The Jarzynski equality relates the free-energy di erence between two equilibrium states to the work done on a system through far-from-equilibrium processes-a milestone that builds on the pioneering work of Clausius and Kelvin. Although experimental tests of the equality have been performed in the classical regime, the quantum Jarzynski equality has not yet been fully verified owing to experimental challenges in measuring work and work distributions in a quantum system. Here, we report an experimental test of the quantum Jarzynski equality with a single 171 Yb + ion trapped in a harmonic potential. We perform projective measurements to obtain phonon distributions of the initial thermal state. We then apply a laser-induced force to the projected energy eigenstate and find transition probabilities to final energy eigenstates after the work is done. By varying the speed with which we apply the force from the equilibrium to the far-from-equilibrium regime, we verify the quantum Jarzynski equality in an isolated system. T here is increasing interest in non-equilibrium dynamics at the microscopic scale, crossing over quantum physics, thermodynamics and information theory as the experimental control and technology at such a scale have been developing rapidly. Most of the principles in non-equilibrium processes are represented in the form of inequalities, as seen in the example of the maximum work principle, W − F ≥ 0, where the average work W is equal to the free-energy difference F only in the case of the equilibrium process. In close-to-equilibrium processes, the fluctuation-dissipation theorem is valid and connects the average dissipated energy W diss ≡ W − F and the fluctuation of the system σ 2 /2k B T . Here σ is the standard deviation of the work distribution, T is the initial temperature of the system in thermal equilibrium and k B is the Boltzmann constant. Beyond the nearequilibrium regime, no exact results were known until Jarzynski found a remarkable equality 1 that relates the free-energy difference to the exponential average of the work done on the system:The Jarzynski equality (1) is satisfied irrespective of the protocols of varying parameters of the system even when the driving is arbitrarily far from equilibrium. The relation enables us to experimentally determine F of a system by repeatedly performing work at any speed. Experimental tests of the classical Jarzynski equality and its relation to the Crooks fluctuation theorem 2 have been successfully performed in various systems 3-12 .In classical systems, work can be obtained by measuring the force and the displacement, and then integrating the force over the displacement during the driving process. In the quantum regime, however, as a result of Heisenberg's uncertainty principle, we cannot determine the position and the momentum simultaneously-thus invalidating the concepts of force and displacement. Instead of measuring these classical observables, it is necessary to carry out projective measurements over the energy eigenstates to determine the work d...

A long-time quantum memory capable of storing and measuring quantum information at the single-qubit level is an essential ingredient for practical quantum computation and com-munication [1,2]. Recently, there have been remarkable progresses of increasing coherence time for ensemble-based quantum memories of trapped ions [3,4], nuclear spins of ionized donors [5] or nuclear spins in a solid [6]. Until now, however, the record of coherence time of a single qubit is on the order of a few tens of seconds demonstrated in trapped ion systems [7][8][9]. The qubit coherence time in a trapped ion is mainly limited by the increasing magnetic field fluctuation and the decreasing state-detection efficiency associated with the motional heating of the ion without laser cooling [10,11]. Here we report the coherence time of a single qubit over 10 minutes in the hyperfine states of a 171 Yb + ion sympathetically cooled by a 138 Ba + ion in the same Paul trap, which eliminates the heating of the qubit ion even at room temperature. To reach such coherence time, we apply a few thousands of dynamical decoupling pulses to suppress the field fluctuation noise [5,6,[12][13][14][15][16]. A long-time quantum memory demonstrated in this experiment makes an important step for construction of the memory zone in scalable quantum computer architectures [17,18] or for ion-trap-based quantum networks [2,19,20]. With further improvement of the coherence time by techniques such as magnetic field shielding and increase of the number of qubits in the quantum memory, our demonstration also makes a basis for other applications including quantum money [21,22].The trapped ion system constitutes one of the leading candidates for the realization of large-scale quantum computers [1]. It also provides a competitive platform for the realization of quantum networks which combines long-distance quantum communication with local quantum computation [2]. One scalable architecture for iontrap quantum computer is to divide the system into operation and memory zones and to connect them through ion shuttling [17,18]. For this architecture, the basic unit of operation zone has been demonstrated [23,24]. As the size of the system scales up, the needed storage time of the qubits in the memory zone will correspondingly increase. To keep the qubit error rates below a certain threshold for fault-tolerant computation, it is crucial to extend the coherence time of qubits. For the quantum network based on probabilistic ion-photon mapping [25], the basic units of ion-photon and ion-ion entanglement have been demonstrated [26][27][28]. The required coherence time of qubits increases in this approach as the size of the system grows. A long-time quantum memory is therefore important for both quantum computation and communication [2,29].For trapped ion qubits, the main noise is not relaxation with time T 1 but instead dephasing with time T * 2 induced by fluctuation of magnetic fields. The current records of single-qubit coherence time in trapped ion systems are around tens of se...

