  We use Monte Carlo techniques to simulate the ability of future large
high-redshift galaxy surveys to measure the temporal evolution of the dark
energy equation-of-state w(z), using the baryonic acoustic oscillations in the
clustering power spectrum as a 'standard ruler'. Our analysis only utilizes the
oscillatory component of the power spectrum and not its overall shape, which is
potentially susceptible to broadband tilts induced by a host of model-dependent
systematic effects. Our results are therefore robust and conservative. We show
that baryon oscillation constraints can be thought of, to high accuracy, as a
direct probe of the distance - redshift and expansion rate - redshift relations
where distances are measured in units of the sound horizon. Distance precisions
of 1% are obtainable for a fiducial redshift survey covering 10,000 deg^2 and
redshift range 0.5 < z < 3.5. If the dark energy is further characterized by
w(z) = w_0 + w_1 z (with a cut-off in the evolving term at z = 2), we can then
measure the parameters w_0 and w_1 with a precision exceeding current knowledge
by a factor of ten: 1 sigma accuracies Delta w_0 ~ 0.03 and Delta w_1 ~ 0.06
are obtainable (assuming a flat universe and that the other cosmological
parameters Omega_m} and h could be measured independently to a precision of +/-
0.01 by combinations of future CMB and other experiments). We quantify how this
performance degrades with redshift/areal coverage and knowledge of Omega_m and
h, and discuss realistic observational prospects for such large-scale
spectroscopic redshift surveys, with a variety of diverse techniques. We also
quantify how large photometric redshift imaging surveys could be utilized to
produce measurements of (w_0,w_1) with the baryonic oscillation method which
may be competitive in the short term.
