Efficient simulation of a pair of dissipative qubits antiferromagnetically coupled

We investigate the efficiency of different quantum Monte Carlo simulations of a pair of antiferromagnetically coupled qubits in an Ohmic dissipative environment. Using a Trotter-Suzuki decomposition and integrating out the degrees of freedom of the thermal bath, the model maps onto a frustrated long-range double-chain Ising lattice. We prove that: (i) due to frustration, the conventional Swendsen-Wang approach to cluster dynamics turns out to suffer from a severe inefficiency, stemming from the mismatch between spin correlations and cluster connectivity; (ii) the Kandel-Domany approach is extremely effective in the study of dissipative quantum qubits. We partition the double-chain into different types of plaquettes and minimize the weight of graphs containing antiferromagnetic bonds by using both analytic and numerical approaches. Monte Carlo simulation results, based on the analysis of the autocorrelation time, show that "long-range" plaquette decompositions are more efficient than the "local" ones, especially for high levels of dissipation.