Particles subject to confinement experience an attractive potential that increases without bound as they separate. A prominent example is colour confinement in particle physics, in which baryons and mesons are produced by quark confinement. Confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here we report the observation of magnetic domain-wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can suppress information propagation and thermalization in such many-body systems. We quantitatively determine the excitation energy of domain-wall bound states from the non-equilibrium quench dynamics. We also study the number of domain-wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating high-energy physics phenomena, such as quark collision and string breaking. Long-range Ising interactions present in one-dimensional spin chains can induce a confining potential between pairs of domain walls, slowing down the thermalization of the system. This has now been observed in a trapped-ion quantum simulator.

}, issn = {1745-2473}, doi = {10.1038/s41567-021-01194-3}, author = {Tan, W. L. and Becker, P. and Liu, F. and Pagano, G. and Collins, K. S. and De, A. and Feng, L. and Kaplan, H. B. and Kyprianidis, A. and Lundgren, R. and Morong, W. and Whitsitt, S. and Gorshkov, A. V. and Monroe, C.} } @article { ISI:000553250400007, title = {Efficient Ground-State Cooling of Large Trapped-Ion Chains with an Electromagnetically-Induced-Transparency Tripod Scheme}, journal = {Phys. Rev. Lett.}, volume = {125}, number = {5}, year = {2020}, month = {JUL 29}, pages = {053001}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We report the electromagnetically-induced-transparency (EIT) cooling of a large trapped Yb-171(+) ion chain to the quantum ground state. Unlike conventional EIT cooling, we engage a four-level tripod structure and achieve fast sub-Doppler cooling over all motional modes. We observe simultaneous groundstate cooling across the complete transverse mode spectrum of up to 40 ions, occupying a bandwidth of over 3 MHz. The cooling time is observed to be less than 300 mu s, independent of the number of ions. Such efficient cooling across the entire spectrum is essential for high-fidelity quantum operations using trapped ion crystals for quantum simulators or quantum computers.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.125.053001}, author = {Feng, L. and Tan, W. L. and De, A. and Menon, A. and Chu, A. and Pagano, G. and Monroe, C.} } @article {zhu_generation_2020, title = {Generation of thermofield double states and critical ground states with a quantum computer}, journal = {Proc. Natl. Acad. Sci. U. S. A.}, volume = {117}, number = {41}, year = {2020}, note = {Place: 2101 CONSTITUTION AVE NW, WASHINGTON, DC 20418 USA Publisher: NATL ACAD SCIENCES Type: Article}, month = {oct}, pages = {25402{\textendash}25406}, abstract = {Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum approximate optimization algorithm (QAOA), we generate nontrivial thermal quantum states of the transversefield Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum?classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest-depth QAOA circuits provide the best results.}, keywords = {Ising model, quantum computing, quantum simulation, thermofield double state, trapped ions}, issn = {0027-8424}, doi = {10.1073/pnas.2006337117}, author = {Zhu, D. and Johri, S. and Linke, N. M. and Landsman, K. A. and Alderete, C. Huerta and Nguyen, N. H. and Matsuura, A. Y. and Hsieh, T. H. and Monroe, C.} } @article { ISI:000500475200001, title = {Benchmarking an 11-qubit quantum computer}, journal = {Nat. Commun.}, volume = {10}, year = {2019}, month = {NOV 29}, pages = {5464}, publisher = {NATURE PUBLISHING GROUP}, type = {Article}, abstract = {The field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 Yb-171(+) ions. We demonstrate average single-qubit gate fidelities of 99.5\%, average two-qubit-gate fidelities of 97.5\%, and SPAM errors of 0.7\%. To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani and Hidden Shift algorithms into our native gates and execute them on the hardware with average success rates of 78\% and 35\%, respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware.}, issn = {2041-1723}, doi = {10.1038/s41467-019-13534-2}, author = {Wright, K. and Beck, K. M. and Debnath, S. and Amini, J. M. and Nam, Y. and Grzesiak, N. and Chen, J. -S. and Pisenti, N. C. and Chmielewski, M. and Collins, C. and Hudek, K. M. and Mizrahi, J. and Wong-Campos, J. D. and Allen, S. and Apisdorf, J. and Solomon, P. and Williams, M. and Ducore, A. M. and Blinov, A. and Kreikemeier, S. M. and Chaplin, V. and Keesan, M. and Monroe, C. and Kim, J.