Split (1)

train · 1.97k rows

shuffled_text stringlengths 268 3.92k	A stringclasses 6 values	B stringclasses 6 values	C stringclasses 6 values	D stringclasses 6 values	label stringclasses 4 values
A: The second is highly non-trivial, since now m1subscript𝑚1m_{1}italic_m start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT is externalB: of the kite in the integrand of (5)C: The relation F1,2,3=F1,4,6subscript𝐹123subscript𝐹146F_{1,2,3}=F_{1,4,6}italic_F start_POSTSUBSCRIPT 1 , 2 , 3 end_POSTSUBSCRIPT = italic_F ...	BAC	CAB	ABC	CAB	Selection 1
A: we used the triangle inequalityB: The third inequality follows again from EqsC: (23). The above arguments prove that ρ𝜌\rhoitalic_ρ can be converted into σ𝜎\sigmaitalic_σ via DIO with approximate catalysis whenever an asymptotic conversion via DIO is possible with rate at least one.	CAB	ABC	CAB	BAC	Selection 2
A: that every PMC solution is a collection of superalgebra irrepsB: This evidence is still missing. C: In order to elevate this simple and elegant argument to the level of a proof of chiral symmetry breaking, one should demonstrate that it works for a generic spectrum with exotics and that it gives the most...	CBA	ABC	BCA	CAB	Selection 3
A: We used predominantly general-purpose software packages to solve the SDPs involved. We used YALMIP [86] for modeling the problems and solved primarily using MOSEK [87]B: The unfavorable memory scaling of interior-point methods (see e.g. [88]) prevented us from going to bond dimensions higher than 7 in the MP...	ACB	CBA	ABC	BCA	Selection 4
A: This model showed the capability to already perform better across all the relevant metrics, achieving a precision of 29%percent2929\%29 %, 1%percent11\%1 % above the benchmark, with just 90909090 learners (against 1200120012001200) and runtimes of around 20202020 minutes compared to more than 3333 hours for the ...	BAC	CBA	BCA	CBA	Selection 3
A: Figure 11: Amplification of the energy (top) and angular momentum (bottom) against the frequency of the Q-ball ωQsubscript𝜔𝑄\omega_{Q}italic_ω start_POSTSUBSCRIPT italic_Q end_POSTSUBSCRIPT with mQ=1subscript𝑚𝑄1m_{Q}=1italic_m start_POSTSUBSCRIPT italic_Q end_POSTSUBSCRIPT = 1B: The coupling is g=1/3𝑔13...	BCA	CAB	ACB	ABC	Selection 3
A: The construction is characterized by a process that finds a multi-linear polynomial, which in this case is the Walsh-Hadamard transformB: The subsequent constructions differ precisely in the process of finding an equivalent multi-linear polynomial for the function. Thus, it is this process alone that disting...	BCA	ACB	BAC	ACB	Selection 1
A: Alternatively, in Fig. 1 the high-level strategy of a repeater protocol following a layered approach for entanglement swapping is illustrated.B: Naturally, the chosen repeater strategy decides which events exactly are used, e.g., a repeater protocol without entanglement purification may decide to schedule an...	ACB	BAC	CBA	BCA	Selection 3
A: As for applications to enhance couplings, the BO is readily applicable to systems with weak couplings to photons and strong intrinsic dephasing so that the squeezing-induced dephasing is marginal. Common examples are quantum dots [9] and spin ensembles [10]B: Yet, the future of BOs is not prescribed to the ...	CBA	BAC	CBA	CAB	Selection 2
A: We begin with the simplest modified conformally flat spacetimes. B: The current benchmark model of cosmology is the flat FLRW solution; therefore, we focus on the way the FLRW model is modified in our approachC: The rest of this paper is devoted to finding the simplest exact cosmological models of modifi...	ACB	CAB	CBA	ABC	Selection 3
A: The fellowship code is LCF/BQ/PI20/11760016B: JCB is also supported by the research grant PID2020-118635GB-I00 from the Spain-Ministerio de Ciencia e Innovación.C: JCB is supported by a fellowship from “la Caixa” Foundation (ID 100010434) and from the European Union’s Horizon 2020 research and innovation...	ABC	BCA	ACB	ACB	Selection 2
A: We allow only configurations that differ by a finite number of sites to produce offspringB: To address the concerns highlighted above, we preserve the framework they used for finite-volume Gibbs measures introducing infertility into the reproduction dynamicsC: This approach is similar to that employed in...	CAB	CAB	BAC	CAB	Selection 3