a b s t r a c tBackground:: Coronavirus disease 2019 is pandemic and has caused illness to many people worldwide. This review aimed to summarize and analyze the herbal formulae provided by the guidelines for their pattern identifications (PIs) and compositions of herbs to treat patients with COVID-19. Methods:: We searched 7 data sources for eligible traditional medicine guidelines up to March 6, 2020 and found a total of 28 traditional medicine guidelines that provide treatment measures for COVID-19. Results:: Of the 28 guidelines, there were 26 government-issued Chinese guidelines and 2 Korean guidelines. After standardizing the terminology of the PIs and herbal formulae, there were 8 PIs and 23 herbal formulae for the mild stage, 11 PIs and 31 herbal formulae for the moderate stage, 8 PIs and 21 herbal formulae for the severe stage, and 6 PIs and 23 herbal formulae for the recovery stage in the Chinese guidelines. In the Korean guidelines, there were 4 PIs and 15 herbal formulae for the mild stage, 3 PIs and 3 herbal formulae for the severe stage, and 2 PIs and 2 herbal formulae for the recovery stage. In the frequency analysis of herbs, Glycyrrhizae Radix et Rhizoma was found to be the herb with the highest frequency of usage in the Chinese guidelines. Conclusion:: This review can be used as guidance for the traditional medicine treatment of COVID-19. Clinical evidence is needed in the future to evaluate the efficacy of traditional medicine.

Large-scale oil production from oil sands deposits in Alberta, Canada has raised concerns about environmental impacts, such as the magnitude of air pollution emissions. This paper reports compound emission rates (E) for 69-89 nonbiogenic volatile organic compounds (VOCs) for each of four surface mining facilities, determined with a top-down approach using aircraft measurements in the summer of 2013. The aggregate emission rate (aE) of the nonbiogenic VOCs ranged from 50 ± 14 to 70 ± 22 t/d depending on the facility. In comparison, equivalent VOC emission rates reported to the Canadian National Pollutant Release Inventory (NPRI) using accepted estimation methods were lower than the aE values by factors of 2.0 ± 0.6, 3.1 ± 1.1, 4.5 ± 1.5, and 4.1 ± 1.6 for the four facilities, indicating underestimation in the reported VOC emissions. For 11 of the combined 93 VOC species reported by all four facilities, the reported emission rate and E were similar; but for the other 82 species, the reported emission rate was lower than E. The median ratio of E to that reported for all species by a facility ranged from 4.5 to 375 depending on the facility. Moreover, between 9 and 53 VOCs, for which there are existing reporting requirements to the NPRI, were not included in the facility emission reports. The comparisons between the emission reports and measurementbased emission rates indicate that improvements to VOC emission estimation methods would enhance the accuracy and completeness of emission estimates and their applicability to environmental impact assessments of oil sands developments.volatile organic compounds | emissions | emission inventory validation | oil sands | aircraft measurements

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