Optimizing tunable qubit arrays for quantum simulation

Quantum simulation in the era of Noisy Intermediate Scale Quantum computing is limited by decoherence times and gate errors. One approach to mitigate this is to create bespoke quantum processing units (QPU) to simulate a particular Hamiltonian. However, when working with superconducting coplanar waveguide qubits one does not want to open a dilution refrigerator to change the QPU in order to simulate a different Hamiltonian. When simulating an atom it is desirable to be able to create many different level-spacings with a single QPU. That can be accomplished with tunable qubits that are capacitively coupled r. In this work, we show that adjusting the resonant frequencies in a tunable qubit array allows one to create a variety of different energy level structures. Here, we use perturbation theory to determine the optimal coupling constants when designing a bespoke n-qubit array to provide the maximal tunable energy level range. In the future we will use this tunable coupling model to simulate a larger class of Hamiltonians.