A: Figure 3 shows that the amount of contextuality decreases monotonically as coherence increases (at least according to these measures of contextuality and coherence)B: However, this intuition only goes so far, as we will give an example below where one achieves twice the robustness to dephasing by including ...	CAB	CBA	ACB	BAC	Selection 3
A: If such an experiment is accomplished, the principles used in the present model could be translated to other systems with the same logical capabilities and even for qudits with d>3𝑑3d>3italic_d > 3B: The latter condition could be also realised using atomic qudits based on an extension of our simple qutrit m...	ACB	BAC	CBA	ABC	Selection 4
A: In this work, we develop a unified treatment of nonlinear quantum optical effects based on phase space fillingB: Our theory is applicable to a wide range of exciton-polariton lattices, also in the presence of both Pauli and Coulomb blockadeC: We describe three distinct NPSF regimes being the planar, fra...	BAC	ABC	BCA	CAB	Selection 2
A: There are plenty of works, devoted to theoretical analysis of the energy propagation, induced by the supratransmission. In general, theoretical studies are focused on determining of conditions of the energy propagation by ILMs, with which emergence of the supratransmission is associated. The bibliography of such...	BCA	CBA	ABC	CAB	Selection 3
A: There arise 4 Higgs particles from the b⁢c𝑏𝑐bcitalic_b italic_c sector. B: Its detailed particle spectrum is shown in table 3C: Model 1 is a rare case without any filler branes and the hidden sector group SU(2) only comes from the d𝑑ditalic_d-stack of D6-branes	CBA	BAC	BCA	ABC	Selection 1
A: The first is the family of tangent X-states previously considered in Sec 5.1B: Now we apply Theorem 9 to two families of statesC: The second is a new family, which we call tangent spheroid states, which includes the family of the tangent sphere states, Sec. 5.3, as a special case. (Note that the canonica...	BAC	CBA	CAB	ABC	Selection 1
A: The type-II model is insteadB: The type-I model corresponds to ϵ𝒅=𝒀𝒖=𝟎superscriptbold-italic-ϵ𝒅superscript𝒀𝒖0\epsilon^{d}=Y^{u}=0bold_italic_ϵ start_POSTSUPERSCRIPT bold_italic_d end_POSTSUPERSCRIPT bold_= bold_italic_Y start_POSTSUPERSCRIPT bold_italic_u end_POSTSUPERSCRIPT bold_= bold_0C: of the...	ABC	ACB	ABC	CBA	Selection 4
A: Orbits evolve to become aligned and prograde with respect to the disc and circularize as they alignB: The final semimajor axis can be estimated analytically. This estimate is exact for circular orbits (see Appendix B, Rauch 1995, and Šubr & Karas 1999).C: Low inclination orbits remain close to their init...	CBA	BCA	BCA	ACB	Selection 4
A: We compare our results with other crystal detectors in literature as shown in Fig. 14. Experiments using doped crystals featured light yields smaller than 20 p.e./keVeeB: Recent results in Ref. Ding et al. (2022) used a 0.6×\times×0.6×\times×1.0 cm3 cryogenic pure CsI crystal readout by SiPM chips and achiev...	CAB	BAC	ABC	ACB	Selection 3
A: Thus we can conclude that small (3%) amount of free spins responsible for the observed absorption signal and for low-temperature magnetization offset (see Fig. 4) is decoupled from the main magnetic system of nabokoiteB: The main copper matrix of nabokoite does not contribute to the observed paramagnetic ES...	CBA	ACB	ABC	BAC	Selection 3
A: This is the effective Majorana neutrino mass parameter of the neutrinoless double beta decay, which gives information on the Majorana nature of the neutrinosB: Furthermore, in our model, another observable can be obtainedC: This mass parameter has the form:	CAB	BAC	ACB	ACB	Selection 2
A: SMaity would like to thank Ms. Diana Vaclavkova, Ms. Anushree Dey, Mr. Sanjib Naskar, Mr. Rahul Paramanik and Mr. Soumik Das. MP and BD is grateful to IACS for the fellowship. SD acknowledges the financial support from DST-SERB grant No. ECR/2017/002037, SCP/2022/000411 and CRG/2021/004334. SD also acknowledges ...	BAC	BCA	BAC	CBA	Selection 4
A: Compared with the classical counterpart, this quantum process has exponential acceleration in terms of data scale and quadratic speedup in data dimensionality. The other is a quantum secure multi-party computation (QSMC) protocol, which allows the aggregation of gradients to securely be done with quantum communi...	CAB	BCA	CBA	CBA	Selection 1
