We investigate the use of machine learning for solving analytic problems in theoretical physics. In particular, symbolic regression (SR) is making rapid progress in recent years as a tool to fit data using functions whose overall form is not known in advance. Assuming that we have a mathematical problem that is posed analytically, e.g. through equations, but allows easy numerical evaluation of the solution for any given set of input variable values, one can generate data numerically and then use SR to identify the closed-form function that describes the data, assuming that such a function exists. In addition to providing a concise way to represent the solution of the problem, such an obtained function can play a key role in providing insight and allow us to find an intuitive explanation for the studied phenomenon. We use a state-of-the-art SR package to demonstrate how an exact solution can be found and make an attempt at solving an unsolved physics problem. We use the Landau-Zener problem and a few of its generalizations as examples to motivate our approach and illustrate how the calculations become increasingly complicated with increasing problem difficulty. Our results highlight the capabilities and limitations of the presently available SR packages, and they point to possible modifications of these packages to make them better suited for the purpose of finding exact solutions as opposed to good approximations. Our results also demonstrate the potential for machine learning to tackle analytically posed problems in theoretical physics.
We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator ([Formula: see text] CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency [Formula: see text] for the coupling between the FQ and the modes in the CPWR, where the coupling grows as [Formula: see text] for [Formula: see text] and decreases as [Formula: see text] for [Formula: see text]. Here [Formula: see text] is the frequency of the nth mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above [Formula: see text] at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3% and the total Lamb shift from all the modes is 96.5%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.
Raw municipal wastewater from five wastewater treatment plants representing the vast majority of the Qatar population was sampled between the third week of June 2020 and the end of August 2020, during the period of declining cases after the peak of the first wave of infection in May 2020. The N1 region of the SARS-CoV-2 genome was used to quantify the viral load in the wastewater using RT-qPCR. The trend in Ct values in the wastewater samples mirrored the number of new daily positive cases officially reported for the country, confirmed by RT-qPCR testing of naso-pharyngeal swabs. SARS-CoV-2 RNA was detected in 100% of the influent wastewater samples (7889 ± 1421 copy/L - 542,056 ± 25,775 copy/L, based on the N1 assay). A mathematical model for wastewater-based epidemiology was developed and used to estimate the number of people in the population infected with COVID-19 from the N1 Ct values in the wastewater samples. The estimated number of infected population on any given day using the wastewater-based epidemiology approach declined from 542,313 ± 51,159 to 31,181 ± 3081 over the course of the sampling period, which was significantly higher than the officially reported numbers. However, seroprevalence data from Qatar indicates that diagnosed infections represented only about 10% of actual cases. The model estimates were lower than the corrected numbers based on application of a static diagnosis ratio of 10% to the RT-qPCR identified cases, which is assumed to be due to the difficulty in quantifying RNA losses as a model term. However, these results indicate that the presented WBE modeling approach allows for a realistic assessment of incidence trend in a given population, with a more reliable estimation of the number of infected people at any given point in time than can be achieved using human biomonitoring alone.
COVID-19 , SARS-CoV-2 , Disease Outbreaks , Humans , Qatar/epidemiology , RNA, Viral , Seroepidemiologic Studies , Wastewater , Wastewater-Based Epidemiological Monitoring
We investigate all-inorganic perovskite CsPbxSn1-xBr3 thin films to determine the variations in the band gap and electronic structure associated with the Pb/Sn ratio. We observe that the band gap can be tuned between 1.86 eV (x = 0) and 2.37 eV (x = 1). Intriguingly, this change is nonlinear in x, with a bowing parameter of 0.9 eV; furthermore, a slight band gap narrowing is found for low Pb content (minimum x â¼ 0.3). The wide tunability of the band gap makes CsPbxSn1-xBr3 a promising material, e.g., for a wide-gap subcell in tandem applications or for color-tunable light-emitting diodes. Employing photoelectron spectroscopy, we show that the valence band varies with the Pb/Sn ratio, while the conduction band is barely affected.
It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum algorithm which could solve this problem via simulated resonant transitions. Using a four-qubit quantum simulator in which two qubits are used as ancillas for control and measurement, we obtain the energy spectrum of a 2-qubit low-energy effective Hamiltonian of the water molecule. The simulated transitions allow the state of the quantum simulator to transform and access large regions of the Hilbert space, including states that have no overlap with the initial state. Furthermore, we make use of this algorithm to efficiently prepare specific eigenstates on the simulator according to the measured eigenenergies.
Hybrid metal-organic halide perovskites have recently attracted a great deal of attention because of their interesting electronic, optical and transport properties, which make them promising materials for high-performance, low-cost solar cells. Fundamental understanding of the formation mechanisms and dynamics of photoinduced charge carriers is essential for improving the performance of perovskite solar cell devices. For example, a significant amount of absorbed solar energy is lost as a result of carrier thermalization. This energy could be harnessed by extracting hot carriers before they cool down to the band edges. Although such hot carrier collection is experimentally challenging, theoretical investigations based on time-dependent methods can guide future experimental research by providing insights into the thermalization process. Here, we perform ab initio nonadiabatic molecular dynamics simulations to study non-radiative relaxation dynamics of charge carriers in hybrid halide perovskites. We find that the carrier relaxation time can be considerably increased by mixing halogen atoms in the perovskite materials. These findings show that simple approaches could be adopted to slow down the thermalization process of hot carriers in perovskite materials.
We present experiments on the driven dynamics of a two-level superconducting artificial atom. The driving strength reaches 4.78 GHz, significantly exceeding the transition frequency of 2.288 GHz. The observed dynamics is described in terms of quasienergies and quasienergy states, in agreement with Floquet theory. In addition, we observe the role of pulse shaping in the dynamics, as determined by nonadiabatic transitions between Floquet states, and we implement subnanosecond single-qubit operations. These results pave the way to quantum control using strong driving with applications in quantum technologies.
We investigate a hybrid electro-optomechanical system that allows us to realize controllable strong Kerr nonlinearities even in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are demonstrated in the weak-coupling regime, making the observation of strong Kerr nonlinearities feasible with currently available optomechanical technology.
