Error Cancellation Research Articles

Haptic Human-Human Interaction During an Ankle Tracking Task: Effects of Virtual Connection Stiffness.

While treating sensorimotor impairments, a therapist may provide physical assistance by guiding their patient's limb to teach a desired movement. In this scenario, a key aspect is the compliance of the interaction, as the therapist can provide subtle cues or impose a movement as demonstration. One approach to studying these interactions involves haptically connecting two individuals through robotic interfaces. Upper-limb studies have shown that pairs of connected individuals estimate one another's goals during tracking tasks by exchanging haptic information, resulting in improved performance dependent on the ability of one's partner and the stiffness of the virtual connection. In this study, our goal was to investigate whether these findings generalize to the lower limb during an ankle tracking task. Pairs of healthy participants (i.e., dyads) independently tracked target trajectories with and without connections rendered between two ankle robots. We tested the effects of connection stiffness as well as visual noise to manipulate the correlation of tracking errors between partners. In our analysis, we compared changes in task performance across conditions while tracking with and without the connection. We found that tracking improvements while connected increased with connection stiffness, favoring the worse partner in the dyad during hard connections. We modeled the interaction as three springs in series, considering the stiffness of the connection and each partners' ankle, to show that improvements were likely due to a cancellation of random tracking errors between partners. These results suggest a simplified mechanism of improvements compared to what has been reported during upper-limb dyadic tracking.

Analyses of Virtual MIMO Multi-User System Performance with Linear Precoding Schemes Using Indoor Measurements at 5 GHz

In this paper, based on 5 GHz indoor multi-user measurements, linear precoding schemes such as zero-forcing (ZF), minimum mean square error (MMSE) and successive interference cancelation (SIC) are applied in the base station in order to investigate the performance of virtual multi-input multi-output (MIMO) over single-user MIMO system. However, to form a virtual MIMO multi-user system, the resources of two users are brought together. In order to achieve a low spatial correlation, two spaced antennas in the MS have been chosen and four spaced antennas elements in BS have been selected. Therefore, the resources of two users (U1 and U2) are brought together to form a 4 × 4 virtual MIMO multi-user system with the BS. The properties of the user_1 (U1) and user_2 (U2) will be analyzed and compared to those properties of virtual MIMO multi-user system formed by U1 and U2. In most cases, the maximum achievable rate is seen with virtual MIMO multi-user compared to single-user MIMO. So virtual MIMO multi-user is desirable for boosting system capacity than single-user MIMO.

FEATURES OF GRAVIMETERS IN MODERN GRAVIMETRIC SYSTEMS

The paper reviews modern gravimeters of aviation gravimetric systems, their design and principle of operation. Their advantages and disadvantages, features of their functioning and processing of the received data are analyzed. It is shown that high-precision measurements of gravitational acceleration (g) are extremely relevant and necessary for many fields of science and technology. The main characteristics of known aviation gravimeters are given. It has been established that known aviation gravimeters have insufficient accuracy (2-10 mGal). Under the action of the g, the armature moves down inside the magnetic circuit and causes a change in the electromagnetic flux. Under the action of an external electromagnetic flow of an obstacle, this flow will induce two EMF obstacles in two sections, which are included in series-opposite. The total effect of these errors on the output signal of the gravimeter-invention will be zero. The mutual connection of the sections provides cancellation of errors due to the influence of external electromagnetic flows, which can be significant when installing the gravimeter on such a moving object as an airplane. In the same way, the device works under the action of the main obstacle for aviation gravimeters of the vertical acceleration of the aircraft, the errors due to the influence of which are cancelled in the TG. In TG, the residual instrumental errors are cancelled, since they will have opposite signs in the two measuring channels of the two sections of the secondary winding, which are connected oppositely. It is shown that the new TG has significantly greater accuracy than known aviation gravimeters due to the cancellation of errors due to the effects of vertical acceleration of the aircraft, external electromagnetic fields, and residual instrumental errors. It is substantiated that the new TG has significantly greater accuracy than known aviation gravimeters due to the cancellation of errors due to the influence of the vertical acceleration of the aircraft, the influence of external electromagnetic fields, and the influence of residual instrumental errors.

