Multi-qubit gate with trapped ions for microwave and laser-based implementation

Abstract

A proposal for a phase gate and a Mølmer-Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups.High-fidelity quantum gates are a crucial element in the growing field of quantum information processing (QIP) [1]. Many theoretical proposals for quantum entangling gates have been considered for trapped ions [2][3][4][5][6][7][8][9][10][11], one of the most promising candidates for QIP [12][13][14]. These proposals have triggered impressive experimental realizations [15][16][17][18][19][20][21][22][23][24][25]. Although these experiments within the laser based designs have achieved high fidelities [16,[22][23][24][25], the achieved fidelities within the microwave based designs have been limited.Considerable theoretical efforts have been made to counter the fidelity-damaging effects. Techniques, such as dynamical decoupling using echo-pulse sequences [26,27], and its continuous version using a continuously applied driving field [28-33], have been proposed and realized experimentally [20,[34][35][36]. Recently, a combination of the continuous techniques with gate operators has been proposed [10,11] and realized [16,17] for the laser-induced implementations.In this manuscript, we introduce a scheme for a geometric gate σ σ ⨂ z z , and a Mølmer-Sørensen (MS) gate σ σ ⨂ x x in the dressed state basis for microwave-based implementations. It can also be implemented in laserbased experimental set-ups. Our scheme combines the gate operator and continuous dynamical decoupling which results in the gate being decoupled from the main fidelity damaging noise sources such as ambient magnetic field and Rabi frequency fluctuations.In what follows, we derive the gate Hamiltonian for a microwave-based design, while highlighting the dynamical decoupling processes which protect from the main noise sources. We then go on showing explicitly how our scheme could also be implemented using laser rather than microwave radiation.

Quantum dynamics of trapped ions in a dynamic field gradient using dressed states

“…Single-qubit gates using the dressed states ñ | as a qubit can be carried out by employing a resonant RF-field [35][36][37]. In order to implement conditional quantum gates, for example 2-qubit gates, the application of an RF-field tuned (close) to resonance with a motional sideband transition between dressed states can be used [1,17,22,38,39]. In this case, the effective Lamb-Dicke parameter j n , e allows for the necessary coupling between qubit states and motional states [10].…”

“…In this case, the effective Lamb-Dicke parameter j n , e allows for the necessary coupling between qubit states and motional states [10]. Gates with dressed states in a static field gradient have been proposed and successfully implemented with high fidelity [17,35,[37][38][39].…”

“…As a concrete example for dynamic MAGIC with dressed states we consider 171 Yb + ions exposed to a resonant driving field with a gradient of B 65 ¢ = T m −1 , 2 500 kHz 1 n p =´leading to 0.01 j,1 e » and a Rabi frequency characterizing the RF gate field of 2 0.1 MHz p´. According to [38] (where dressed states in a static gradient are considered), we expect a gate time of 200 s m and a gate fidelity in the regime of 0.998.…”

“…In existing implementations of dynamic MAGIC, a static bias magnetic field having a well defined magnitude is applied to a qubit resonance in order to make it to first order field insensitive and therefore only weakly sensitive to ambient magnetic fields, and thus enhance its coherence time [13,24,29,40]. An additional benefit from using dressed states that exist in a non-zero dynamic gradient field would be that dressed qubits are already resistant against dephasing by ambient noise fields [17,[35][36][37][38][39] without application of an accurately controlled, strong bias field. The dressed state qubit's coherence time would be sensitive to fluctuations in the amplitude of the dressing field.…”

Simulating the Haldane phase in trapped-ion spins using optical fields

“…Instead of having the XX (flipflop) Hamiltonian S i y S j y + S i x S j x as our starting point, in the new approach we engineer a Mølmer-Sørensen (MS) like gate [44] for spin-one systems that takes the form of an Ising Hamiltonian S i x S j x . We have found three ways to implement the MS gate for spin-one systems [44][45][46]. These schemes were originally proposed for two-level system (qubits), but can be extrapolated to three-level systems (qutrits).…”