Dead gate elimination in hybrid quantum–classical programs

Hybrid quantum algorithms combine the strengths of quantum and classical computing. Many such algorithms, including the variational quantum eigensolver (VQE), embed parameterized quantum circuits as subroutines inside a classical host program. In current toolchains these circuits are executed in full, even when only a subset of measurement outcomes actually contributes to subsequent classical computations. In this manuscript, we propose a circuit optimization technique that uses information from the host program to identify and remove dead gates, i.e. quantum operations whose effects propagate only into measurement outcomes that are never semantically consumed. We formalize equivalence of circuits relative to the valid measurement outcomes, characterize dead gates, and give a polynomial-time elimination algorithm. We prove that removing dead gates does not change the probability distribution of the contributory measurement outcomes and therefore preserves the semantics of the overall hybrid program. We also discuss the challenges in host-side analysis. We implement our optimization and evaluate it on instances of VQE, quantum phase estimation (QPE), a QAOA-based MaxCut solver, and a Trotterised Hamiltonian-simulation algorithm, as well as on randomly generated hybrid programs. Across all benchmarks, our method removes a non-trivial fraction of gates even on circuits that have already been pre-optimized by state-of-the-art transpilers; in some cases it can eliminate entire quantum blocks when all measurement outcomes are dead. This article is an extended journal version of our conference paper 1 .