Efficient implementation of arbitrary Hermitian-preserving and trace-preserving maps

Abstract

Quantum control has been a cornerstone of quantum information science, driving major advances in quantum computing, quantum communication, and quantum sensing. Over the years, it has enabled the implementation of arbitrary completely positive and trace-preserving (CPTP) maps; an important next step is to extend control to Hermitian-preserving and trace-preserving (HPTP) maps, which underpin applications such as entanglement detection, quantum error mitigation, quantum simulation, and quantum machine learning. Here we present an efficient and fully constructive method for implementing arbitrary HPTP maps. Unlike existing methods that decompose an HPTP map into multiple CPTP maps or approximate it using bipartite Hamiltonians with large Hilbert spaces, our approach compiles a target HPTP map into a single executable CPTP map whose Kraus rank is guaranteed to be no larger than the intrinsic rank of the target HPTP map plus one, followed by simple classical post-processing. Numerical results for inverse noise channels used in quantum error mitigation, including bosonic photon loss, confirm substantial reductions in resources and highlight scalability in higher-dimensional settings. Together with our numerical benchmarks, these results validate the efficiency and versatility of the proposed framework, opening a route to broader quantum-information applications enabled by HPTP processing.