This work presents a generalization of NchooseK, a constraint satisfaction system designed to target both quantum circuit devices and quantum annealing devices. Previously, NchooseK supported only hard constraints, which made it suitable for expressing problems in NP (e.g., 3-SAT) but not NP-hard problems (e.g., minimum vertex cover). In this paper we show how support for soft constraints can be added to the model and implementation, broadening the classes of problems that can be expressed elegantly in NchooseK without sacrificing portability across different quantum devices. Through a set of examples, we argue that this enhanced version of NchooseK enables problems to be expressed in a more concise, less error-prone manner than if these problems were encoded manually for quantum execution. We include an empirical evaluation of performance, scalability, and fidelity on both a large IBM Q system and a large D- Wave system.

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%.