Machine Learned Composite Methods for Electronic Structure Theory

Because of the prohibitive scaling of ab initio techniques for modeling chemical species with high accuracy, they are not generally tractable for large systems. It is therefore of considerable interest to develop high-accuracy computational models with low computational cost that can afford predictions of electronic structure and properties of macromolecular species. Composite methods, as first introduced by Pople [Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys.1989, 90, 5622.], are an intuitive solution to this problem as they seek to systematically increase accuracy in model chemistries by taking advantage of favorable error cancellation among reasonably low-cost models. By linearly combining a series of carefully chosen model chemistries, the result of a prohibitive-scaling correlated model chemistry with a large basis set may be approximated with relatively good fidelity. However, the full extent to which the choice of low-cost models dictates the predictive accuracy of composite methods is not known, and a full exploration of all model chemistries would be advantageous for the design and validation of a generalizable composite method for widespread application. Here, we show that remarkable accuracy can be generally achieved with composite methods that are more judiciously constructed, leading to increased accuracy with significantly reduced computational cost. By designing a systematic procedure for the automated generation and assessment of over 10 billion unique composite methods, we have extensively explored the space of modern model chemistries to elucidate important design principles in the construction of reliable composite procedures. We anticipate our work to be the starting point in the pursuit of creative approaches to modeling large chemical systems with high accuracy by using novel combinatorial modeling.

Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects.

When described by a one-dimensional reaction coordinate, pair-reaction rates in a solvent depend, in addition to the potential barrier height and the friction coefficient, on the potential shape, the effective mass, and the friction relaxation spectrum, but a rate theory that accurately accounts for all of these effects does not exist. After a review of classical reaction-rate theories, we show how to extract all parameters of the generalized Langevin equation (GLE) and, in particular, the friction memory function from molecular dynamics (MD) simulations of two prototypical pair reactions in water, the dissociation of NaCl and of two methane molecules. The memory exhibits multiple time scales and, for NaCl, pronounced oscillatory components. Simulations of the GLE by Markovian embedding techniques accurately reproduce the pair-reaction kinetics from MD simulations without any fitting parameters, which confirms the accuracy of the approximative form of the GLE and of the parameter extraction techniques. By modification of the GLE parameters, we investigate the relative importance of memory, mass, and potential shape effects. Neglect of memory slows down NaCl and methane dissociation by roughly a factor of 2; neglect of mass accelerates reactions by a similar factor, and the harmonic approximation of the potential shape gives rise to slight acceleration. This partial error cancellation explains why Kramers' theory, which neglects memory effects and treats the potential shape in harmonic approximation, describes reaction rates better than more sophisticated theories. In essence, all three effects, friction memory, inertia, and the potential shape nonharmonicity, are important to quantitatively describe pair-reaction kinetics in water.

Quantum Chemical Prediction of the Acidities of Sulfonamide Inhibitors of Carbonic Anhydrase.

This study examined two pKa calculation approaches (direct and proton exchange schemes) that employ high-level quantum chemical methods and implicit solvent models to predict aqueous Brønsted acidities of a large set of sulfonamides. For gas-phase deprotonation energies, the DSD-PBEP86-D3(BJ) double-hybrid functional provided the best agreement with the LNO-CCSD(T)/CBS benchmark with a mean absolute deviation less than 2 kJ mol-1 when the aug-cc-pVTZ or larger basis sets are used. For a large test set of 54 primary and secondary sulfonamides, the use of the DSD-PBEP86-D3(BJ)/aug-cc-pVTZ level of theory in conjunction with SM12 solvation free energies predict their pKa values with a mean accuracy of 0.9 units. In comparison, the SMD and ADF-COSMO-RS models have slightly higher mean errors of 1.4 and 1.1 pKa units provided that the proton exchange scheme was employed to cancel the systematic errors in these models. The performance of these protocols was less ideal when applied to sulfonic acids, sulfamates, and N-substituted sulfonamides, indicating that the degree of error cancellation is sensitive to the chemical environment around the -NH2 head group. The validated protocols were then used to estimate the pKa values of arylsulfonamide carbonic anhydrase inhibitors, which are used to correct their experimentally measured binding free energies to account for deprotonation of the sulfonamide group upon binding to the enzyme. These corrected values did not have a significant impact on the correlation with MMGBSA binding free energies obtained from classical MD simulations where the ligand is usually considered in the deprotonated form.

