This paper investigates a turbo receiver employing a variational quantum circuit (VQC). The VQC is configured with an ansatz of the quantum approximate optimization algorithm (QAOA). We propose a 'learning to learn' (L2L) framework to optimize the turbo VQC decoder such that high fidelity soft-decision output is generated. Besides demonstrating the proposed algorithm's computational complexity, we show that the L2L VQC turbo decoder can achieve an excellent performance close to the optimal maximum-likelihood performance in a multiple-input multiple-output system.