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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 cross-talk 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&#x0027;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&#x0027;s devices than was feasible before, sometimes even with a gain in overall precision by up to 60&#x0025;.

Empirical Evaluation of Circuit Approximations on Noisy Quantum Devices