A: In Sec. III, the model of the likelihood and the Bayesian method are introduced. The constraints and relevant discussion are given in Sec. IV. Conclusions are given in Sec. V. B: In Sec. II, we briefly describe the galaxy catalog and FRB dataC: This paper is organized as follows	BAC	CAB	CAB	CBA	Selection 4
A: As we mentioned previously, the chip architecture will influence our parameterization. Depending on the architecture, the depth of the parameterization will be seriously influenced due to the need to apply several SWAP portsB: Thus, we are naturally led to ask whether for quantum machine learning models it ...	ABC	CBA	ACB	BAC	Selection 3
A: The basic idea is to study the Heisenberg evolution of an operator 𝒪𝒪\mathcal{O}caligraphic_O in a given quantum system governed by a Hamiltonian H𝐻Hitalic_H. The time evolution of 𝒪𝒪\mathcal{O}caligraphic_O is determined by the Heisenberg equationB: In this section we provide an outline of the recursi...	BAC	ACB	CAB	BAC	Selection 3
A: The importance of the bulk viscosity in the hydrodynamic evolution of quark gluon plasma has been emphasized in Refs. [51, 52, 53]. Our framework provides a direct control over this first-order transport coefficient through a choice of matching condition via b0subscript𝑏0b_{0}italic_b start_POSTSUBSCRIPT 0 end_...	CBA	BCA	ACB	ACB	Selection 1
A: The structure of the behavioral landscape is similar to the one found in wild type [19], with the dominating kinetics being the transitions between “runs” and “pirouettes”, see Fig. S7(a). However, mutants and wild type crucially differ at long timescales as mutants do not exhibit heavy tails, see Fig. 6(b). Ins...	ACB	ABC	CAB	BCA	Selection 3
A: The signatures of Virgo West and the group around NGC4709, that are respectively beyond Virgo and Centaurus in the lines-of-sight, can also be identified as secondary wavesB: There exist a visual agreement between the observed lines-of-sight dynamical state of Virgo and Centaurus and those reproduced by CLON...	ABC	BCA	CAB	ACB	Selection 4
A: In this section, we demonstrate the superiority of the enhanced EPR over the HJB loss alone and over the normalizing flow (NF), which is a class of generative models used for density estimation that leverage invertible transformations to map between complex data distributions and simple latent distributions [39]...	ACB	CAB	ABC	BCA	Selection 3
A: The generalization can be done in multiple ways, differing in the number of required stochastic variables and the symmetry properties of the non-unitary perturbation. B: Notice the difference between 𝒩𝒩\mathcal{N}caligraphic_N (the size of the measurement apparatus) and N𝑁Nitalic_N (the number of pointer ...	BAC	CBA	BCA	BCA	Selection 2
A: We also showed that training and generalization are also possible using time series dataB: As expected, there exists a limit for how much generalization can be achieved, however, we note the presence of regularity that is observed in the gradual increase in test loss. Using the proposed d𝑑ditalic_d-statisti...	BCA	CAB	BAC	CBA	Selection 1
A: The simulation geometry is described in more detail in Section A.2. Fig. 2 shows these simulated measurements on an α𝛼\alphaitalic_α-curve for the {6,4}64\{6,4\}{ 6 , 4 } MeV case, demonstrating that the theoretically predicted α𝛼\alphaitalic_α-line overlaps are present both at low area densities and at high-Z...	BAC	ACB	CAB	BCA	Selection 3
A: This method combines the linear decomposition method Cho & Lazarian (2003), singular value decomposition (SVD) method Santolík et alB: (2003), and multi-spacecraft timing analysis Pincon & Glassmeier (2008). We perform the calculations in each moving time window with a five-hour length and five-minute moving...	ABC	CAB	BCA	ACB	Selection 3
A: These are the generalizations of closed string operators in the case of anyons. These operators are not necessarily unitary.B: The first step to generalizing this construction to more general excitation types (in general dimension, and including gapped boundaries) is the notion of flexible operator algebra**...	CBA	BCA	ACB	CAB	Selection 4