} } @article { ISI:000447062400001, title = {Cryogenic trapped-ion system for large scale quantum simulation}, journal = {QUANTUM SCIENCE AND TECHNOLOGY}, volume = {4}, number = {1}, year = {2019}, month = {JAN}, pages = {UNSP 014004}, issn = {2058-9565}, doi = {10.1088/2058-9565/aae0fe}, author = {Pagano, G. and Hess, P. W. and Kaplan, H. B. and Tan, W. L. and Richerme, P. and Becker, P. and Kyprianidis, A. and Zhang, J. and Birckelbaw, E. and Hernandez, M. R. and Wu, Y. and Monroe, C.} } @article { ISI:000488282800085, title = {High purity single photons entangled with an atomic qubit}, journal = {Opt. Express}, volume = {27}, number = {20}, year = {2019}, month = {SEP 30}, pages = {28143-28149}, publisher = {OPTICAL SOC AMER}, type = {Article}, abstract = {Trapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on the purity of single photons produced by the quantum memory. Here, we demonstrate a single-photon source for quantum networking based on a trapped Ba-138(+) ion with a single photon purity of g((2))(0) = (8.1 +/- 2.3) x 10(-5) without background subtraction. We further optimize the tradeoff between the photonic generation rate and the memory-photon entanglement fidelity for the case of polarization photonic qubits by tailoring the spatial mode of the collected light. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement}, issn = {1094-4087}, doi = {10.1364/OE.27.028143}, author = {Crocker, C. and Lichtman, M. and Sosnova, K. and Carter, A. and Scarano, S. and Monroe, C.} } @article { ISI:000502778700003, title = {Toward convergence of effective-field-theory simulations on digital quantum computers}, journal = {Phys. Rev. A}, volume = {100}, number = {6}, year = {2019}, month = {DEC 16}, pages = {062319}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansatze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion, and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of E-4 = - 2.220 +/- 0.179 MeV may be compared with the exact deuteron ground-state energy -2.224 MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.}, issn = {2469-9926}, doi = {10.1103/PhysRevA.100.062319}, author = {Shehab, O. and Landsman, K. and Nam, Y. and Zhu, D. and Linke, N. M. and Keesan, M. and Pooser, R. C. and Monroe, C.} } @article {14841, title = {Training of quantum circuits on a hybrid quantum computer}, journal = {Science Advances}, volume = {5}, year = {2019}, abstract = {Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.

}, doi = {10.1126/sciadv.aaw9918}, url = {https://advances.sciencemag.org/content/5/10/eaaw9918}, author = {Zhu, D. and Linke, N. M. and Benedetti, M. and Landsman, K. A. and Nguyen, N. H. and Alderete, C. H. and Perdomo-Ortiz, A. and Korda, N. and Garfoot, A. and Brecque, C. and Egan, L. and Perdomo, O. and Monroe, C.} } @article {ISI:000482579500007, title = {Two-qubit entangling gates within arbitrarily long chains of trapped ions}, journal = {Phys. Rev. A}, volume = {100}, number = {2}, year = {2019}, month = {AUG 26}, pages = {022332}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {Ion trap quantum computers are based on modulating the Coulomb interaction between atomic ion qubits using external forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals by using a small and fixed number of motional modes, simplifying the scaling of ion trap quantum computers. We present analytical work that shows that gate operations need not couple to the motion of distant ions, allowing parallel entangling gates with a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also experimentally demonstrate high-fidelity entangling gates on a fully connected set of seventeen Yb-171(+) qubits using simple laser pulse shapes that primarily couple to just a few modes.}, issn = {2469-9926}, doi = {10.1103/PhysRevA.100.022332}, author = {Landsman, K. A. and Wu, Y. and Leung, P. H. and Zhu, D. and Linke, N. M. and Brown, K. R. and Duan, L. and Monroe, C.} } @article { ISI:000439334800001, title = {Demonstration of a Bayesian quantum game on an ion-trap quantum computer}, journal = {QUANTUM SCIENCE AND TECHNOLOGY}, volume = {3}, number = {4}, year = {2018}, month = {OCT}, pages = {UNSP 045002}, keywords = {ion traps, quantum computation, quantum games}, issn = {2058-9565}, doi = {10.1088/2058-9565/aacf0e}, author = {Solmeyer, Neal and Linke, Norbert M. and Figgatt, Caroline and Landsman, Kevin A. and Balu, Radhakrishnan and Siopsis, George and Monroe, C.