  Noisy Intermediate-Scale Quantum (NISQ) devices fail to produce outputs with
sufficient fidelity for deep circuits with many gates today. Such devices
suffer from read-out, multi-qubit gate and crosstalk noise combined with short
decoherence times limiting circuit depth. This work develops a methodology to
generate shorter circuits with fewer multi-qubit gates whose unitary
transformations approximate the original reference one. It explores the benefit
of such generated approximations under NISQ devices. Experimental results with
Grover's algorithm, multiple-control Toffoli gates, and the Transverse Field
Ising Model show that such approximate circuits produce higher fidelity results
than longer, theoretically precise circuits on NISQ devices, especially when
the reference circuits have many CNOT gates to begin with. With this ability to
fine-tune circuits, it is demonstrated that quantum computations can be
performed for more complex problems on today's devices than was feasible
before, sometimes even with a gain in overall precision by up to 60%.
