From the 7 Li nuclear magnetic resonance (NMR) and specific heat measurements of LiNiO 2 , consisting of a spin-1/2 triangular lattice, it is demonstrated that the previously suggested spin-glass-like freezing below T sg = 8 K, which is caused by defects of Li ions, is not the true ground state, but rather a quantum disordered state is realized without a spin gap. This state is characterized by power-law behavior of the temperature dependence of the specific heat below 0.5 K. A spin-liquid state with short-range ferromagnetic correlations is suggested from new insight into the frustration of orbital ordering for doubly degenerate e g shells in the triangular lattice.KEYWORDS: orbital degree of freedom, quantum spin system, triangular lattice, resonating valence bond, NMR, specific heat
Quantum annealing is a heuristic algorithm that solves combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware implementation of this algorithm. However, in general, we cannot embed all the logical variables of a large-scale problem, since the number of available qubits is limited. In order to handle a large problem, qbsolv has been proposed as a method for partitioning the original large problem into subproblems that are embeddable in the D-Wave quantum annealer, and it then iteratively optimizes the subproblems using the quantum annealer. Multiple logical variables in the subproblem are simultaneously updated in this iterative solver, and using this approach we expect to obtain better solutions than can be obtained by conventional local search algorithms. Although embedding of large subproblems is essential for improving the accuracy of solutions in this scheme, the size of the subproblems are small in qbsolv since the subproblems are basically embedded by using an embedding of a complete graph even for sparse problem graphs. This means that the resource of the D-Wave quantum annealer is not exploited efficiently. In this paper, we propose a fast algorithm for embedding larger subproblems, and we show that better solutions are obtained efficiently by embedding larger subproblems.
Quantum annealing is a heuristic algorithm for solving combinatorial optimization problems, and hardware for implementing this algorithm has been developed by D-Wave Systems Inc. The current version of the D-Wave quantum annealer can solve unconstrained binary optimization problems with a limited number of binary variables. However, the cost functions of several practical problems are defined by a large number of integer variables. To solve these problems using the quantum annealer, integer variables are generally binarized with one-hot encoding, and the binarized problem is partitioned into small subproblems. However, the entire search space of the binarized problem is considerably larger than that of the original integer problem and is dominated by infeasible solutions. Therefore, to efficiently solve large optimization problems with one-hot encoding, partitioning methods that extract subproblems with as many feasible solutions as possible are required. In this study, we propose two partitioning methods and demonstrate that they result in improved solutions.
We numerically test an optimization method for deep neural networks (DNNs) using quantum fluctuations inspired by quantum annealing. For efficient optimization, our method utilizes the quantum tunneling effect beyond the potential barriers. The path integral formulation of the DNN optimization generates an attracting force to simulate the quantum tunneling effect. In the standard quantum annealing method, the quantum fluctuations will vanish at the last stage of optimization. In this study, we propose a learning protocol that utilizes a finite value for quantum fluctuations strength to obtain higher generalization performance, which is a type of robustness. We demonstrate the performance of our method using two well-known open datasets: the MNIST dataset and the Olivetti face dataset. Although computational costs prevent us from testing our method on large datasets with high-dimensional data, results show that our method can enhance generalization performance by induction of the finite value for quantum fluctuations.
Several powerful machines, such as the D-Wave 2000Q, dedicated to solving combinatorial optimization problems through the Ising-model formulation have been developed. To input problems into the machines, the unknown parameters on the Ising model must be determined, and this is necessarily a nontrivial task. It could be beneficial to construct a method to estimate the parameters of the Ising model from several pairs of values of the energy and spin configurations. In the present paper, we propose a simple method employing the L 1 -norm minimization, which is based on the concept of the compressed sensing. Moreover, we analyze the typical performance of our proposed method of the Hamiltonian estimation by using the replica method. We also compare our analytical results through several numerical experiments using the alternating direction method of multipliers.
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