The ASM thesis says that every algorithm, of any kind, can be modeled step by step and on its natural abstraction level by
an abstract state machine. The thesis has been derived from basic principles for sequential algorithms, and for parallel synchronous
algorithms. The main result of this paper is that the ASM thesis also holds for quantum algorithms.
We first show that, and how, a general model of quantum algorithms (based on the combination of a classical computer with
quantum circuits) can be modeled by abstract state machines. Following the approach of Blass and Gurevich to parallel algorithms,
we then formulate general postulates for quantum algorithms and show that every algorithm satisfying these postulates is simulated
by an appropriate ASM. These “quantum ASMs” are special cases of the parallel ASMs of Blass and Gurevich, but the only unbounded
parallelism is inside the quantum operations (unitary transformations and measurements).