Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.\

}, url = {https://arxiv.org/abs/1906.02700}, author = {G. Pagano and A. Bapat and P. Becker and K. S. Collins and A. De and P. W. Hess and H. B. Kaplan and A. Kyprianidis and W. L. Tan and C. Baldwin and L. T. Brady and A. Deshpande and F. Liu and S. Jordan and A. V. Gorshkov and C. Monroe} } @article {2289, title = {Cryogenic Trapped-Ion System for Large Scale Quantum Simulation}, year = {2018}, abstract = {We present a cryogenic ion trapping system designed for large scale quantum simulation of spin models. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap over 100 171Yb+ ions in a linear configuration for hours due to a low background gas pressure from differential cryo-pumping. We characterize the cryogenic vacuum by using trapped ion crystals as a pressure gauge, measuring both inelastic and elastic collision rates with the molecular background gas. We demonstrate nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials. This reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of spin models that are intractable with classical computer modelling.

}, url = {https://arxiv.org/abs/1802.03118}, author = {G. Pagano and P. W. Hess and H. B. Kaplan and W. L. Tan and P. Richerme and P. Becker and A. Kyprianidis and J. Zhang and E. Birckelbaw and M. R. Hernandez and Y. Wu and C. Monroe} } @article {2287, title = {Machine learning assisted readout of trapped-ion qubits}, journal = { J. Phys. B: At. Mol. Opt. Phys.}, volume = {51}, year = {2018}, month = {2018/05/01}, chapter = {174006}, abstract = {We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30\% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.

}, doi = {https://doi.org/10.1088/1361-6455/aad62b}, url = {https://arxiv.org/abs/1804.07718}, author = {Alireza Seif and Kevin A. Landsman and Norbert M. Linke and Caroline Figgatt and C. Monroe and Mohammad Hafezi} } @article {2286, title = {Parallel Entangling Operations on a Universal Ion Trap Quantum Computer}, year = {2018}, abstract = {The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor\&$\#$39;s factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

}, url = {https://arxiv.org/abs/1810.11948}, author = {C. Figgatt and A. Ostrander and N. M. Linke and K. A. Landsman and D. Zhu and D. Maslov and C. Monroe} } @article {2053, title = {Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator}, journal = {Nature}, volume = {551}, year = {2017}, month = {2017/11/29}, pages = {601-604}, abstract = {A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99\% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

}, doi = {10.1038/nature24654}, url = {https://www.nature.com/articles/nature24654}, author = {J. Zhang and G. Pagano and P. W. Hess and A. Kyprianidis and P. Becker and H. Kaplan and Alexey V. Gorshkov and Z. -X. Gong and C. Monroe} } @article {1915, title = {Demonstration of a small programmable quantum computer with atomic qubits}, journal = {Nature}, volume = {536}, year = {2016}, month = {2016/08/04}, pages = {63-66}, abstract = {Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 \%. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 \% and 90 \%, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 \% and 84 \%, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

}, doi = {10.1038/nature18648}, url = {http://www.nature.com/nature/journal/v536/n7614/full/nature18648.html}, author = {S. Debnath and N. M. Linke and C. Figgatt and K. A. Landsman and K. Wright and C. Monroe} } @article {1910, title = {Experimental demonstration of quantum fault tolerance}, year = {2016}, month = {2016/11/21}, abstract = {Quantum computers will eventually reach a size at which quantum error correction (QEC) becomes imperative. In order to make quantum information robust to errors introduced by qubit imperfections and flawed control operations, QEC protocols encode a logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent correction or detection of errors without destroying the logical state itself through direct measurement. While several experiments have shown a reduction of high intrinsic or artificially introduced errors in logical qubits, fault-tolerant encoding of a logical qubit has never been demonstrated. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. This advantage persists in the face of large added error rates and experimental calibration errors.

}, url = {https://arxiv.org/abs/1611.06946}, author = {N. M. Linke and M. Gutierrez and K. A. Landsman and C. Figgatt and S. Debnath and K. R. Brown and C. Monroe} } @article {2005, title = {{O}bservation of {P}rethermalization in {L}ong-{R}ange {I}nteracting {S}pin {C}hains}, year = {2016}, month = {2016/08/02}, abstract = {Statistical mechanics can predict thermal equilibrium states for most classical systems, but for an isolated quantum system there is no general understanding on how equilibrium states dynamically emerge from the microscopic Hamiltonian. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale and, instead, relax to quasi-stationary prethermal states that can be described by statistical mechanics when approximately conserved quantities are appropriately included in a generalized Gibbs ensemble (GGE). Here we experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse field Ising Hamiltonian following a sudden quench. For sufficiently long-ranged interactions the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. In this case, the prethermal state cannot be described by a GGE, but rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a significantly broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.

}, url = {https://arxiv.org/abs/1608.00681}, author = {B. Neyenhuis and J. Smith and A. C. Lee and J. Zhang and P. Richerme and P. W. Hess and Z. -X. Gong and Alexey V. Gorshkov and C. Monroe} }