One of the main important features of the noisy intermediate-scale quantum(NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyze the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover’s algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator’s results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99% of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.

Despite many of the applications of graphene rely on its uneven stiffness and high thermal conductivity, the mechanical properties of graphene, and in general of all 2D materials, are still elusive. The harmonic theory predicts a quadratic dispersion for the flexural acoustic vibrational mode, which leads the unphysical result that long wavelength in-plane acoustic modes decay before vibrating one period, preventing the propagation of sound. The robustness of the quadratic dispersion has been questioned by arguing that the anharmonic phonon-phonon interaction linearizes it. However, this implies a divergent bending rigidity in the long wavelength limit not reproduced experimentally. Here we show that rotational symmetry protects the quadratic flexural dispersion against phonon-phonon interactions and that, consequently, the bending stiffness is non-divergent irrespective of the temperature. Our non-perturbative anharmonic calculations also determine that sound propagation coexists with a quadratic dispersion. We also show that the temperature dependence of the height fluctuations of the membrane, known as ripples, is fully determined by thermal or quantum fluctuations, but without the anharmonic suppression of their amplitude previously assumed. The universality of our conclusions reconcile experimental evidence and theory not just in graphene, but all 2D materials.

Mid-infrared (mid-IR) optical spectroscopy of molecules is of large interest in physics, chemistry, and biology. However, probing nanometric volumes of molecules is challenging because of the strong mismatch of their mid-infrared absorption and scattering cross-sections with the free-space wavelength. We suggest overcoming this difficulty by nanofocusing acoustic graphene plasmon polaritons (AGPs) – oscillations of Dirac charge carriers coupled to electromagnetic fields with extremely small wavelengths – using a taper formed by a graphene sheet above a metallic surface. We demonstrate that due to the appreciable field enhancement and mode volume reduction, the nanofocused AGPs can efficiently sense molecular fingerprints in nanometric volumes. We illustrate a possible realistic sensing sсenario based on AGP interferometry performed with a near-field microscope. Our results can open new avenues for designing tiny sensors based on graphene and other 2D polaritonic materials.

Despite the interest raised by graphene and 2D materials, their mechanical and acoustic properties are still highly debated. Harmonic theory predicts a quadratic dispersion for the flexural acoustic mode. Such a quadratic dispersion leads to diverging atomic fluctuations and a constant linewidth of in-plane acoustic phonon modes at small momentum, which implies that graphene cannot propagate sound waves. Many works based on membrane theory questioned the robustness of the quadratic dispersion, arguing that the anharmonic phonon-phonon interaction linearizes it, which implies a divergent bending rigidity (stiffness) in the long wavelength limit. However, these works are based on effective low-energy models that explicitly break the rotational invariance. Here we show that rotational symmetry protects the quadratic flexural dispersion against phonon-phonon interaction, and that the bending stiffness of graphene is unaffected by temperature and quantum fluctuations. Nevertheless, our non-perturbative anharmonic calculations predict that sound propagation coexists with such a quadratic dispersion. Since our conclusions are universal properties of membranes, they apply not just to graphene, but to all 2D materials.

Since 2014 the layered semiconductor SnSe in the high-temperature Cmcm phase is known to be the most efficient intrinsic thermoelectric material. Making use of first-principles calculations we show that its vibrational and thermal transport properties are determined by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Pnma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temperature. Our calculations show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calculate the lattice thermal conductivity obtaining good agreement with experiments only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelectric efficiency of SnSe is strongly affected by the nonperturbative anharmonicity.

SnS and SnSe are isoelectronic materials with a common phase diagram. Recently, SnSe was found to be the most efficient intrinsic thermoelectric material in its high-temperature Cmcm phase above 800 K. Making use of first-principles calculations, here we show that the electronic and vibrational properties of both materials are very similar in this phase and, consequently, SnS is also expected to have a high thermoelectric figure of merit at high temperature in its Cmcm phase. In fact, the electronic power factor and lattice thermal conductivity are comparable for both materials, which ensures a similar figure of merit. As in the case of SnSe, the vibrational properties of SnS in the Cmcm phase are far from trivial and are dominated by huge anharmonic effects. Its phonon spectra are strongly renormalized by anharmonicity and the spectral functions of some particular in-plane modes depict anomalous non-Lorentzian profiles. Finally, we show that nonperturbative anharmonic effects in the third-order force-constants are crucial in the calculation of the lattice thermal conductivity. Our results motivate new experiments in the high-temperature regime to measure the figure of merit of SnS.

Recent experiments [Schaeffer 2015] have shown that lithium presents an extremely anomalous isotope effect in the 15-25 GPa pressure range. In this article we have calculated the anharmonic phonon dispersion of $\mathrm{^7Li}$ and $\mathrm{^6Li}$ under pressure, their superconducting transition temperatures, and the associated isotope effect. We have found a huge anharmonic renormalization of a transverse acoustic soft mode along $\Gamma$K in the fcc phase, the expected structure at the pressure range of interest. In fact, the anharmonic correction dynamically stabilizes the fcc phase above 25 GPa. However, we have not found any anomalous scaling of the superconducting temperature with the isotopic mass. Additionally, we have also analyzed whether the two lithium isotopes adopting different structures could explain the observed anomalous behavior. According to our enthalpy calculations including zero-point motion and anharmonicity it would not be possible in a stable regime.

We study the dynamical stability of face centered cubic lithium at 25 GPa within ab initio density functional theory calculations. The system shows an extremely softened transverse acoustic mode in the Γ–K high symmetry line, whose frequency is difficult to converge within a first-principles harmonic approach. We estimate the anharmonic correction of this value within the frozen phonon approximation assuming that the transverse acoustic mode only interacts with itself. By solving the Schrödinger equation for the potential energy curve and displacements along the vibrational mode of interest, we obtain the anharmonic eigenvalues and eigenfunctions. While the harmonic approach yields a phonon frequency of −28.6 cm−1 for this mode, anharmonicity renormalizes dramatically this value up to 115.3 cm−1. Thus, anharmonic effects seem to dynamically stabilize this system.