Most efficient state-vector quantum simulation frameworks are imperative. They work by having circuit gates operate on the global state vector in sequence and with each gate operation accessing and updating, in parallel, all (or large subsets of) the elements of the state vector. The precise access and update patterns used by a particular gate operation depend on which qubits the individual gate operates on.

Imperative implementations of state-vector simulators, however, often lack a more declarative specification, which may hinder reasoning and optimisations. For instance, correctness is often argued for using reasoning that involves bit-operations on state-vector indexes, which make it difficult for compilers to perform high-level index-optimisations.

In this work, we demonstrate how gate operations can be understood as maps over index-transformed state-vectors. We demonstrate correctness of the approach and implement a library for gate-operations in the data-parallel programming language Futhark. We further demonstrate that Futhark's fusion-engine is sufficiently powerful that it will ensure that consecutive gate operations on identical qubits are fused using map-map fusion. Moreover, we demonstrate that, using Futhark's uniqueness type system, state vectors may be updated in place. We evaluate the approach by comparing it with the state-of-the art state-vector simulators qsim and QuEST.