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Journal of the American Chemical Society

Dipolar-Coupled Entangled Molecular 4f Qubits

Bela E. Bode, Edoardo Fusco, Rachel Nixon, Christian D. Buch, Høgni Weihe, Stergios Piligkos

Published Jan 25, 2023• 24 citations
Publisher

Abstract

High Resolution Image Download MS PowerPoint Slide We demonstrate by use of continuous wave- and pulse-electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute Yb III ions in Yb 0.01 Lu 0.99 (trensal) that molecular entangled two-qubit systems can be constructed by exploiting dipolar interactions between neighboring Yb III centers. Furthermore, we show that the phase memory time and Rabi frequencies of these dipolar-interaction-coupled entangled two-qubit systems are comparable to the ones of the corresponding single qubits.

DOI
10.1021/jacs.2c10902

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High Resolution Image Download MS PowerPoint Slide We demonstrate by use of continuous wave- and pulse-electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute Yb III ions in Yb 0.01 Lu 0.99 (trensal) that molecular entangled two-qubit systems can be constructed by exploiting dipolar interactions between neighboring Yb III centers. Furthermore, we show that the phase memory time and Rabi frequencies of these dipolar-interaction-coupled entangled two-qubit systems are comparable to the ones of the corresponding single qubits.
We herein probe the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagetic Resonance measurements at X-band (9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10^-1 , 10^-2 and 10^-3 % doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, Tm, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields Tm is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a Tm in the range 1 – 11 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10^-3 %, and under dynamic decoupling conditions, the ratio of Tm versus the time it takes t0 implement a quantum gate, TG, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to a gate fidelity of 99.99 %, reaching thus the lower limit for implementations in Quantum Information Technologies.
Abstract Nuclear spins are candidates to encode qubits or qudits due to their isolation from magnetic noise and potentially long coherence times. However, their weak coupling to external stimuli makes them hard to integrate into circuit quantum electrodynamics architectures, the leading technology for solid-state quantum processors. Here, we study the coupling of 173 Yb(III) nuclear spin states in an [Yb(trensal)] molecule to superconducting cavities. Experiments have been performed on magnetically dilute single crystals placed on the inductors of lumped-element LC superconducting resonators with characteristic frequencies spanning the range of nuclear and electronic spin transitions. We achieve a high cooperative coupling to all electronic and most nuclear [ 173 Yb(trensal)] spin transitions, a necessary ingredient for the implementation of qudit protocols with molecular spins using a hybrid architecture.
Nuclear spins are candidates to encode qubits or qudits due to their isolation from magnetic noise and potentially long coherence times. However, their weak coupling to external stimuli makes them hard to integrate into circuit-QED architectures, the leading technology for solid-state quantum processors. Here, we study the coupling of 173^{173}173Yb(III) nuclear spin states in an [Yb(trensal)] molecule to superconducting cavities. Experiments have been performed on magnetically diluted single crystals placed on the inductors of lumped-element LCLCLC superconducting resonators with characteristic frequencies spanning the range of nuclear and electronic spin transitions. We achieve a high cooperative coupling to all electronic and most nuclear [173^{173}173Yb(trensal)] spin transitions. This result is a big leap towards the implementation of qudit protocols with molecular spins using a hybrid architecture.
Coherent spin dynamics of impurity Yb3+{\text{Yb}}^{3+}Yb3+ ions in the CaWO4{\text{CaWO}}_{4}CaWO4​ single crystal has been studied using XXX- and WWW-band EPR. Rabi oscillations of the sample magnetization with damping times comparable to their period, driven by pulses of the microwave field with duration up to $5\text{ }\ensuremath{\mu}\text{s}$, were observed. The largest value of the single-qubit figure of merit $(\ensuremath{\sim}6400)$ is obtained for the high-field component in the 171Yb^{171}\text{Y}\text{b}171Yb XXX-band EPR spectrum. The spin-lattice relaxation time of the Yb3+{\text{Yb}}^{3+}Yb3+ ions shortens with the increasing resonance frequency while the phase memory time, in contrast, grows noticeably. Variations of the phase memory times are interpreted in terms of spectral and instantaneous diffusions. The increase of the coherence time at the WWW band can be used for the application of rare-earth ions as qubits in quantum computing as it has been proposed recently.
We study collective excitations of rotational and spin states of an ensemble of polar molecules, which are prepared in a dipolar crystalline phase, as a candidate for a high-fidelity quantum memory. While dipolar crystals are formed in the high-density limit of cold clouds of polar molecules under one- and two-dimensional trapping conditions, the crystalline structure protects the molecular qubits from detrimental effects of short-range collisions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms, and estimate their effects on gate operations, when a molecular ensemble qubit is transferred to a superconducting strip line cavity (circuit QED). In the case of rotational excitations coupled by dipole-dipole interactions we identify phonons as the main limitation of the lifetime of qubits. We study specific setups and conditions, where the coupling to the phonon modes is minimized. Detailed results are presented for a one-dimensional dipolar chain.