Statistical-Mechanical Analysis of Compressed Sensing for Hamiltonian Estimation of Ising Spin Glass

Abstract

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.

Dynamics of order parameters of nonstoquastic Hamiltonians in the adaptive quantum Monte Carlo method

“…We numerically compute the trace of the Jacobian matrix, the determinant, and the condition with real roots of eigenvalues by utilizing the equilibrium solutions (m * , m * x ) of Eqs. (22) and (23). We plot the behavior of the trace of the Jacobian matrix, the determinant, and the condition with real roots of eigenvalues with and without anti-ferromagnetic XX interaction in Fig.…”

“…x ) of Eqs. ( 22) and (23). We plot the behavior of the trace of the Jacobian matrix, the determinant, and the condition with real roots of eigenvalues with and without anti-ferromagnetic XX interaction in Fig.…”

“…Finally, we can obtain the differential equations for each Trotter slices k as dm k dt = −m k + σ k path . (22) and (23). The horizontal axis denotes the strength of the transverse magnetic field.…”

“…Nevertheless the quantum annealer has been tested for numerous applications such as portfolio optimization [11], protein folding [12], the molecular similarity problem [13], computational biology [14], job-shop scheduling [15], traffic optimization [16], election forecasting [17], machine learning [18][19][20], and automated guided vehicles in plant [21]. In addition, researches on implementing various problems into quantum annealer have been performed [22][23][24][25].…”

Item Listing Optimization for E-Commerce Websites Based on Diversity

“…The quantum annealer has been tested for numerous applications, including portfolio optimization [28], protein folding simulation [27], molecular similarity problem [14], computational biology [18], job-shop scheduling [31], traffic optimization [21], election forecasting [13], machine learning [10,17,22], and for automated guided vehicles in plants [23]. In addition, several other studies have been conducted to efficiently solve various problems using the quantum annealer [5,[24][25][26]29].…”