  Near-term quantum computations are limited by high error rates, the scarcity
of qubits and low qubit connectivity. Increasing support for mid-circuit
measurements and qubit reset in near-term quantum computers enables qubit reuse
that may yield quantum computations with fewer qubits and lower errors. In this
work, we introduce a formal model for qubit reuse optimization that delivers
provably optimal solutions with respect to quantum circuit depth, number of
qubits, or number of swap gates for the first time. This is in contrast to
related work where qubit reuse is used heuristically or optimally but without
consideration of the mapping effort. We further investigate reset errors on
near-term quantum computers by performing reset error characterization
experiments. Using the hereby obtained reset error characterization and
calibration data of a near-term quantum computer, we then determine a qubit
assignment that is optimal with respect to a given cost function. We define
this cost function to include gate errors and decoherence as well as the
individual reset error of each qubit. We found the reset fidelity to be
state-dependent and to range, depending on the reset qubit, from 67.5% to 100%
in a near-term quantum computer. We demonstrate the applicability of the
developed method to a number of quantum circuits and show improvements in the
number of qubits and swap gate insertions, estimated success probability, and
Hellinger fidelity of the investigated quantum circuits.