A: In this work we have connected several problems of majorization to the theory of preordered semiringsB: Using this framework, we have derived new sufficient and generically necessary conditions for large-sample and catalytic matrix majorization, i.e., Blackwell dominance in the finite-outcome settingC: I...	CBA	ABC	CAB	ACB	Selection 2
A: Also a large non-zero 𝐄⋅𝐁⋅𝐄𝐁{\bf E}\cdot{\bf B}bold_E ⋅ bold_B can enhance production of axions. The gravitational waves, in the early Universe also have the potential to generate large-scale magnetic fields, corresponding to resonant modes. B: Our numerical simulations suggest that gravitational waves a...	CBA	CBA	CAB	BAC	Selection 3
A: We receive support from Ontario Research Fund—research Excellence Program (ORF-RE), Natural Sciences and Engineering Research Council of Canada (NSERC) [funding reference number RGPIN-2019-067, CRD 523638-18, 555585-20], Canadian Institute for Advanced Research (CIFAR), Canadian Foundation for Innovation (CFI),...	CBA	CAB	ACB	CAB	Selection 3
A: If ΩΩ\Omegaroman_Ω is semisimple, its topological part can be evaluated explicitly in the idempotent basis, see e.gB: Generating functions of a CohFT ΩΩ\Omegaroman_Ω can be defined by integrating CohFT classesC: [18, Section 2.5.1]. A consequence of the Givental-Teleman classification is that the genera...	CBA	BAC	CBA	CBA	Selection 2
A: This pattern has been demonstrated to be independent of the input data which exhibits white noiseB: Since the input data consists of real world natural language sentences that our brain processes, our results demonstrate that artificial neural networks with close to human-level performance exhibit very simil...	ABC	CAB	CBA	BCA	Selection 4
A: To investigate the properties of non-equilibrium QGP medium, we take into account the viscous effect and study the responses of viscous QGP medium to the magnetic fieldB: Subsequently, we explore how the magnetized viscous effect impacts both the HQ potential and momentum diffusion coefficientC: In the s...	CBA	ACB	ABC	ACB	Selection 3
A: This allows us to provide a rigorous error and complexity analysis when uploading first a truncated and discretized approximation of the multivariate log-normal distribution and then uploading an approximation of the CPWA payoff function in rotated form, where the approximation consists of truncation as well as ...	BAC	BCA	BAC	BAC	Selection 2
A: We see that the traditional method accepts some regions of meta-stable EW-breaking vacuum, but checking the cosmological history proves that incorrectB: The exclusion of such regions is computationally fast, because one only needs to trace the minima of the potential with temperatureC: On the other hard...	BAC	ABC	CBA	BCA	Selection 2
A: We then add nodes and links following preferential attachment as described in [2] where each new node (labeled with a consecutive number) is attached to existing nodes via two linksB: BA: For this network, we start with a simple path graph with 4 numbered nodesC: However, and in contrast to the referenc...	BCA	BAC	CBA	ACB	Selection 2
A: Since the current can be polarization, time and space dependent, the effective speed can also have the same dependencyB: In this approach the effects of the current on the propagation of the EMWs has been encoded in the effective speedC: This is in agreement with the experimental evidence of the change ...	BCA	ABC	BAC	ACB	Selection 3
A: Figure 9 shows the Tully-Fisher relation from a single mock catalogue, for comparison with Figure 3B: There are no outliers as the generating model is purely Gaussian. Figure 10 shows the distributions of the actual and mock observables for the CF4 Tully-Fisher dataset and their pairwise correlations. It dem...	ACB	CBA	CBA	CAB	Selection 1
A: For MCMC, this is in some part due to higher mean values, and partly due to inflated errors. B: For GP, the alleviation is primarily because of the shifting of the mean to somewhat higher valuesC: With F1 (ΛΛ\Lambdaroman_ΛCDM), F2 (CPL) and F3 (PEDE), tensions decrease progressively from Fisher to MCMC t...	BAC	BCA	CAB	CBA	Selection 4
A: In the finite system, there is a small energy gap even in the gapless system. Thus, we make use of the finite-size scaling to check the energy gap in the thermodynamic limitB: In the VBS phase (Fig.6(a)), the energy gaps at different sizes are larger than 12⁢t3/V212superscript𝑡3superscript𝑉212t^{3}/V^{2}1...	ABC	CAB	BAC	CAB	Selection 1