Either Accurate Singlet-Triplet Gaps or Excited-State Structures: Testing and Understanding the Performance of TD-DFT for TADF Emitters.

The energy gap between the lowest singlet and triplet excited states (ΔEST) is a key property of thermally activated delayed fluorescence (TADF) emitters, where these states are dominated by charge-transfer (CT) character. Despite its well-known shortcomings concerning CT states, time-dependent density functional theory (TD-DFT) is widely used to predict this gap and study TADF. Moreover, polar CT states exhibit a strong interaction with their molecular environment, which further complicates their computational description. Addressing these two major challenges, this work studies the performance of Tamm-Dancoff-approximated TD-DFT (TDA-DFT) on the recent STGABS27 benchmark set,1 exploring different strategies to include orbital and structural relaxation, as well as dielectric embedding. The results show that the best-performing strategy is to calculate ΔEST at the ground-state structure using functionals with a surprisingly small amount of Fock exchange of ≈10% and without a (complete) solvent model. However, as this approach heavily relies on error cancellation to mimic dielectric relaxation, it is not robust and exhibits large systematic deviations in excited state energies, state characters, and structures. More rigorous approaches, including state-specific solvation, do not share these systematic deviations, but their predicted ΔEST values exhibit larger statistical errors. We thus conclude that for the description of CT states in dielectric environments, none of the tested TDA-DFT methods is competitive with the recently presented ROKS/PCM approach regarding robustness, accuracy, and computational efficiency.

Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials

AbstractWe provide theoretical investigations and empirical evidence that the effective stresses in computational homogenization of inelastic materials converge with a higher rate than the local solution fields. Due to the complexity of industrial‐scale microstructures, computational homogenization methods often utilize a rather crude approximation of the microstructure, favoring regular grids over accurate boundary representations. As the accuracy of such an approach has been under continuous verification for decades, it appears astonishing that this strategy is successful in homogenization, but is seldom used on component scale. A part of the puzzle has been solved recently, as it was shown that the effective elastic properties converge with twice the rate of the local strain and stress fields. Thus, although the local mechanical fields may be inaccurate, the averaging process leads to a cancellation of errors and improves the accuracy of the effective properties significantly. Unfortunately, the original argument is based on energetic considerations. The straightforward extension to the inelastic setting provides superconvergence of (pseudoelastic) potentials, but does not cover the primary quantity of interest: the effective stress tensor. The purpose of the work at hand is twofold. On the one hand, we provide extensive numerical experiments on the convergence rate of local and effective quantities for computational homogenization methods based on the fast Fourier transform. These indicate the superconvergence effect to be valid for effective stresses, as well. Moreover, we provide theoretical justification for such a superconvergence based on an argument that avoids energetic reasoning.

Hydrophilic Versus Hydrophobic Coupling in the Pressure Dependence of the Chemical Potential of Alkali Metal and Halide Ions in Water.

