped ions for simulating open quantum systems and shall facilitate further investigations of DPT with various dissipation terms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03690v1-abstract-full').style.display = 'none'; document.getElementById('2202.03690v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Chin. Phys. Lett. 2022, 39 (2): 020502 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.09234">arXiv:2201.09234</a> <span> [<a href="https://arxiv.org/pdf/2201.09234">pdf</a>, <a href="https://arxiv.org/format/2201.09234">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s42005-022-01001-2">10.1038/s42005-022-01001-2 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observation of topological Euler insulators with a trapped-ion quantum simulator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhao%2C+W+-">W. -D. Zhao</a>, <a href="/search/quant-ph?searchtype=author&query=Yang%2C+Y+-">Y. -B. Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+Y">Y. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Mao%2C+Z+-">Z. -C. Mao</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+W+-">W. -X. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Qiu%2C+L+-">L. -Y. Qiu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+G+-">G. -X. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y">Y. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.09234v1-abstract-short" style="display: inline;"> Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.09234v1-abstract-full').style.display = 'inline'; document.getElementById('2201.09234v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.09234v1-abstract-full" style="display: none;"> Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and higher-order topology. However, as a minimum model of fragile topology, the two-dimensional topological Euler insulator consisting of three bands remains a significant challenge to be implemented in experiments. Here, we experimentally realize a three-band Hamiltonian to simulate a topological Euler insulator with a trapped-ion quantum simulator. Through quantum state tomography, we successfully evaluate the Euler class, Wilson loop flow and entanglement spectra to show the topological properties of the Hamiltonian. We also measure the Berry phases of the lowest energy band, illustrating the existence of four crossing points protected by the Euler class. The flexibility of the trapped-ion quantum simulator further allows us to probe dynamical topological features including skyrmion-antiskyrmion pairs and Hopf links in momentum-time space from quench dynamics. Our results show the advantage of quantum simulation technologies for studying exotic topological phases and open a new avenue for investigating fragile topological phases in experiments. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.09234v1-abstract-full').style.display = 'none'; document.getElementById('2201.09234v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages including appendixes, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Commun Phys 5, 223 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.14906">arXiv:2106.14906</a> <span> [<a href="https://arxiv.org/pdf/2106.14906">pdf</a>, <a href="https://arxiv.org/format/2106.14906">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41567-022-01661-5">10.1038/s41567-022-01661-5 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Realizing coherently convertible dual-type qubits with the same ion species </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Yang%2C+H+-">H. -X. Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Ma%2C+J+-">J. -Y. Ma</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Cao%2C+M+-">M. -M. Cao</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+W+-">W. -X. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+Y+-">Y. -Y. Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Feng%2C+L">L. Feng</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.14906v1-abstract-short" style="display: inline;"> Trapped ions constitute one of the most promising systems for implementing quantum computing and networking. For large-scale ion-trap-based quantum computers and networks, it is critical to have two types of qubits, one for computation and storage, while the other for auxiliary operations like runtime qubit detection, sympathetic cooling, and repetitive entanglement generation through photon links… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.14906v1-abstract-full').style.display = 'inline'; document.getElementById('2106.14906v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.14906v1-abstract-full" style="display: none;"> Trapped ions constitute one of the most promising systems for implementing quantum computing and networking. For large-scale ion-trap-based quantum computers and networks, it is critical to have two types of qubits, one for computation and storage, while the other for auxiliary operations like runtime qubit detection, sympathetic cooling, and repetitive entanglement generation through photon links. Dual-type qubits have previously been realized in hybrid systems using two ion species, which, however, introduces significant experimental challenges for laser setup, gate operations as well as the control of the fraction and positioning of each qubit type within an ion crystal. Here we solve these problems by implementing two coherently-convertible qubit types using the same ion species. We encode the qubits into two pairs of clock states of the 171Yb+ ions, and achieve fast and high-fidelity conversion between the two types using narrow-band lasers. We further demonstrate that operations on one qubit type, including sympathetic laser cooling, gates and qubit detection, have crosstalk errors less than 0.03% on the other type, well below the error threshold for fault-tolerant quantum computing. Our work showcases the feasibility and advantages of using coherently convertible dual-type qubits with the same ion species for future large-scale quantum computing and networking. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.14906v1-abstract-full').style.display = 'none'; document.getElementById('2106.14906v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nat. Phys. 2022 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.05409">arXiv:2102.05409</a> <span> [<a href="https://arxiv.org/pdf/2102.05409">pdf</a>, <a href="https://arxiv.org/format/2102.05409">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41467-021-21425-8">10.1038/s41467-021-21425-8 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cai%2C+M+-">M. -L. Cai</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+Z+-">Z. -D. Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhao%2C+W+-">W. -D. Zhao</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Mei%2C+Q+-">Q. -X. Mei</a>, <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+Y">Y. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+L">L. He</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+X">X. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2102.05409v1-abstract-short" style="display: inline;"> Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the control parameter of the Hamiltonian is scanned across a quantum critical point. Recently it has been realized that a QPT can also occur in a simple system comp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.05409v1-abstract-full').style.display = 'inline'; document.getElementById('2102.05409v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.05409v1-abstract-full" style="display: none;"> Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the control parameter of the Hamiltonian is scanned across a quantum critical point. Recently it has been realized that a QPT can also occur in a simple system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report the first experimental demonstration of a QPT in the QRM using a single trapped ion. We measure the average spin-up state population of the ion and the average phonon number in its spatial oscillation mode as two order parameters and observe the clear evidences of the phase transition via slow quench of the coupling between the ion and its spatial motion. An experimental probe of the phase transitions in a fundamental quantum optics model without imposing the thermodynamic limit opens up a new window for the controlled study of QPTs and quantum critical phenomena. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.05409v1-abstract-full').style.display = 'none'; document.getElementById('2102.05409v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 9 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1308.5673">arXiv:1308.5673</a> <span> [<a href="https://arxiv.org/pdf/1308.5673">pdf</a>, <a href="https://arxiv.org/format/1308.5673">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.88.061802">10.1103/PhysRevA.88.061802 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Nonlocal linear compression of two-photon time interval distribution </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Pan%2C+J+-">J. -S. Pan</a>, <a href="/search/quant-ph?searchtype=author&query=Zou%2C+X+-">X. -B. Zou</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -Y. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Ding%2C+D+-">D. -S. Ding</a>, <a href="/search/quant-ph?searchtype=author&query=Shi%2C+B+-">B. -S. Shi</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+G+-">G. -C. Guo</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1308.5673v3-abstract-short" style="display: inline;"> We propose a linear compression technique for the time interval distribution of photon pairs. Using a partially frequency-entangled two-photon (TP) state with appropriate mean time width, the compressed TP time interval width can be kept in the minimum limit set by the phase modulation, and is independent of its initial width. As a result of this effect, ultra-narrow TP time interval distribution… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.5673v3-abstract-full').style.display = 'inline'; document.getElementById('1308.5673v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1308.5673v3-abstract-full" style="display: none;"> We propose a linear compression technique for the time interval distribution of photon pairs. Using a partially frequency-entangled two-photon (TP) state with appropriate mean time width, the compressed TP time interval width can be kept in the minimum limit set by the phase modulation, and is independent of its initial width. As a result of this effect, ultra-narrow TP time interval distribution can be compressed with relatively slow phase modulators to decrease the damage of the phase-instability arising from the phase modulation process. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.5673v3-abstract-full').style.display = 'none'; document.getElementById('1308.5673v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages, 8 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 88, 061802 (2013) </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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