A: For example, in [9] the asymptotics of the fundamental solution was constructed depending on the properties of the kernel of the process describing the jumpsB: It was also noted that in the case of pure jumps (without diffusion), the fundamental solution always contains a singular component.C: The prope...	BAC	BCA	CBA	ACB	Selection 2
A: The work demonstrates evidence that the feature of non-linearity from classical ML might be useful in quantum circuit models. B: This work put forth a preliminary investigation into the learning capabilities of the entire generative model, known as the Quantum Neuron Born Machine (QNBM), along with a demonst...	CAB	ABC	CAB	CBA	Selection 4
A: Despite the fact that the coded-aperture telescopes are unable to construct the images of extended objects, some information about their angular sizes can still be obtained from the IBIS data (see, e.g., Kuznetsova et al., 2019)B: In addition, special methods different from those that are used for point sour...	BCA	CAB	ABC	CAB	Selection 1
A: We have that the bulk where the branes are embedded has a particular distribution of matter, however the homogeneity and isotropy is fulfilled in the internal space of the brane, having in turn an arbitrary sectional curvatureB: For this case, we also find equations for the evolution of perturbations in bran...	CBA	BCA	BAC	CAB	Selection 2
A: Gamma-ray bursts are some of the most powerful astrophysical phenomena in the universeB: The collapsar model describes GRBs as the consequence of a failed supernova where all the energy of the gravitational collapse is funneled into a jet (Woosley, 1993)C: The jet is fed by the rotation of a central eng...	CAB	ABC	BCA	CBA	Selection 2
A: Linear combinations of spectral projections are simple functions on the spectrum — “simple” here is a technical term, meaning a finite linear combination of indicator functions. The statement that a positive operator can be approximated arbitrarily well with simple functions is then the standard measure theory f...	ACB	ABC	CBA	BCA	Selection 4
A: The alignment of FTLE behaviour, particularly into the neutral subspace, has been previously observed in similar conceptual chaotic models when they undergo a transition between regions of the attractor, as well as in models of regime shifts in atmospheric flows [16, 17, 18]B: [20], [21]). C: In general,...	CBA	CAB	ACB	BCA	Selection 3
A: The operator form of (1) first appeared in [15] in relation with conformal field theoryB: In [16] it was considered inside the context of three-dimensional integrable systems, while the set-theoretical version of (1) was studied in [17] in connection with Poisson maps, see also [18]C: Furthermore, the p...	CAB	ABC	ACB	CAB	Selection 2
A: NHSE can also occur in the synthetic field moments space of zero-dimensional bosonic quantum dimers [372]. An new, interacting form of the NHSE also occurs in the presence of interacting impurities, as manifested by so-called squeezed polarons which are impurity-localized dipole-like density profiles that are im...	CBA	ACB	BCA	CAB	Selection 4
A: and P.Y. were supported by NSFC Grant No. 12074438, Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B1515120100, and the Open Project of Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices under Grant No. 2022B1212010008. M.CB: acknowledges support from NSF un...	ACB	ABC	BAC	BCA	Selection 4
A: The red cross marks the estimate in (37). The color encodes the expectation value (left) or the average (right) of the cut sizeB: On the left, we mimic an ideal quantum device by evaluation of (19). On the right, values are results from the quantum hardware. Here, every pixel represents the average taken ove...	CAB	ABC	BCA	BAC	Selection 3
A: 4(a)-(d), respectively. Around the cross points in the curves, the interference stripes are clearly visible,B: by shifting the phase will be discussed in the next subsectionC: The quantum Lissajous scars for ωx/ωy=2/1,3/1,3/2,4/3subscript𝜔𝑥subscript𝜔𝑦21313243\omega_{x}/\omega_{y}=2/1,3/1,3/2,4/3itali...	CAB	ACB	ABC	BAC	Selection 1
