Modesto Orozco-Ruiz

Entangling interactions between distant qubits can be mediated via an additional degree of freedom. In conventional trapped-ion schemes, realizing a well-defined, coherent gate typically requires spectrally addressing a specific bus mode. As the ion number increases, the coupling to each individual motional mode becomes weaker, so gates on large ion strings mediated by a single mode are necessarily slow. Moreover, addressing a large number of modes demands complex driving schemes, and the fundamentally perturbative character of these approaches imposes constraints on achievable gate speed and fidelity. Here, we introduce a scheme for entangling trapped-ion qubits using a time-dependent magnetic-field gradient, in which all axial motional modes participate in mediating the interaction and the gate construction is nonperturbative. The framework can be used to implement both multi-qubit gates and two-qubit gates between arbitrary pairs in a linear ion string. Through several explicit examples, we highlight the advantages over existing magnetic-gradient schemes and show how gates on multiple ion pairs can be carried out simultaneously.

Noise resilience of quantum information processing is a crucial precondition to reach the fault-tolerance threshold. While resilience to many types of noise can be achieved through suitable control schemes, resilience to amplitude noise seems to be elusive within the common harmonic approximation for the bus mode of trapped ions. We show that weak an-harmonicities admit control schemes that achieve amplitude noise-resilience consistent with state-of-the-art experimental requirements, and that the required an-harmonicities can be achieved with current standards of micro-structured traps or even the intrinsically an-harmonic Coulomb interaction. This approach applies broadly to any platform that employs a bosonic bus as a qubit coupler.

We present an entangling gate scheme for trapped-ion chains that achieves high-fidelity operations with excited motional states despite multiple error sources. Our approach incorporates all relevant motional modes and exhibits enhanced robustness against both motional heating effects and detuning errors, critical features for building robust and scalable trapped-ion quantum computers.

Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity of such problems, but it requires the knowledge of an invariant compatible with the Hamiltonian of the system in question. We explore the potential of a Gaussian invariant that is suitable for quadratic Hamiltonians with any given number of motional degrees of freedom for quantum optimal control problems that are inspired by current challenges in ground-state-to-ground-state shuttling of trapped-ions.