Local spin operators for fermion simulations

Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on spins. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here we re-examine an auxiliary fermion construction which maps fermionic operators to local operators on spins. The local simulation is performed by relaxing the requirement that the number of spins should match the number of fermionic modes. Instead, auxiliary modes are introduced to enable non-consecutive fermionic couplings to be simulated with constant low-rank tensor products on spins. We connect the auxiliary fermion construction to other topological models and give examples of the construction

Training A Quantum Optimizer

We study a variant of the quantum approximate optimization algorithm [ E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with slightly different parametrization and different objective: rather than looking for a state which approximately solves an optimization problem, our goal is to find a quantum algorithm that, given an instance of MAX-2-SAT, will produce a state with high overlap with the optimal state. Using a machine learning approach, we chose a "training set" of instances and optimized the parameters to produce large overlap for the training set. We then tested these optimized parameters on a larger instance set. As a training set, we used a subset of the hard instances studied by E. Crosson, E. Farhi, C. Yen-Yu Lin, H.-H. Lin, and P. Shor (CFLLS) [arXiv:1401.7320]. When tested on the full set, the parameters that we find produce significantly larger overlap than the optimized annealing times of CFLLS. Testing on other random instances from $20$ to $28$ bits continues to show improvement over annealing, with the improvement being most notable on the hardest instances. Further tests on instances of MAX-3-SAT also showed improvement on the hardest instances. This algorithm may be a possible application for near-term quantum computers with limited coherence times.Comment: 10 pages, 5 figure

Loop Algorithms for Asymmetric Hamiltonians

Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is possible from these rules to select a new algorithm which performs significantly better than the standard loop algorithm in strong magnetic fields at low temperatures.Comment: Replaced measurement of helicity modulus at H=2J with a measurement at H=3.95J + other small changes in the section on numerical result

Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

We use a nonperturbative extended contractor renormalization (ENCORE) method for engineering quantum devices for the implementation of topologically protected quantum bits described by an effective quantum dimer model on the triangular lattice. By tuning the couplings of the device, topological protection might be achieved if the ratio between effective two-dimer interactions and flip amplitudes lies in the liquid phase of the phase diagram of the quantum dimer model. For a proposal based on a quantum Josephson junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503 (2002)] our results show that optimal operational temperatures below 1 mK can only be obtained if extra interactions and dimer flips, which are not present in the standard quantum dimer model and involve three or four dimers, are included. It is unclear if these extra terms in the quantum dimer Hamiltonian destroy the liquid phase needed for quantum computation. Minimizing the effects of multi-dimer terms would require energy scales in the nano-Kelvin regime. An alternative implementation based on cold atomic or molecular gases loaded into optical lattices is also discussed, and it is shown that the small energy scales involved--implying long operational times--make such a device impractical. Given the many orders of magnitude between bare couplings in devices, and the topological gap, the realization of topological phases in quantum devices requires careful engineering and large bare interaction scales.Comment: 12 pages, 10 figure

Unconventional continuous phase transition in a three dimensional dimer model

Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and are compatible with a tricritical universality class, at variance with previous proposals.Comment: 4 pages, 3 figures; v2: minor changes, published versio

Quantum spin correlations in an organometallic alternating sign chain

High resolution inelastic neutron scattering is used to study excitations in the organometallic magnet DMACuCl$_3$. The correct magnetic Hamiltonian describing this material has been debated for many years. Combined with high field bulk magnetization and susceptibility studies, the new results imply that DMACuCl$_3$ is a realization of the $S=1/2$ alternating antiferromagnetic-ferromagnetic (AFM-FM) chain. Coupled-cluster calculations are used to derive exchange parameters, showing that the AFM and FM interactions have nearly the same strength. Analysis of the scattering intensities shows clear evidence for inter-dimer spin correlations, in contrast to existing results for conventional alternating chains. The results are discussed in the context of recent ideas concerning quantum entanglement.Comment: 5 pages, 4 figures included in text. Submitted to APS Journal