A: [Eq. (14)]B: We have taken theC: This has the effect of replacing D𝐷Ditalic_D in A⁢(ℓ−)𝐴superscriptℓA(\ell^{-})italic_A ( roman_ℓ start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT ) with Dnsubscript𝐷𝑛D_{n}italic_D start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT	BCA	ACB	CAB	BAC	Selection 2
A: Furthermore, this method could miss potential dark UDGs — ones with extremely faint stellar light that are of high astrophysical interest (see Li et al., 2022, for more detailed discussions). B: The two major challenges with this method are: (1) the high computational cost of image segmentation needed to sep...	CBA	ACB	BCA	ACB	Selection 1
A: The completeness (or recall rate) of the RF classifier for different bins in planetary period-radius space is measured using the full set of synthetic planetary injections based on the Kepler planet sample (§4.1). The analysis is based on 7,751 of the 10,850 synthetic planetary injections that were processed by ...	ACB	CAB	CAB	CBA	Selection 4
A: The DTARPS-S Candidates catalog (Table 1) and DTARPS Galactic Plane list (Table 4) are ready for spectroscopic follow-up to remove remaining False Positives, measure other planetary properties, and further investigate the planetary systemsB: The results are informed by preliminary results of reconnaissance ...	CBA	CAB	ACB	CAB	Selection 3
A: In case of EqB: (8) with (12), the heavy-light diquarks satisfy the universal description irrespective of both mass of the light constituents and mass of the heavy constituentC: In case of Eq. (14) with (15), the heavy-light diquarks satisfy the universal description irrespective of mass of the heavy con...	BCA	ACB	BAC	ABC	Selection 4
A: Though we have provided some lower bounds on the size, we are also lacking a non-trivial upper bound. A second problem that we left open is the efficient construction of minimal generating sets of qudit Pauli subgroups in all cases. The missing step to get from a near-minimal generating set to a minimal one invo...	CAB	ACB	CBA	ABC	Selection 1
A: Here, polarized electron beams can play a crucial role in increasing the capability of analysisB: It allows a more selective probing of the process by enhancing the deviations from the SM via anomalous couplings and also the signal-background ratio. Eventually, it provides to make stringent tests and to get ...	ACB	BCA	BAC	BAC	Selection 2
A: These algorithms are based on iterative optimization techniques, such as the Gerchberg-Saxton algorithm, the Hybrid Input-Output algorithm, and the Error Reduction algorithm. They are powerful and can recover images with high qualities. However most of the time, iterative phase retrieval algorithms suffers from ...	ABC	BCA	BAC	ACB	Selection 2
A: 3B: Taking the indirect effects in the production network into account leads to 3 to 42 times higher estimates of job loss and 6 to 23 times higher estimates of economic output loss for the decarbonization strategies depicted in FigC: Note that EW-ESRI and OW-ESRI enable us to calculate both, the direct...	ABC	BAC	CBA	CAB	Selection 3
A: It is tantalizing that the rich theoretical scenario of USC has an experimental counterpart limited so far to standard spectroscopyB: What has prevented a broader experimental investigation? To gain insight into this issue we address a fundamental problem posed since the birth of the field [1] namely the exp...	ACB	ABC	ACB	CAB	Selection 2
A: In general, Q-ball potentials produce non-linearities in the equation of motion which require higher order modes to be nonzero. We have shown that this suggests the existence of a non-local, hence radiating, portion of the scalar fieldB: For small rotation, however, these radiation modes are only required to...	CAB	BAC	ABC	CBA	Selection 3
A: On the other hand, with rigid confinement, dilation is frustrated. When the dimension of a local high-density region is comparable to the gap between boundaries, a sudden rise in the stress response is expected [9, 5]B: The intense stress compels particles into profound interactions, revealing features that ...	CAB	ACB	CAB	BCA	Selection 4
A: The Pcal can give a modulation the mirror surface with photon pressureB: The summary of the calibration overview in O3GK is described in the summary paper. [8] The initial characterization of photon calibrator instruments are summarized elsewhere. [17, 18] Pcal can modulate the mirror displacement by inject...	BCA	CBA	ABC	ACB	Selection 4
