Ultra-fast two-qubit ion gate using sequences of resonant pulses

Abstract

We propose a new protocol to implement ultra-fast two-qubit phase gates with trapped ions using spin-dependent kicks induced by resonant transitions. By only optimizing the allocation of the arrival times in a pulse train sequence the gate is implemented in times faster than the trapping oscillation period T < 2π/ω. Such gates allow us to increase the number of gate operations that can be completed within the coherence time of the ion-qubits favoring the development of scalable quantum computers.

Multi-GHz repetition rate, multi-watt average power, ultraviolet laser pulses for fast trapped-ion entanglement operations

“…The experimental setup described in [20] combined with the ultrafast pulsed laser source based on a frequency comb presented above constitute the basis for the implementation of a fast two-qubit phase gate [26]. We propose an implementation using 40 Ca + ions where the qubit is stored in the 4S 1/2 and 3D 5/2 internal states and we use the 4S 1/2 ↔ 4P 3/2 transition for applying state-dependent momentum kicks to the ions via resonant laser pulses.…”

“…The unitary generated by a sequence containing N pulses expressed in the center-of-mass and stretch coordinates takes the form U = U c U s , where U c,s = N n=1 U c,s (t n ) are the unitary operators produced by H 1 and an interspersed free evolution H 0 during a t n time [26]. In phase space, the Heisenberg representation allows us to interpret these interactions as displacements of the Fock operators a c,s by a complex number A c,s that depends on the collective state of the ions…”

“…In the following we solve the set of equations ( 2) and ( 4). The fastest allowed gate will depend on the controllability degree, however, this simple scenario which relies only on pulse picking [26], and fixes the strength, direction, and repetition rate of the pulses, leads to gates faster than the trapping period T < 2π/ω. Due to the finite repetition rate of the source generator, the pulse sequence design combines i) simple continuous solutions with ii) fine-tuned pulse picking based on a genetic algorithm [26] leading to optimal solutions that minimize the gate error = |A c | 2 + |A s | 2 that quantifies the deviations to recover the original position after the whole kicking sequence.…”