Abstract
Fast entangling gates for trapped ion pairs offer vastly improved gate operation times relative to implemented gates, as well as approaches to trap scaling. Gates on a neighbouring ion pair only involve local ions when performed sufficiently fast, and we find that even a fast gate between a pair of 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 two neighbouring 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.
Highlights
Trapped ion systems have performed quantum algorithms on small scales [1,2,3,4,5], achieving results inaccessible to the classical regime remains a significant challenge
The quantised motional modes can be used as an information bus, where spin-state information can be mapped onto the motional state, and subsequently onto another ion’s spin-state. This idea was outlined in the original proposal for quantum information processing (QIP) using trapped ions [6]
We will focus on the GZC and Fast Robust Antisymmetric Gate (FRAG) gates, with very high fidelities, as we extend the fast gate schemes to target two ions in ion crystals of varying length
Summary
Trapped ion systems have performed quantum algorithms on small scales [1,2,3,4,5], achieving results inaccessible to the classical regime remains a significant challenge. Gates exceeding the local ion oscillation frequency only need consider the motion of neighbouring ions to those entangled by the gate This locality allows a small number of degrees of freedom to determine a high-fidelity two-qubit gate scheme addressing two ions in an arbitrary length ion crystal. Recent progress has been made towards fast gates using high repetition-rate pulsed lasers [47, 48, 50,51,52], including implementation of the pulse pairs required for the gate [51, 52] and an exploration of spin-motion entanglement in the strong coupling regime [48] We present our results that a distant, non-neighbouring ion pair can be coupled in the fast regime using large momentum transfers, with motional restoration from simple symmetries in the pulse scheme
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