The state complexity of a finite(-state) automaton intuitively measures the size of the description of the automaton. Sakoda and Sipser [STOC 1972, pp. 275–286] were concerned with nonuniform families of finite automata and they discussed the behaviors of the nonuniform complexity classes defined by such families of finite automata having polynomial-size state complexity. In a similar fashion, we introduce nonuniform state complexity classes using nonuniform families of quantum finite automata empowered by the flexible use of garbage tapes. We first present general inclusion and separation relationships among nonuniform state complexity classes of various one-way finite automata, including deterministic, nondeterministic, probabilistic, and quantum finite automata having polynomially many inner states. For two-way quantum finite automata equipped with flexible garbage tapes, we show a close relationship between the nonuniform state complexity of the family of such polynomial-size quantum finite automata and the parameterized complexity class induced by logarithmic-space quantum computation assisted by polynomial-size advice. We further establish a direct connection between space-bounded quantum computation with quantum advice and quantum finite automata whose transitions are dictated by superpositions of transition tables.

有限（-state）自动机的状态的复杂性直观测量自动机的说明的大小。迫田和Sipser [STOC 1972，第275-286]与有限自动机的不均匀家庭而言，他们讨论了由具有多项式尺寸的状态的复杂性有限自动机的这样的家庭中定义的不均匀的复杂类的行为。以类似的方式，介绍使用的灵活运用垃圾带的授权量子有限自动机的不均匀家庭不均匀状态的复杂性类。我们首先介绍了各种单向有限自动机的非均匀状态复杂度类之间的一般包含和分离关系，包括具有多项式多个内部状态的确定性、非确定性、概率和量子有限自动机。对于双向量子有限自动机配有灵活的垃圾带，我们将展示由polynomial-协助家庭这样的多项式大小的量子有限自动机，并通过对数空间量子计算引起的参数复杂类的不均匀状态的复杂性之间的密切关系大小建议。我们进一步建立与量子建议和量子有限自动机，其通过过渡转变表的叠加都决定空间有界量子计算之间的直接连接。