High-fidelity quantum control using ion crystals in a penning trap

Abstract

We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] forexperiments in quantum information. Macroscopic Penning traps allow for the contain-ment of a few to a few million atomic ions whose internal states may be used in quantuminformation experiments. Ions are laser Doppler cooled [1], and the mutual Coulomb re-pulsion of the ions leads to the formation of crystalline arrays [5, 6, 7, 8]. The structureand dimensionality of the resulting ion crystals may be tuned using a combination ofcontrol laser beams and external potentials [9, 10]. We discuss the use of two-dimensional 9Be+ ion crystals for experimental tests ofquantum control techniques. Our primary qubit is the 124 GHz ground-state electronspin flip transition, which we drive using microwaves [11, 12]. An ion crystal representsa spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystalare small, and as such we treat the ensemble as a single effective spin. We are able toinitialize the qubits in a simple state and perform a projective measurement [1] on thesystem. We demonstrate full control of the qubit Bloch vector, performing arbitrary high-fidelity rotations (τπ ∼200 µs). Randomized Benchmarking [13] demonstrates an errorper gate (a Pauli-randomized π=2 and π pulse pair) of 8±1×10-4. Ramsey interferome-try and spin-locking [14] measurements are used to elucidate the limits of qubit coherencein the system, yielding a typical free-induction decay coherence time of T2 ∼2 ms, and alimiting T1ρ ∼688 ms. These experimental specifications make ion crystals in a Penningtrap ideal candidates for novel experiments in quantum control. As such, we brieflydescribe recent efforts aimed at studying the error-suppressing capabilities of dynamicaldecoupling pulse sequences [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], demonstratingan ability to extend qubit coherence and suppress phase errors [11, 12]. We concludewith a discussion of future avenues for experimental exploration, including the use of ad-ditional nuclear-spin-flip transitions for effective multiqubit protocols, the potential forhardware refinements to suppress qubit error rates well-below predicted fault-tolerancethresholds, and possibilities for single-ion addressing useful for the realization of complexentangled states.