Fast mixed-species quantum logic gates for trapped-ion quantum networks

TL;DR

The proposed mixed-species gate mechanism can be used for fast transfer of quantum information between specialized qubits and quantum memories, which it is shown enables the protection of matter-photon interfaces against rapid spin dephasing in optical networks of trapped-ion processors.

Abstract

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.

Figures (6)

• Figure 1: (a) Fast gate solutions with state-averaged fidelities above $99.9\%$, assuming idealised SDKs, demonstrating a trade-off between the gate time ($\tau_{\rm G}$) and number of SDKs ($\mathcal{N}$). (b) A universal trend is revealed under the rescaling $\mathcal{N}\rightarrow \bar{\eta}_{\rm eff}\mathcal{N}, \tau_{\rm G}\rightarrow \Delta\omega \tau_{\rm G}/(2\pi)$, with the exception of the large-mass-imbalance pair $^{171}$Yb--$^{9}$Be. (c-d) The motional dynamics of exemplary gate solutions in terms of the means of the mode quadratures, $\hat{X}=(\hat{a}+\hat{a}^\dag)/\sqrt{2}$ and $\hat{Y}=i(\hat{a}^\dag-\hat{a})/\sqrt{2}$, for the in-phase (ip) and out-of-phase (op) motional modes. (c) illustrates a $1.5\mu$s gate between $^{43}$Ca and $^{88}$Sr ($\varepsilon_{\rm av}\approx 2\times 10^{-10}$). (d) shows a $560$ns gate between $^{171}$Yb and $^{9}$Be using $\mathcal{N}=25$ SDKs ($\varepsilon_{\rm av}\approx 10^{-4}$). (e-f) Sensitivity of select gate solutions against timing jitter in the SDK pulse sequence, with the gate error averaged over $10^{4}$ noise realisations. Errorbars indicate the standard deviation in the ensemble average. (g-h) Impact of frequency drifts of the high-frequency op mode on the state-averaged gate error, for select gate solutions.
• Figure 2: Implementation of SDKs in a dual-species $^{133}$Ba$^+$--$^{138}$Ba$^+$ chain. (a) Configuration of Raman beam orientations, polarizations and magnetic field directions relative to the 2-ion chain. (b) i. Energy levels of the $6s_{1/2}$ manifold in $^{133}$Ba$^+$ illustrating the two qubit states and Raman couplings between them. ii. Energy levels and Raman couplings between the qubit states in the $6s_{1/2}$ manifold of $^{138}$Ba$^+$. (c) SDKs can be implemented asynchronously, e.g. first an SDK is implemented on $^{133}$Ba$^+$ using nanosecond sequences of ultrafast pulses (i.) followed by a single-pulse SDK on $^{138}$Ba$^+$ (ii.), as described in the main text.
• Figure [S1]: Sensitivity of MHz-speed gate solutions against timing jitter in the SDK pulse sequence, with the gate error averaged over $10^{4}$ noise realisations. Errorbars indicate the standard deviation in the ensemble average.
• Figure [S2]: Effect of frequency drift on the out-of-phase ('op') motional mode, for a range of gate times. Dashed (dotted) lines indicates contribution of phase (motional) errors to the total gate infidelity given by Eq. \ref{['eq:infidelityfunction_modebasis_appendix']}.
• Figure [S3]: Effect of frequency drifts common to both motional modes, for a range of gate times. Dashed (dotted) lines indicates contribution of phase (motional) errors to the total gate infidelity given by Eq. \ref{['eq:infidelityfunction_modebasis_appendix']}.