Abstract
Quantum computing is an emerging area within the information sciences revolving around the concept of quantum bits (qubits). A major obstacle is the extreme fragility of these qubits due to interactions with their environment that destroy their quantumness. This phenomenon, known as decoherence, is of fundamental interest1,2. There are many competing candidates for qubits, including superconducting circuits3, quantum optical cavities4, ultracold atoms5 and spin qubits6,7,8, and each has its strengths and weaknesses. When dealing with spin qubits, the strongest source of decoherence is the magnetic dipolar interaction9. To minimize it, spins are typically diluted in a diamagnetic matrix. For example, this dilution can be taken to the extreme of a single phosphorus atom in silicon6, whereas in molecular matrices a typical ratio is one magnetic molecule per 10,000 matrix molecules10. However, there is a fundamental contradiction between reducing decoherence by dilution and allowing quantum operations via the interaction between spin qubits. To resolve this contradiction, the design and engineering of quantum hardware can benefit from a ‘bottom-up’ approach whereby the electronic structure of magnetic molecules is chemically tailored to give the desired physical behaviour. Here we present a way of enhancing coherence in solid-state molecular spin qubits without resorting to extreme dilution. It is based on the design of molecular structures with crystal field ground states possessing large tunnelling gaps that give rise to optimal operating points, or atomic clock transitions, at which the quantum spin dynamics become protected against dipolar decoherence. This approach is illustrated with a holmium molecular nanomagnet in which long coherence times (up to 8.4 microseconds at 5 kelvin) are obtained at unusually high concentrations. This finding opens new avenues for quantum computing based on molecular spin qubits.
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Acknowledgements
We thank L. Song and J. van Tol for technical assistance with the X-band EPR spectrometer. This work was supported by the NSF (grant DMR-1309463) and the US AFOSR (AOARD contract 134031 FA2386-13-1-4029). Work performed at the NHMFL was supported by the NSF (DMR-1157490) and by the State of Florida. Work performed at the Instituto de Ciencia Molecular was supported by the European Research Council (grants SPINMOL and DECRESIM), by the Spanish MINECO (projects MAT-2014-56143-R, CTQ2014-52758-P and Excellence Unit Maria de Maeztu MDM-2015-0538) and by the Generalidad Valenciana (Prometeo and ISIC-Nano Programs of Excellence). A.G.-A. thanks the Spanish MINECO for a Ramón y Cajal Fellowship.
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S.H., E.C. and A.G.-A. conceived the research and wrote the paper. Y.D. prepared the samples. S.H., M.S. and D.K. designed the experiments, while M.S. and D.K. performed the measurements. S.H., M.S. and D.K. analysed the results.
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Extended data figures and tables
Extended Data Figure 1 T2 scaling.
a, b, Field-swept T2 measurements for the x = 0.001 (a) and x = 0.01 (b) concentrations at 5 K; the data are plotted as a function of (B0z − Bmin) on both log–log (main panels) and linear (insets) scales. The blue lines are power-law fits to the positive (B0z − Bmin) data (green points), with the obtained exponents (‘slope’) given in the figures. Error bars, ±standard error in T2.
Extended Data Figure 2 T2 divergence at the x = 0.01 concentration.
Shown are field-swept T2 measurements recorded at 5.0 K for two separate crystals at frequencies of 9.12 GHz (blue squares) and 9.20 GHz (red circles). Error bars, ±standard error in T2.
Extended Data Figure 3 ESE-detected spectra for the x = 0.01 concentration.
Variable frequency measurements at 5.0 K, with θ = 30°; the frequencies are indicated above each trace. Similar to spectra for the x = 0.001 sample, the broad 9.2 GHz CT peak splits into two upon moving away from the tunnelling gap minimum (see also Fig. 2). However, weak ESE intensity can still be detected at B0z = 165 mT at all four frequencies. This is due to vertical broadening of the CT, caused by a Gaussian distribution in 
.
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Shiddiq, M., Komijani, D., Duan, Y. et al. Enhancing coherence in molecular spin qubits via atomic clock transitions. Nature 531, 348–351 (2016). https://doi.org/10.1038/nature16984
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DOI: https://doi.org/10.1038/nature16984
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