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In the emerging field of cavity optomagnonics, photons are coupled coherently to magnons in solidstate systems. These new systems are promising for implementing hybrid quantum technologies. Being able to prepare Fock states in such platforms is an essential step towards the implementation of quantum information schemes. We propose a magnon-heralding protocol to generate a magnon Fock state by detecting an optical cavity photon. Due to the peculiarities of the optomagnonic coupling, the protocol involves two distinct cavity photon modes. Solving the quantum Langevin equations of the coupled system, we show that the temporal scale of the heralding is governed by the magnon-photon cooperativity and derive the requirements for generating high fidelity magnon Fock states. We show that the nonclassical character of the heralded state, which is imprinted in the autocorrelation of an optical "read" mode, is only limited by the magnon lifetime for small enough temperatures. We address the detrimental effects of nonvacuum initial states, showing that high fidelity Fock states can be achieved by actively cooling the system prior to the protocol. * Electronic address: victor.bittencourt@mpl.mpg.de †

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The ground state properties of the two-dimensional J1 − J2-model are very challenging to analyze via classical numerical methods due to the high level of frustration. This makes the model a promising candidate where quantum computers could be helpful and possibly explore regimes that classical computers cannot reach. The J1 − J2-model is a quantum spin model composed of Heisenberg interactions along the rectangular lattice edges and along diagonal edges between next-nearest neighbor spins. We propose an ansatz for the Variational Quantum Eigensolver (VQE) to approximate the ground state of an antiferromagnetic J1 − J2-Hamiltonian for different lattice sizes and different ratios of J1 and J2. Moreover, we demonstrate that this ansatz can work without the need for gates along the diagonal next-nearest neighbor interactions. This simplification is of great importance for solid state based hardware with qubits on a rectangular grid, where it eliminates the need for SWAP gates. In addition, we provide an extrapolation for the number of gates and parameters needed for larger lattice sizes, showing that these are expected to grow less than quadratically in the qubit number up to lattice sizes which eventually can no longer be treated with classical computers.