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

TL;DR

This paper demonstrates high-fidelity quantum control of ion crystals in a Penning trap, achieving precise qubit manipulations with long coherence times, and explores their potential for advanced quantum experiments.

Contribution

It introduces a method for controlling and measuring qubits in ion crystals with high fidelity and long coherence, advancing quantum control techniques in Penning traps.

Findings

Achieved arbitrary high-fidelity qubit rotations with error per gate of 8±1×10⁻⁴.

Measured a qubit coherence time of approximately 2 ms.

Demonstrated the extension of coherence using dynamical decoupling sequences.

Abstract

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. 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 on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary high-fidelity rotations ($\tau_{\pi}\sim$200 $\mu$s). Randomized Benchmarking demonstrates an error per gate (a Pauli-randomized $\pi/2$ and $\pi$ pulse pair) of $8\pm1\times10^{-4}$. Ramsey interferometry and spin-locking measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical free-induction decay coherence time of $T_{2}\sim$2 ms, and a limiting $T_{1\rho}\sim$688 ms. 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, demonstrating an ability to extend qubit coherence and suppress phase errors. We conclude with a discussion of future avenues for experimental exploration, including the use of additional nuclear-spin-flip transitions for effective multiqubit protocols, and the potential for Coulomb crystals to form a useful testbed for studies of large-scale entanglement.