} } @article { ISI:000442340900001, title = {Machine learning assisted readout of trapped-ion qubits}, journal = {JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS}, volume = {51}, number = {17}, year = {2018}, month = {SEP 14}, pages = {174006}, keywords = {ion traps, machine learning, quantum computing}, issn = {0953-4075}, doi = {10.1088/1361-6455/aad62b}, author = {Seif, Alireza and Landsman, Kevin A. and Linke, Norbert M. and Figgatt, Caroline and Monroe, C. and Hafezi, Mohammad} } @article { ISI:000451329500012, title = {Measuring the Renyi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer}, journal = {PHYSICAL REVIEW A}, volume = {98}, number = {5}, year = {2018}, month = {NOV 26}, pages = {052334}, abstract = {The efficient simulation of correlated quantum systems is a promising near-term application of quantum computers. Here, we present a measurement of the second Renyi entropy of the ground state of the two-site Fermi-Hubbard model on a five-qubit programmable quantum computer based on trapped ions. Our work illustrates the extraction of a nonlinear characteristic of a quantum state using a controlled-swap gate acting on two copies of the state. This scalable measurement of entanglement on a universal quantum computer will, with more qubits, provide insights into many-body quantum systems that are impossible to simulate on classical computers.}, issn = {2469-9926}, doi = {10.1103/PhysRevA.98.052334}, author = {Linke, N. M. and Johri, S. and Figgatt, C. and Landsman, K. A. and Matsuura, A. Y. and Monroe, C.} } @article {ISI:000424750200005, title = {Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain}, journal = {PHYSICAL REVIEW LETTERS}, volume = {120}, number = {7}, year = {2018}, month = {FEB 12}, pages = {073001}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {The local phonon modes in a Coulomb crystal of trapped ions can represent a Hubbard system of coupled bosons. We selectively prepare single excitations at each site and observe free hopping of a boson between sites, mediated by the long-range Coulomb interaction between ions. We then implement phonon blockades on targeted sites by driving a Jaynes-Cummings interaction on individually \%\%Addressed ions to couple their internal spin to the local phonon mode. The resulting dressed states have energy splittings that can be tuned to suppress phonon hopping into the site. This new experimental approach opens up the possibility of realizing large-scale Hubbard systems from the bottom up with tunable interactions at the single-site level.}, \%\%Address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.120.073001}, author = {Debnath, S. and Linke, N. M. and Wang, S. -T. and Figgatt, C. and Landsman, K. A. and Duan, L. -M. and Monroe, C.} } @article {ISI:000417029900008, title = {Complete 3-Qubit Grover search on a programmable quantum computer}, journal = {NATURE COMMUNICATIONS}, volume = {8}, year = {2017}, month = {DEC 4}, pages = {1918}, publisher = {NATURE PUBLISHING GROUP}, type = {Article}, abstract = {The Grover quantum search algorithm is a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state marking scheme required to perform a classical search. We also report the deterministic implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5\% and 89.6\%, respectively.}, \%\%Address = {MACMILLAN BUILDING, 4 CRINAN ST, LONDON N1 9XW, ENGLAND}, issn = {2041-1723}, doi = {10.1038/s41467-017-01904-7}, author = {Figgatt, C. and Maslov, D. and Landsman, K. A. and Linke, N. M. and Debnath, S. and Monroe, C.} } @article {ISI:000417492500001, title = {Demonstration of Two-Atom Entanglement with Ultrafast Optical Pulses}, journal = {PHYSICAL REVIEW LETTERS}, volume = {119}, number = {23}, year = {2017}, month = {DEC 8}, pages = {230501}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We demonstrate quantum entanglement of two trapped atomic ion qubits using a sequence of ultrafast laser pulses. Unlike previous demonstrations of entanglement mediated by the Coulomb interaction, this scheme does not require confinement to the Lamb-Dicke regime and can be less sensitive to ambient noise due to its speed. To elucidate the physics of an ultrafast phase gate, we generate a high entanglement rate using just ten pulses, each of similar to 20 ps duration, and demonstrate an entangled Bell state with (76 +/- 1)\% fidelity. These results pave the way for entanglement operations within a large collection of qubits by exciting only local modes of motion.