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.

1 aPagano, G.1 aBapat, A.1 aBecker, P.1 aCollins, K., S.1 aDe, A.1 aHess, P., W.1 aKaplan, H., B.1 aKyprianidis, A.1 aTan, W., L.1 aBaldwin, C.1 aBrady, L., T.1 aDeshpande, A.1 aLiu, F.1 aJordan, S.1 aGorshkov, A., V.1 aMonroe, C. uhttps://arxiv.org/abs/1906.0270001463nas a2200229 4500008004100000245006800041210006700109520082000176100001500996700001701011700001901028700001601047700001701063700001501080700002001095700001401115700001901129700002201148700001101170700001501181856003701196 2018 eng d00aCryogenic Trapped-Ion System for Large Scale Quantum Simulation0 aCryogenic TrappedIon System for Large Scale Quantum Simulation3 aWe 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.

1 aPagano, G.1 aHess, P., W.1 aKaplan, H., B.1 aTan, W., L.1 aRicherme, P.1 aBecker, P.1 aKyprianidis, A.1 aZhang, J.1 aBirckelbaw, E.1 aHernandez, M., R.1 aWu, Y.1 aMonroe, C. uhttps://arxiv.org/abs/1802.0311801952nas a2200229 4500008004100000245009200041210006900133260001500202300001200217490000800229520128300237100001401520700001501534700001701549700002001566700001501586700001501601700002501616700001801641700001501659856004801674 2017 eng d00aObservation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator0 aObservation of a ManyBody Dynamical Phase Transition with a 53Qu c2017/11/29 a601-6040 v5513 aA 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.

1 aZhang, J.1 aPagano, G.1 aHess, P., W.1 aKyprianidis, A.1 aBecker, P.1 aKaplan, H.1 aGorshkov, Alexey, V.1 aGong, Z., -X.1 aMonroe, C. uhttps://www.nature.com/articles/nature2465402050nas a2200205 4500008004100000245008900041210006900130260001500199520143900214100001801653700001401671700001601685700001401701700001701715700001701732700001801749700002501767700001501792856003701807 2016 eng d00a{O}bservation of {P}rethermalization in {L}ong-{R}ange {I}nteracting {S}pin {C}hains0 aO bservation of P rethermalization in L ong R ange I nteracting c2016/08/023 aStatistical 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.

1 aNeyenhuis, B.1 aSmith, J.1 aLee, A., C.1 aZhang, J.1 aRicherme, P.1 aHess, P., W.1 aGong, Z., -X.1 aGorshkov, Alexey, V.1 aMonroe, C. uhttps://arxiv.org/abs/1608.00681