Decision’s biggest challenge is uncertainty. We propose a quantum expected value theory for decision-making under uncertainty. Decision-making under uncertainty is the unification of people’s subjective beliefs and the objective world. Quantum density operator as value operator which we call it quantum circuit is proposed to simulate people’s subjective beliefs. Quantum circuit guides people to choose corresponding actions based on their subjective beliefs through objective world. The quantum circuit is a decision tree constructed from quantum gates and logic operations. The genetic programming can be used to optimize and auto-generate quantum circuits. Our proposed synapse’s quantum circuit hypothesis states that the combination of neurotransmitter and receptor functioned as quantum circuit open or close ion channels probabilistically which determines the excitation or inhibition of synapse.