Orkan: Cache-friendly simulation of quantum operations on hermitian operators

Classical simulation of quantum operations is essential for algorithm design, noise characterisation, and benchmarking of quantum hardware. The most general physically realisable operation can be described by a positive linear map acting on a hermitian operator, representing either a density matrix or an observable. Established simulators vectorise the density matrix on an $n$-qubit Hilbert space and reuse state-vector kernels, storing all $2^{2n}$ elements and forgoing the benefits of hermitian symmetry. In this work, I introduce \emph{Orkan}, a simulation library that uses a tiled memory layout storing only the lower triangle of the hermitian matrix at tile granularity, roughly halving both the memory footprint and the wall time to simulate the evolution of quantum states under generic quantum operations. The implementation treats any hermitian operator uniformly and is agnostic to whether the Schr\"{o}dinger or Heisenberg picture is used. Dedicated $k$-local conjugation algorithms update all entries of the hermitian matrix in a single pass. Benchmarks against Qiskit Aer, QuEST, and Qulacs show consistent wall-clock speedups of $2$-$4{\times}$ partly attributable to the reduced memory footprint.