Abstract
We introduce a simple widely applicable formalism for designing ``error-divisible'' two-qubit gates: a quantum gate set where fractional rotations have proportionally reduced error compared to the full entangling gate. In current noisy intermediate-scale quantum (NISQ) algorithms, performance is largely constrained by error proliferation at high circuit depths, of which two-qubit gate error is generally the dominant contribution. Further, in many hardware implementations, arbitrary two-qubit rotations must be composed from multiple two-qubit stock gates, further increasing error. This work introduces a set of criteria, and example wave forms and protocols to satisfy them, using superconducting qubits with tunable couplers for constructing continuous gate sets with significantly reduced leakage and dynamic $ZZ$ errors for small-angle rotations. If implemented at scale, NISQ-algorithm performance could be significantly improved by our error-divisible gate protocols.
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