C D B Bentley

Fast entangling gates have been proposed for trapped ions that are orders of magnitude faster than current implementations. We present here a detailed analysis of the challenges involved in performing a successful fast gate. We show that the RWA is a stable approximation with respect to pulse numbers: the timescale on which we can neglect terms rotating at the atomic frequency is negligibly affected by the number of pulses in the fast gate. In contrast, we show that the laser pulse instability does give rise to a pulse-number dependent effect; the fast gate infidelity is compounded with the number of applied imperfect pulses. Using a dimensional reduction method presented here, we find bounds on the pulse stability required to achieve two-qubit gate fidelity thresholds.

Large-scale digital quantum simulations require thousands of fundamental entangling gates to construct the simulated dynamics. Despite success in a variety of small-scale simulations, quantum information processing platforms have hitherto failed to demonstrate the combination of precise control and scalability required to systematically outmatch classical simulators. We analyse how fast gates could enable trapped-ion quantum processors to achieve the requisite scalability to outperform classical computers without error correction. We analyze the performance of a large-scale digital simulator, and find that fidelity of around 70% is realizable for pi-pulse infidelities below $10^{-5}$ in traps subject to realistic rates of heating and dephasing. This scalability relies on fast gates: entangling gates faster than the trap period.

Fast entangling gates for trapped ions offer vastly improved gate operation times relative to implemented gates, as well as approaches to trap scaling. Gates on neighbouring ions only involve local ions when performed sufficiently fast, and we find that even a fast gate between distant ions with few degrees of freedom restores all the motional modes given more stringent gate speed conditions. We compare pulsed fast gate schemes, defined by a timescale faster than the trap period, and find that our proposed scheme has less stringent requirements on laser repetition rate for achieving arbitrary gate time targets and infidelities well below $10^{-4}$. By extending gate schemes to ion crystals, we explore the effect of ion number on gate fidelity for coupling neighbouring pairs of ions in large crystals. Inter-ion distance determines the gate time, and a factor of five increase in repetition rate, or correspondingly the laser power, reduces the infidelity by almost two orders of magnitude. We also apply our fast gate scheme to entangle the first and last ions in a crystal. As the number of ions in the crystal increases, significant increases in the laser power are required to provide the short gate times corresponding to fidelity above 0.99.

Driven dissipative steady state entanglement schemes take advantage of coupling to the environment to robustly prepare highly entangled states. We present a scheme for two trapped ions to generate a maximally entangled steady state with fidelity above 0.99, appropriate for use in quantum protocols. Furthermore, we extend the scheme by introducing detection of our dissipation process, significantly enhancing the fidelity. Our scheme is robust to anomalous heating and requires no sympathetic cooling.

We present a fast phase gate scheme that is experimentally achievable and has an operation time more than two orders of magnitude faster than current experimental schemes for low numbers of pulses. The gate time improves with the number of pulses following an inverse power law. Unlike implemented schemes which excite precise motional sidebands, thus limiting the gate timescale, our scheme excites multiple motional states using discrete ultra-fast pulses. We use beam-splitters to divide pulses into smaller components to overcome limitations due to the finite laser pulse repetition rate. This provides gate times faster than proposed theoretical schemes when we optimise a practical setup.