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: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.} }