Britton, JWSawyer, BCKeith, ACWang, CCJFreericks, JKUys, HBiercuk, MJBollinge, JJ2012-07-172012-07-172012-04Britton, JW, Sawyer, BC, Keith, AC, Wang, CCJ, Freericks, JK, Uys, H, Biercuk, MJ and Bollinge, JJ. 2012. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature, vol. 484, pp 489-4920028-08361476-4687http://www.nature.com/nature/journal/v484/n7395/full/nature10981.htmlhttp://hdl.handle.net/10204/5999Copyright: 2012 Macmillan Publishers Limited. This is the post-print version of the work. The definitive version is published in Nature, vol. 484, pp 489-492The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. 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˜30 particles. Feynman predicted that a quantum simulator—a special-purpose ‘analogue’ processor built using quantum bits (qubits)—would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, 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, Ji,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 , where 0=a=3 and di,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=a=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.enQuantum physicsIsing interactionsCondensed-matter physicsArticleBritton, J., Sawyer, B., Keith, A., Wang, C., Freericks, J., Uys, H., ... Bollinge, J. (2012). Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. http://hdl.handle.net/10204/5999Britton, JW, BC Sawyer, AC Keith, CCJ Wang, JK Freericks, H Uys, MJ Biercuk, and JJ Bollinge "Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins." (2012) http://hdl.handle.net/10204/5999Britton J, Sawyer B, Keith A, Wang C, Freericks J, Uys H, et al. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. 2012; http://hdl.handle.net/10204/5999.TY - Article AU - Britton, JW AU - Sawyer, BC AU - Keith, AC AU - Wang, CCJ AU - Freericks, JK AU - Uys, H AU - Biercuk, MJ AU - Bollinge, JJ AB - The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. 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˜30 particles. Feynman predicted that a quantum simulator—a special-purpose ‘analogue’ processor built using quantum bits (qubits)—would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, 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, Ji,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 , where 0=a=3 and di,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=a=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. DA - 2012-04 DB - ResearchSpace DP - CSIR KW - Quantum physics KW - Ising interactions KW - Condensed-matter physics LK - https://researchspace.csir.co.za PY - 2012 SM - 0028-0836 SM - 1476-4687 T1 - Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins TI - Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins UR - http://hdl.handle.net/10204/5999 ER -