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Compressing neural networks is a key step when deploying models for real-time or embedded applications. Factorizing the model's matrices using low-rank approximations is a promising method for achieving compression. While it is possible to set the rank before training, this approach is neither flexible nor optimal. In this work, we propose a post-training rank-selection method called Rank-Tuning that selects a different rank for each matrix. Used in combination with training adaptations, our method achieves high compression rates with no or little performance degradation. Our numerical experiments on signal processing tasks show that we can compress recurrent neural networks up to 14x with at most 1.4% relative performance reduction.

Hybrid quantum-classical adaptive Variational Quantum Eigensolvers (VQE) already hold the potential to outperform classical computing for simulating quantum many-body systems. However, their practical implementation on current quantum processing units (QPUs) is very challenging due to the noisy evaluation of a polynomially scaling number of observables, undertaken for operator selection and optimisation of a high-dimensional cost function. To overcome this, we propose new techniques to execute adaptive algorithms on a 25-qubit error-mitigated QPU coupled to a GPU-accelerated HPC simulator. Targeting physics applications, we compute the ground state of a 25-body Ising model using the newly introduced Greedy Gradient-free Adaptive VQE (CGA-VQE) requiring only five circuit measurements per iteration, regardless of the number of qubits and size of the operator pool. Towards chemistry, we combine the GGA-VQE and Overlap-ADAPT-VQE algorithms to approximate a molecular system ground state. We show that the QPU successfully executes the algorithms and yields the correct choice of parametrised unitary operators. While the QPU evaluation of the resulting ansatz wave-function is polluted by hardware noise, a single final evaluation of the sought-after observables on a classical GPU-accelerated/noiseless simulator allows the recovery of the correct approximation of the ground state, thus highlighting the need for hybrid quantum-classical observable measurement.