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 present a protocol for encoding N real numbers stored in N memory registers into the amplitudes of the quantum superposition that describes the state of log_{2}N qubits. This task is one of the ...main steps in quantum machine learning algorithms applied to classical data. The protocol combines partial CNOT gate rotations with probabilistic projection onto the desired state. The number of additional ancilla qubits used during the implementation of the protocol, as well as the number of quantum gates, scales linearly with the number of qubits in the processing register and hence logarithmically with N. The average time needed to successfully perform the encoding scales logarithmically with the number of qubits, in addition to being inversely proportional to the acceptable error in the encoded amplitudes. It also depends on the structure of the dataset in such a way that the protocol is most efficient for nonsparse data.
The interaction between an atom and the electromagnetic eld inside a cavity16 has played a crucial role in developing our understanding of lightmatter interaction, and is central to various quantum ...technologies, including lasers and many quantum computing architectures. Superconducting qubits7,8 have allowed the realization of strong9,10 and ultrastrong1113 coupling between articial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies ( and !o, respectively), the energy eigenstates including the ground state are predicted to be highly entangled14. There has been an ongoing debate1517 over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a ux qubit and an LC oscillator via Josephson junctions, we have realized circuits with g/!o ranging from0.72 to 1.34 and g/ 1. Using spectroscopy measurements,
Remarkable progress towards realizing quantum computation has been achieved using natural and artificial atoms as qubits. This paper presents a brief overview of the current status of different types ...of qubits. On the one hand, natural atoms (such as neutral atoms and ions) have long coherence times, and could be stored in large arrays, providing ideal 'quantum memories'. On the other hand, artificial atoms (such as superconducting circuits or semiconductor quantum dots) have the advantage of custom-designed features and could be used as 'quantum processing units'. Natural and artificial atoms can be coupled with each other and can also be interfaced with photons for long-distance communications. Hybrid devices made of natural/artificial atoms and photons may provide the next-generation design for quantum computers.
This paper starts with a brief review of the topic of strong and weak pre- and post-selected (PPS) quantum measurements, as well as weak values, and afterwards presents original work. In particular, ...we develop a nonperturbative theory of weak PPS measurements of an arbitrary system with an arbitrary meter, for arbitrary initial states of the system and the meter. New and simple analytical formulas are obtained for the average and the distribution of the meter pointer variable. These formulas hold to all orders in the weak value. In the case of a mixed preselected state, in addition to the standard weak value, an associated weak value is required to describe weak PPS measurements. In the linear regime, the theory provides the generalized Aharonov–Albert–Vaidman formula. Moreover, we reveal two new regimes of weak PPS measurements: the strongly-nonlinear regime and the inverted region (the regime with a very large weak value), where the system-dependent contribution to the pointer deflection decreases with increasing the measurement strength. The optimal conditions for weak PPS measurements are obtained in the strongly-nonlinear regime, where the magnitude of the average pointer deflection is equal or close to the maximum. This maximum is independent of the measurement strength, being typically of the order of the pointer uncertainty. In the optimal regime, the small parameter of the theory is comparable to the overlap of the pre- and post-selected states. We show that the amplification coefficient in the weak PPS measurements is generally a product of two qualitatively different factors. The effects of the free system and meter Hamiltonians are discussed. We also estimate the size of the ensemble required for a measurement and identify optimal and efficient meters for weak measurements. Exact solutions are obtained for a certain class of the measured observables. These solutions are used for numerical calculations, the results of which agree with the theory. Moreover, the theory is extended to allow for a completely general post-selection measurement. We also discuss time-symmetry properties of PPS measurements of any strength and the relation between PPS and standard (not post-selected) measurements.
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.
Abstract
We investigate the dynamics of a qubit-oscillator system under the influence of a linear sweep of system parameters. We consider two main cases. In the first case, we consider sweeping the ...parameters between the regime of a weakly correlated ground state and the regime of a strongly correlated ground state, a situation that can be viewed as a finite-duration quench between two phases of matter: the normal phase and the superradiant phase. Excitations are created as a result of this quench. We investigate the dependence of the excitation probabilities on the various parameters. We find a qualitative asymmetry in the dynamics between the cases of a normal-to-superradiant and superradiant-to-normal quench. The second case of parameter sweeps that we investigate is the problem of a Landau–Zener sweep in the qubit bias term for a qubit coupled to a harmonic oscillator. We analyze a theoretical formula based on the assumption that the dynamics can be decomposed into a sequence of independent Landau–Zener transitions. In addition to establishing the conditions of validity for the theoretical formula, we find that under suitable conditions, deterministic and robust multi-photon state preparation is possible in this system.
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.
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•First study that reports the detection of SARS-CoV-2 RNA fragments in wastewater in Qatar.•SARS-CoV-2 RNA was detected in all the influent wastewater samples (7,889 ± 1,421 copy/L – 542,056 ± 25,775) copy/L).•WBE modeling gives good estimation of infected population numbers supported by clinical seroprevalence data•WBE model shows that the number of infected people dropped from 542,313 ± 51,159 to 31,181± 3,081 over the sampling period
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.
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.
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