HIGH-FIDELITY QUANTUM CONTROL USING ION CRYSTALS IN A PENNING TRAP
We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled [1], and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays [5, 6, 7, 8]. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials [9, 10]. We discuss the use of two-dimensional (9)Be(+) ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz ground-state electron spin flip transition, which we drive using microwaves [11, 12]. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement [1] on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary high-fidelity rotations (tau(pi) similar to 200 mu s). Randomized Benchmarking [13] demonstrates an error per gate (a Pauli-randomized pi/2 and pi pulse pair) of 8 +/- 1 x 10(-4). Ramsey interferometry and spin-locking [14] measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical free-induction decay coherence time of T(2) similar to 2 ms, and a limiting T(1 rho) similar to 688 iris. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the error-suppressing capabilities of dynamical decoupling pulse sequences [15, 16, 17, 18, 19, 20, 21, 22, 23; 24, 25, 26], demonstrating an ability to extend qubit coherence and suppress phase errors [11, 12]. We conclude with a discussion of future avenues for experimental exploration, including the use of additional nuclear-spin-flip transitions for effective multiqubit protocols, the potential for hardware refinements to suppress qubit error rates well-below predicted fault-tolerance thresholds, and possibilities for single-ion addressing useful for the realization of complex entangled states.
quantum control penning trap dynamical decoupling trapped ion coulomb crystal