Parallel hybrid quantum circuits in trapped ions with phonon-error mitigation

Essential to quantum information processing (QIP) are entangling gates, where errors arising from imperfect qubit manipulations cause undesirable decoherence. Error mitigation techniques are hence important for scaling to larger qubit system sizes in the near term. Trapped ion systems are a leading platform for QIP on both the digital and analog fronts, however, quantum simulators in the dispersive coupling regime suffer from phonon errors due to residual spin-phonon entanglements. We develop a scheme to mitigate such errors by utilizing the axial normal-mode structure, while simultaneously offering fast entangling gates with all-to-all connectivity. Such parallel gates are ideal for hybrid analog-digital quantum circuits, with potential applications for studying non-equilibrium quantum many-body physics and quantum chaos. Our regime goes beyond the long-range power-law interactions demonstrated thus far, and can be combined with individual qubit gates to achieve universal quantum computing.