Gleipnir: toward practical error analysis for Quantum programs

Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum (NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the ( ρ, 𝛿)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance 𝛿 to the ideal state 𝜌. This predicate ( ρ, 𝛿) can be computed adaptively using tensor networks based on Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the ( ρ, 𝛿)-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.