}, \%\%Address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.119.230501}, author = {Wong-Campos, J. D. and Moses, S. A. and Johnson, K. G. and Monroe, C.} } @article {7296, title = {Multispecies Trapped-Ion Node for Quantum Networking}, journal = {Phys. Rev. Lett.}, volume = {118}, year = {2017}, month = {Jun}, pages = {250502}, doi = {10.1103/PhysRevLett.118.250502}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.118.250502}, author = {Inlek, I. V. and Crocker, C. and Lichtman, M. and Sosnova, K. and Monroe, C.} } @article { ISI:000413927000009, title = {Non-thermalization in trapped atomic ion spin chains}, journal = {PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, volume = {375}, number = {2108}, year = {2017}, month = {DEC 13}, issn = {1364-503X}, doi = {10.1098/rsta.2017.0107}, author = {Hess, P. W. and Becker, P. and Kaplan, H. B. and Kyprianidis, A. and Lee, A. C. and Neyenhuis, B. and Pagano, G. and Richerme, P. and Senko, C. and Smith, J. and Tan, W. L. and Zhang, J. and Monroe, C.} } @article {7641, title = {Ultrafast creation of large Schr{\"o}dinger cat states of an atom}, journal = {Nature Communications}, volume = {8}, year = {2017}, pages = {697}, abstract = {Mesoscopic quantum superpositions, or Schr{\"o}dinger cat states, are widely studied for fundamental investigations of quantum measurement and decoherence as well as applications in sensing and quantum information science. The generation and maintenance of such states relies upon a balance between efficient external coherent control of the system and sufficient isolation from the environment. Here we create a variety of cat states of a single trapped atom{\textquoteright}s motion in a harmonic oscillator using ultrafast laser pulses. These pulses produce high fidelity impulsive forces that separate the atom into widely separated positions, without restrictions that typically limit the speed of the interaction or the size and complexity of the resulting motional superposition. This allows us to quickly generate and measure cat states larger than previously achieved in a harmonic oscillator, and create complex multi-component superposition states in atoms.

}, isbn = {2041-1723}, doi = {10.1038/s41467-017-00682-6}, url = {https://doi.org/10.1038/s41467-017-00682-6}, author = {Johnson, K. G. and Wong-Campos, J. D. and Neyenhuis, B. and Mizrahi, J. and Monroe, C.} } @article {ISI:000379187600030, title = {Active stabilization of ion trap radiofrequency potentials}, journal = {REVIEW OF SCIENTIFIC INSTRUMENTS}, volume = {87}, number = {5}, year = {2016}, month = {JUN}, pages = {053110}, issn = {0034-6748}, doi = {10.1063/1.4948734}, author = {Johnson, K. G. and Wong-Campos, J. D. and Restelli, A. and Landsman, K. A. and Neyenhuis, B. and Mizrahi, J. and Monroe, C.} } @article {ISI:000385239800002, title = {Engineering large Stark shifts for control of individual clock state qubits}, journal = {PHYSICAL REVIEW A}, volume = {94}, number = {4}, year = {2016}, month = {OCT 7}, pages = {042308}, issn = {2469-9926}, doi = {10.1103/PhysRevA.94.042308}, author = {Lee, A. C. and Smith, J. and Richerme, P. and Neyenhuis, B. and Hess, P. W. and Zhang, J. and Monroe, C.} } @article {ISI:000382800500015, title = {High-resolution adaptive imaging of a single atom}, journal = {NATURE PHOTONICS}, volume = {10}, number = {9}, year = {2016}, month = {SEP}, pages = {606-610}, issn = {1749-4885}, author = {Wong-Campos, J. D. and Johnson, K. G. and Neyenhuis, B. and Mizrahi, J. and Monroe, C.} } @article { ISI:000375997100002, title = {Kaleidoscope of quantum phases in a long-range interacting spin-1 chain}, journal = {PHYSICAL REVIEW B}, volume = {93}, number = {20}, year = {2016}, month = {MAY 11}, pages = {205115}, issn = {2469-9950}, doi = {10.1103/PhysRevB.93.205115}, author = {Gong, Z. -X. and Maghrebi, M. F. and Hu, A. and Foss-Feig, M. and Richerme, P. and Monroe, C. and Gorshkov, A. V.} } @article {4115, title = {Sensing Atomic Motion from the Zero Point to Room Temperature with Ultrafast Atom Interferometry}, journal = {Phys. Rev. Lett.}, volume = {115}, year = {2015}, month = {Nov}, pages = {213001}, doi = {10.1103/PhysRevLett.115.213001}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.115.213001}, author = {Johnson, K. G. and Neyenhuis, B. and Mizrahi, J. and Wong-Campos, J. D. and Monroe, C.} }