A: Set v⁢(x)=∫0x∫0t{q⁢(s)⁢u⁢(s)−g⁢(s)}⁢𝑑s⁢𝑑t𝑣𝑥superscriptsubscript0𝑥superscriptsubscript0𝑡𝑞𝑠𝑢𝑠𝑔𝑠differential-d𝑠differential-d𝑡v(x)=\int_{0}^{x}\int_{0}^{t}\{q(s)u(s)-g(s)\}dsdtitalic_v ( italic_x ) = ∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_x end_POSTSUPERSCRIPT ∫ start_...	ABC	BAC	CBA	BAC	Selection 1
A: We believe MIQS can simplify initialization of a qutrit, by coupling it to a qubit. B: However, controlling qutrits can be a difficult taskC: There are various factors that need to be calibrated, such as frequency of the drive, amplitidue of the drive, leakage, etc	CAB	CBA	ACB	BAC	Selection 1
A: The structure of this paper is as follows. In Sec. II, we provide the general equations required to construct a bouncing solutionB: To begin with, we demonstrate how two popular inflationary models can be tweaked (albeit in an ad-hoc manner) to achieve this goal. Thereafter, we show how a simple augmentation...	CAB	ACB	CBA	ABC	Selection 2
A: Another domain feature that we have not considered is the inclusion of more than one target, one or more of which may be of non-circular shapeB: The multiple-target problem has been considered at length for Brownian motion on flat 2- and 3-dimensional geometries using hybrid asymptotic-numerical methods see...	BCA	BCA	BAC	ABC	Selection 4
A: In the convention, θ~−,csubscript~𝜃𝑐\tilde{\theta}_{-,c}over~ start_ARG italic_θ end_ARG start_POSTSUBSCRIPT - , italic_c end_POSTSUBSCRIPT is locked at 0 and π/2𝜋2\pi/2italic_π / 2 for s𝑠sitalic_s- and d𝑑ditalic_d- pairing states respectively. Thus if C0=Cπsubscript𝐶0subscript𝐶𝜋C_{0}=C_{\pi}italic_C st...	ACB	BCA	ABC	BAC	Selection 3
A: The entanglement spectrum can show different behaviors from the energy spectrum of the subsystem as an independent system under open boundary condition. Tuning the coupling between the subsystem and environment can change the ES gap, which indicates that the coupling accounts for the inconsistency of the Li-Hald...	BAC	CAB	ABC	ACB	Selection 1
A: In particular, it would be interesting to compare a policy that incorporates entanglement distillation to one without entanglement distillation that simply does the memory-cutoff policy with a single memory [72]. It is not obvious that entanglement distillation will always give a better overall fidelity, and und...	CBA	ACB	CAB	BCA	Selection 3
A: Sequences of symbols that disagree in every place could find application in authentication protocols [14]B: The use of checking sequences for elements that were not sent, that is the sequence of states sent and the sequence of measurement results disagree, has been used in digital signature schemes [15].**C...	CAB	BAC	CAB	ACB	Selection 4
A: When the HNLS condition is satisfied and the HL is achievable, for qubit probes where the signal and noise acts individually on each probe, an optimal ancilla-free repetition code can be constructed Dür et al. (2014); Arrad et alB: (2019). In the case where the HNLS condition is violated, weakly spin-squeeze...	ACB	CBA	BAC	CBA	Selection 1
A: N000142212764. B.P and A.M.A. acknowledge support from ONR Grant No. N000141712793. B: Office of Naval Research (ONR) through Grants No. N000142112450 and MURI NoC: This work is supported in part by DARPA Topological Excitations in Electronics (TEE) program under grant No. DP18AP900007, the U.S	CBA	CAB	BCA	BAC	Selection 1
A: Figure 3: (a) Energy errors for TC calculations of the H2 bond dissociation w.r.tB: Å). TC-VarQITE calculations are based on HF orbitals in a STO-6G (4 qubits), 6-31G (8 qubits), and cc-pVDZ (20 qubits) basis sets. Also shown are no-TC FCI/cc-pVDZ calculations.C: CBS limit results (mH vs	ACB	CBA	BAC	BCA	Selection 1
A: It started with Sutherland’s discovery of a flat band in the dice lattice [28]B: Historically, developing flat band models has been a long and arduous processC: It continued with Lieb’s work on the Hubbard model, demonstrating that certain bipartite lattices with chiral flat bands exhibit ferromagnetism ...	ABC	BAC	CBA	ACB	Selection 2
A: It is worth mentioning that the studies in RefsB: predictions regarding the mixing angles with θ23=π4subscript𝜃23𝜋4\theta_{23}=\frac{\pi}{4}italic_θ start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT = divide start_ARG italic_π end_ARG start_ARG 4 end_ARG and θ13=0subscript𝜃130\theta_{13}=0italic_θ start_POSTSUBSCR...	ACB	BAC	ABC	CBA	Selection 2
