Alexander K. Ratcliffe

We propose high-fidelity single-qubit spin-dependent kicks (SDKs) for trapped ions using nanosecond Raman pulses via amplitude modulation of a continuous-wave laser with a tunable beat frequency. We develop a general method for maintaining SDK performance in the presence of micromotion by identifying optimal choices of the RF phase and frequency that suppress unwanted backward kicks. The proposed scheme enables SDK infidelities as low as $10^{-9}$ in the absence of micromotion, and below $10^{-5}$ with micromotion. This study lays the foundation for the realization of sub-trap-period and high-fidelity two-qubit gates based on SDKs.

Micromotion in radio-frequency ion traps is generally considered detrimental for quantum logic gates, and is typically minimized in state-of-the-art experiments. However, as a deterministic effect, it can be incorporated into quantum control frameworks aimed at designing high-fidelity quantum logic controls. In this work, we demonstrate that micromotion can be beneficial to the design of fast gates utilizing the radial modes of a two-ion crystal, particularly in the sub-trap-period regime where high-fidelity control sequences are identified with operation times ranging from hundreds of nanoseconds to microseconds. Through analysis of select fast gate solutions, we uncover the physical origin of micromotion enhancement and further study the induced gate error under experimental noises and control imperfections. This analysis establishes the feasibility of realising high-fidelity entangling gates in hundreds of nanoseconds using the micromotion-sensitive radial modes of trapped-ion crystals.

Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multi-mode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to $50$ ions with fidelities approaching $99.9\%$.

We present a theoretical study of fast all-to-all entangling gates in trapped-ion quantum processors, based on impulsive excitation of spin-dependent motion with broadband laser pulses. Previous studies have shown that such fast gate schemes are highly scalable and naturally performant outside the Lamb-Dicke regime, however are limited to nearest-neighbour operations. Here we demonstrate that impulsive spin-dependent excitation can be used to perform high-fidelity non-local entangling operations in quasi-uniform chains of up to 40 ions. We identify a regime of phonon-mediated entanglement between arbitrary pairs of ions in the chain, where any two pairs of ions in the chain can be entangled in approximately 1.3-2 centre-of-mass oscillation periods. We assess the experimental feasibility of the proposed gate schemes, which reveals pulse error requirements that are weakly dependent on the length of the ion chain and the distance between the target qubits. These results suggest entangling gates based on impulsive spin-dependent excitation presents new possibilities for large-scale computation in near-term ion-trap devices.

Quantum logic operations between physically distinct qubits is an essential aspect of large-scale quantum information processing. We propose an approach to high-speed mixed-species entangling operations in trapped-ion quantum computers, based on mechanical excitation of spin-dependent ion motion by ultrafast pulsed lasers. We develop the theory and machine-design of pulse sequences that realise MHz-speed `fast gates' between a range of mixed-isotope and mixed-species ion pairings with experimentally-realistic laser controls. We demonstrate the robustness of the gate mechanism against expected experimental errors, and identify errors in ultrafast single-qubit control as the primary technical limitation. The proposed mixed-species gate mechanism can be used for fast transfer of quantum information between specialized qubits and quantum memories, which we show enables the protection of matter-photon interfaces against rapid spin dephasing in optical networks of trapped-ion processors.

We theoretically investigate the use of fast pulsed two-qubit gates for trapped ion quantum computing in a two-dimensional microtrap architecture. In one dimension, such fast gates are optimal when employed between nearest neighbours, and we examine the generalisation to a two-dimensional geometry. We demonstrate that fast pulsed gates are capable of implementing high-fidelity entangling operations between ions in neighbouring traps faster than the trapping period, with experimentally demonstrated laser repetition rates. Notably, we find that without increasing the gate duration, high-fidelity gates are achievable even in large arrays with hundreds of ions. To demonstrate the usefulness of this proposal, we investigate the application of these gates to the digital simulation of a 40-mode Fermi-Hubbard model. This also demonstrates why shorter chains of gates required to connect arbitrary pairs of ions makes this geometry well suited for large-scale computation.

We present an efficient approach to optimising pulse sequences for implementing fast entangling two-qubit gates on trapped ion quantum information processors. We employ a two-phase procedure for optimising gate fidelity, which we demonstrate for multi-ion systems in linear Paul trap and microtrap architectures. The first phase involves a global optimisation over a computationally inexpensive cost function constructed under strong approximations of the gate dynamics. The second phase involves local optimisations that utilise a more precise ODE description of the gate dynamics, which captures the non-linearity of the Coulomb interaction and the effects of finite laser repetition rate. We propose two novel gate schemes that are compatible with this approach, and we demonstrate that they outperform existing schemes in terms of achievable gate speed and fidelity for feasible laser repetition rates. In optimising sub-microsecond gates in microtrap architectures, the proposed schemes achieve orders of magnitude higher fidelities than previous proposals. Finally, we investigate the impact of pulse imperfections on gate fidelity and evaluate error bounds for a range of gate speeds.

RF-induced micromotion in trapped ion systems is typically minimised or circumvented to avoid off-resonant couplings for adiabatic processes such as multi-ion gate operations. Non-adiabatic entangling gates (so-called `fast gates') do not require resolution of specific motional sidebands, and are therefore not limited to timescales longer than the trapping period. We find that fast gates designed for micromotion-free environments have significantly reduced fidelity in the presence of micromotion. We show that when fast gates are designed to account for the RF-induced micromotion, they can, in fact, out-perform fast gates in the absence of micromotion. The state-dependent force due to the laser induces energy shifts that are amplified by the state-independent forces producing the micromotion. This enhancement is present for all trapping parameters and is robust to realistic sources of experimental error. This result paves the way for fast two-qubit entangling gates on scalable 2D architectures, where micromotion is necessarily present on at least one inter-ion axis.

Most attempts to produce a scalable quantum information processing platform based on ion traps have focused on the shuttling of ions in segmented traps. We show that an architecture based on an array of microtraps with fast gates will outperform architectures based on ion shuttling. This system requires higher power lasers, but does not require the manipulation of potentials or shuttling of ions. This improves optical access, reduces the complexity of the trap, and reduces the number of conductive surfaces close to the ions. The use of fast gates also removes limitations on gate time. The performance of the gates is shown to be robust to the limitations in laser repetition rate and the presence of many ions in the trap array.