  We propose and demonstrate transmission-based dispersive readout of a
superconducting qubit using an all-pass resonator, which preferentially emits
readout photons toward the output. This is in contrast to typical readout
schemes, which intentionally mismatch the feedline at one end so that the
readout signal preferentially decays toward the output. We show that this
intentional mismatch creates scaling challenges, including larger spread of
effective resonator linewidths due to non-ideal impedance environments and
added infrastructure for impedance matching. A future architecture using
multiplexed all-pass readout resonators would avoid the need for intentional
mismatch and potentially improve the scaling prospects of quantum computers. As
a proof-of-concept demonstration of "all-pass readout," we design and fabricate
an all-pass readout resonator that demonstrates insertion loss below 1.17 dB at
the readout frequency and a maximum insertion loss of 1.53 dB across its full
bandwidth for the lowest three states of a transmon qubit. We demonstrate qubit
readout with an average single-shot fidelity of 98.1% in 600 ns; to assess the
effect of larger dispersive shift, we implement a shelving protocol and achieve
a fidelity of 99.0% in 300 ns.
