  The basic framework for this article is the causal set approach to discrete
quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with
cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of
complex-valued functions on $Q_n$. The formalism of DQG presents us with a
decoherence matrix $D_n(x,y)$, $x,y\in Q_n$. There is a growth order in $Q_n$
and a path in $Q_n$ is a maximal chain relative to this order. We denote the
set of paths in $Q_n$ by $\Omega_n$. For $\omega, \omega '\in\Omega_n$ we
define a bidifference operator $\varbigtriangledown_{\omega, \omega '}^n$ on
$K_n\otimes K_n$ that is covariant in the sense that
$\varbigtriangledown_{\omega, \omega '}^n$ leaves $D_n$ stationary. We then
define the curvature operator $\rscript_{\omega,
\omega'}^n=\varbigtriangledown_{\omega, \omega '}^n-\varbigtriangledown_{\omega
', \omega}^n$. It turns out that $\rscript_{\omega, \omega '}^n$ naturally
decomposes into two parts $\rscript_{\omega, \omega '}^n=\dscript_{\omega,
\omega '}^n+\tscript_{\omega, \omega '}^n$ where $\dscript_{\omega, \omega
'}^n$ is closely associated with $D_n$ and is called the metric operator while
$\tscript_{\omega, \omega '}^n$ is called the mass-energy operator. This
decomposition is a discrete analogue of Einstein's equation of general
relativity. Our analogue may be useful in determining whether general
relativity theory is a close approximation to DQG.
