Variational optimization of parametrized quantum circuits is an integral component for many hybrid quantum-classical algorithms, which are arguably the most promising applications of Noisy Intermediate-Scale Quantum (NISQ) computers [1]. Applications include the Variational Quantum Eigensolver (VQE) [2], Quantum Approximate Optimization Algorithm (QAOA) [3] and Quantum Neural Networks (QNNs) [4-6]. All the above are examples of stochastic optimization problems whereby one minimizes the expected value of a random cost function over a set of variational parameters, using noisy estimates of the cost and/or its gradient. In the quantum setting these estimates are obtained by repeated measurements of some Hermitian observables for a quantum state which depends on the variational parameters. A variety of optimization methods have been proposed in the variational quantum circuit literature for determining optimal variational parameters, including derivative-free (zeroth-order) methods such as Nelder-Mead, finite-differencing [7] or SPSA [8].

We propose generative neural network methods to generate DNA sequences and tune them to have desired properties. We present three approaches: creating synthetic DNA sequences using a generative adversarial network; a DNA-based variant of the activation maximization ("deep dream") design method; and a joint procedure which combines these two approaches together. We show that these tools capture important structures of the data and, when applied to designing probes for protein binding microarrays, allow us to generate new sequences whose properties are estimated to be superior to those found in the training data. We believe that these results open the door for applying deep generative models to advance genomics research.