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A trapped-ion quantum simulator is used to demonstrate tunable long-range spin-spin couplings in two dimensions, relevant to studies of quantum magnetism at a scale that is intractable for classical computers. Scaling up quantum simulation Quantum simulations could be used to study currently intractable many-body problems, such as quantum magnetism. However, technical challenges have so far limited simulations to a few tens of qubits, which is not enough to be computationally relevant. Here, Britton et al. demonstrate that a naturally occurring two-dimensional triangular crystal lattice of a few hundred beryllium ions held in an electromagnetic Penning trap can be used to simulate tunable antiferromagnetic interactions. This approach should bring the power of quantum simulation to a range of interesting problems in quantum magnetism. The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity.sup.1,2. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N [almost equal to] 30 particles.sup.3. Feynman predicted that a quantum simulator--a special-purpose 'analogue' processor built using quantum bits (qubits)--would be inherently suited to solving such problems.sup.4,5. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach.sup.6,7,8,9,10,11,12,13,14, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction, J.sub.i,j , on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction [Formula omitted], where 0 [less than or equal to] a [less than or equal to] 3 and d.sub.i,j is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb-like (a = 1), monopole-dipole (a = 2) and dipole-dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 [less-than or equivalent to] a [less-than or equivalent to] 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism., Author(s): Joseph W. Britton [sup.1] , Brian C. Sawyer [sup.1] , Adam C. Keith [sup.2] [sup.3] , C.-C. Joseph Wang [sup.2] , James K. Freericks [sup.2] , Hermann Uys [sup.4] [...]

Any quantum system, such as those used in quantum information or magnetic resonance, is subject to random phase errors that can dramatically affect the fidelity of a desired quantum operation or measurements. In the context of quantum information, quantum error correction techniques have been developed to correct these errors, but resource requirements are extraordinary. The realization of a physically tractable quantum information system will therefore be facilitated if qubit (quantum bit) error rates are far below the so-called fault-tolerance error threshold(1), predicted to be of the order Of [10.sup.-3]-[10.sup.-6]. The need to realize such low error rates motivates a search for alternative strategies to suppress dephasing in quantum systems(2). Here we experimentally demonstrate massive suppression of qubit error rates by the application of optimized dynamical decoupling(3-8) pulse sequences, using a model quantum system capable of simulating a variety of qubit technologies. We demonstrate an analytically derived pulse sequence(9), UDD, and fmd novel sequences through active, real-time experimental feedback. The latter sequences are tailored to maximize error suppression without the need for a priori knowledge of the ambient noise environment, and are capable of suppressing errors by orders of magnitude compared to other existing sequences (including the benchmark multi-pulse spin echos(10,11)). Our work includes the extension of a treatment to predict qubit decoherences(12,13)is under realistic conditions, yielding strong agreement between experimental data and theory for arbitrary pulse sequences incorporating non-idealized control pulses. These results demonstrate the robustness of qubit memory error suppression through dynamical decoupling techniques across a variety of qubit technologies(11,14-16)., We consider classical phase randomization of a qubit due to the action of the environment as the dominant source of memory errors. Accordingly, we may write a Hamiltonian as H [...]