We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential application to quantum computational problems. We numerically solve for the phase structure of a connectivity
q=3 transverse field Ising model on a Bethe lattice with $\ifmmode\pm\else\textpm\fi{}J$ couplings and investigate the distribution of various classical and quantum observables.
We discuss generation of series expansions for Ising spin glasses with a symmetric $\ifmmode\pm\else\textpm\fi{}J$ (i.e., bimodal) distribution on
d-dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us to go to higher order than for a general distribution. We discuss two types of problems, one classical and one quantum. The classical problem is that of the Ising spin glass in a longitudinal magnetic field
h, for which we obtain high temperature series expansions in variables
tanh(J/T) and
tanh(h/T). The quantum problem is a
T=0 study of the Ising spin glass in a transverse magnetic field
hT for which we obtain a perturbation theory in powers of
J/hT. These methods require (i) enumeration and counting of all connected clusters that can be embedded in the lattice up to some order
n, and (ii) an evaluation of the contribution of each cluster for the quantity being calculated, known as the weight. We discuss a general method that takes the much smaller list (and count) of all no free-end (NFE) clusters on a lattice up to some order
n and automatically generates all other clusters and their counts up to the same order. The weights for finite clusters in both cases have a simple graphical interpretation that allows us to proceed efficiently for a general configuration of the $\ifmmode\pm\else\textpm\fi{}J$ bonds and at the end perform suitable disorder averaging. The order of our computations is limited by the weight calculations for the high-temperature expansions of the classical model, while they are limited by graph counting for the
T=0 quantum system. Details of the calculational methods are presented.