Near-term quantum computing (QC) systems have limited qubit counts, high gate (instruction) error rates, and typically support a minimal instruction set having one type of two-qubit gate (2Q). To reduce program instruction counts and improve application expressivity, vendors have proposed, and shown proof-of-concept demonstrations of richer instruction sets such as XY gates (Rigetti) and fSim gates (Google). These instruction sets comprise of families of 2Q gate types parameterized by continuous qubit rotation angles. However, having such a large number of gate types is problematic because each gate type has to be calibrated periodically, across the full system, to obtain high fidelity implementations. This results in substantial recurring calibration overheads even on current systems which use only a few gate types. Our work aims to navigate this tradeoff between application expressivity and calibration overhead, and identify what instructions vendors should implement to get the best expressivity with acceptable calibration time. We develop NuOp, a flexible compilation pass based on numerical optimization, to efficiently decompose application operations into arbitrary hardware gate types. Using NuOp and four important quantum applications, we study the instruction set proposals of Rigetti and Google, with realistic noise simulations and a calibration model. Our experiments show that implementing 4-8 types of 2Q gates is sufficient to attain nearly the same expressivity as a full continuous gate family, while reducing the calibration overhead by two orders of magnitude. With several vendors proposing rich gate families as means to higher fidelity, our work has potential to provide valuable instruction set design guidance for near-term QC systems.
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