A: The circuit is characterized by less depth and only one layer gives high accuracy of classification resultsB: The variant (B) of the circuit was created to directly build states consistent with the general structure of the data encoded in the undertaken classification taskC: This allowed us to built less...	CBA	ACB	BAC	CAB	Selection 3
A: The authors are grateful to Oleg Teryaev for useful discussions and to Andrey Kotov for the help at the initial stage of the projectB: This work has been carried out using computing resources of the Federal collective usage center Complex for Simulation and Data Processing for Mega-science Facilities at NRC ...	CAB	ABC	CBA	BAC	Selection 2
A: The paramagnet is a channel spin liquid, since local moments are screened, and no local order parameter existsB: The transition between Phase Ia and Ib is reminiscent of the phase diagram of the NLσ𝜎\sigmaitalic_σM describing a channel ferromagnet and a quantum paramagnet with order destroyed by topological...	CAB	ACB	BAC	ACB	Selection 3
A: In Section 2, we discuss the spectral decomposition of multimode thermal states after providing the necessary mathematical backgroundB: The structure of this article is as followsC: In Section 3, we include the main results of this article where Subsection 3.1 discusses the case of thermal states, and Su...	BAC	BCA	BCA	CAB	Selection 1
A: We start from Eq. (21), up until which every computation was exact for finite L𝐿Litalic_LB: In this section, we numerically analyse the behaviour of the S-matrix for a finite number of interaction sitesC: Note that throughout this section we do not use the circulant approximation used previously, in Se...	BCA	CAB	BAC	ABC	Selection 3
A: The first lemma contains the Sobolev embedding and the trace theoremB: These results are well-known so we omit the proof.C: We remind the reader that their constants are uniform for all 𝖢∈𝒞(1)𝖢superscript𝒞1\mathsf{C}\in\mathcal{C}^{(1)}sansserif_C ∈ caligraphic_C start_POSTSUPERSCRIPT ( 1 ) end_POST...	CAB	ACB	BCA	CBA	Selection 2
A: The AMPT model includes four main processes: initial conditions, partial scattering, hadronisation, and hadronic interactionsB: The initial conditions are generated from the heavy ion jet interaction generator (HIJING) model Wang:1991hta ; Gyulassy:1994ew , where minijet partons and soft-excited strings are ...	CBA	BAC	BCA	CAB	Selection 3
A: The relevant information necessary to formulate the problem is discussed in Sec. IIB: This includes identifying the system Hamiltonian, the initial state, and providing a formal definition of local temperature of the individual qubits. In Section III, we analyseC: The remainder of the paper is arranged a...	ACB	CBA	BCA	CBA	Selection 3
A: In 2014, the transmission phase limit theory for multilayer TA designs was introduced [5]B: 1(a) depicts a schematic illustration of the multilayer TA. Using microwave network models and S-parameters, researchers discovered the constraints on the transmission amplitude and phase of TA elements, demonstrating...	CAB	ACB	CAB	CAB	Selection 2
A: In this way, when passing from the limit cycle to the stationary solution the time-averaged magnetizations change continuously, i.e., the system undergoes a second-order phase transition. On the other hand, above the tricritical point, when passing from one phase to the other, the system experiences sudden jumps...	ACB	CAB	ABC	ACB	Selection 2
A: In this section, we will apply the results of the simulations describing the formation of PBHs to the calculation of the PBH mass function and abundance. It is desirable to compute the PBH abundance and mass function directly from ζ𝜁\zetaitalic_ζ, which appears in the FLRW metric, equation (11). To perform the ...	BAC	ACB	CAB	BCA	Selection 2
A: Even though this qubit is not measured for adding the next qubit, it still influences the corresponding constraint measurement via a CNOT gate. This influence must be taken into account in the fully parallel implementation, where all measurements are performed before the corrections (see Fig. 5). B: Similarl...	ACB	CBA	CAB	ACB	Selection 3

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.