  Due to the beyond-classical capability of quantum computing, quantum machine
learning is applied independently or embedded in classical models for decision
making, especially in the field of finance. Fairness and other ethical issues
are often one of the main concerns in decision making. In this work, we define
a formal framework for the fairness verification and analysis of quantum
machine learning decision models, where we adopt one of the most popular
notions of fairness in the literature based on the intuition -- any two similar
individuals must be treated similarly and are thus unbiased. We show that
quantum noise can improve fairness and develop an algorithm to check whether a
(noisy) quantum machine learning model is fair. In particular, this algorithm
can find bias kernels of quantum data (encoding individuals) during checking.
These bias kernels generate infinitely many bias pairs for investigating the
unfairness of the model. Our algorithm is designed based on a highly efficient
data structure -- Tensor Networks -- and implemented on Google's TensorFlow
Quantum. The utility and effectiveness of our algorithm are confirmed by the
experimental results, including income prediction and credit scoring on
real-world data, for a class of random (noisy) quantum decision models with 27
qubits ($2^{27}$-dimensional state space) tripling ($2^{18}$ times more than)
that of the state-of-the-art algorithms for verifying quantum machine learning
models.
