We offer an improved method for using a nuclear-magnetic-resonance quantum
computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to
the application of the NMRQC are an exponential diminishment of density-ma
trix elements with the number of bits, threatening weak signal levels; and
the high cost of preparing a suitable starting state. A third obstacle is a
heretofore unnoticed restriction on measurement operators available for us
e by a NMRQC. Variations on the function classes of the Deutsch-Jozsa probl
em are introduced, both to extend the range of problems advantageous for qu
antum computation and to escape all three obstacles to the use of a NMRQC.
At the cost of an extra work bit and a polynomial increase in the number of
gate operations required, the method solves the Deutsch-Jozsa problem whil
e avoiding an exponential loss of the signal, preparation of a pseudopure s
tate, and temporal averaging.