We computed the chemical potential for some alkali metal ions (K+, Rb+, and Cs+) and two halide ions (Br- and I-) in aqueous solution at ambient T and various pressures in the range 1-8000 atm. Results were obtained from classic Monte Carlo simulations in the NPT ensemble by means of the free energy perturbation method. Here, the chemical potential is computed as the sum of a term relative to a Lennard-Jones solute and a term relative to the process in which this solute is transformed into the ion. Hydrophobic and hydrophilic features of these two components of the chemical potential show opposite behaviors under isothermal compression. The increase in pressure determines an increase in the hydrophobic component, which becomes more positive with a stronger effect for larger ions. Correspondingly, the values of the hydrophilic component become more negative for alkali ions, whereas they are only slightly affected by compression for halide ions. Hydrophobic-hydrophilic quasi-compensation in the slopes is observed for Rb+. For a smaller ion, such as K+, the dependence on pressure of the hydrophilic component is slightly dominant. For a larger ion, as observed in the cases of Cs+, Br-, and I-, the hydrophobic component assumes the determinant role. Pressure dependence of the chemical potential is little affected by corrections introduced for molecular potential truncation. This view can change for possible boundary artifacts that could have affected the static electrostatic potential. Some inference is obtained from comparison with experimental data at 1 atm on the free energy of hydration. Discrepancies show the characteristic asymmetry between cations and anions. The further addition of a correction based on the static potential significantly reduces these discrepancies with important error cancellation on the sum of chemical potentials of ions of opposite charge. The correction is applied also at higher pressures, and results are compared with those obtained by adding an alternative correction that is based on the water number density. Regardless of the ion, changes of the chemical potential induced by an increase in pressure appear to be dominated by the hydrophobic component, in particular when using the alternative correction. For bromide and iodide electrolytes, the two corrections give chemical potentials in good agreement.

Reducing false-positive rates in virtual screening via cancellation of systematic errors in the scoring function

Here we propose an over-the-hood docking method that compensates for systematic errors in the docking force fields. This method explicitly estimates the interaction energy of the ligand with the protein surface and uses it as a baseline to estimate the actual binding energy in the active site. It improves the accuracy of virtual screening in the LeadFinder package by up to 48%.

Difference of measured proton and He3 EDMs: a reduced systematics test of T-reversal invariance

The upper limit on (time reversal symmetry T-violating) permanent hadron electric dipole moments (EDMs) is the PSI neutron EDM value; dn = (0.0 ± 1.1stat ± 0.2sys × 10-26) e cm. This paper describes an experiment to be performed at a BNL-proposed CLIP project which is to be capable of producing intense polarized beams of protons, p, helions (He3 nuclei), h, and other isotopes. The EDM prototype ring PTR (proposed at COSY Lab, Juelich) is expected to measure individual particle EDMs (for example EDM_p for the proton) using simultaneous counter-rotating polarized proton beams, with statistical error ±10-30e.cm after one year running time, four orders of magnitude less than the PSI neutron EDM upper limit, and with comparable systematic error. A composite particle, the helion faces T-symmetry constraints more challenging than the proton. Any measurably large value of Δ= EDM h - EDM p , the difference of helion and proton EDMs, would represent BSM physics. The plan is to replicate PTR at BNL. The dominant systematic error would be canceled two ways, both made possible by phase-locking “doubly-magic” 38.6 MeV proton and 39.2 MeV helion spin tunes. This stabilizes their MDM-induced in-plane precessions, without affecting their EDM-induced out-of-plane precessions. The dominant systematic error would therefore cancel in the meaurement of Δ in a fixed field configuration. Another systematic error cancellation will come from averaging runs for which both magnetic field and beam circulation directions are reversed. Precise magnetic field reversal is made possible by the reproducible absolute frequency phase-locking over long runs to eliminate the need for (impractically precise) magnetic field measurement. Risk of EDM measurement failure is discussed in a final appendix.

Predicting Solvent Effects on SN2 Reaction Rates: Comparison of QM/MM, Implicit, and MM Explicit Solvent Models.

Solvents are one of the key variables in the optimization of a synthesis yield or properties of a synthesis product. In this paper, contemporary solvent models are applied to predict the rates of SN2 reactions in a range of aqueous and non-aqueous solvents. High-level CCSD(T)/CBS//M06-2X/6-31+G(d) gas phase energies were combined with solvation free energies from SMD, SM12, and ADF-COSMO-RS continuum solvent models, as well as molecular mechanics (MM) explicit solvent models with different atomic charge schemes to predict the rate constants of three SN2 reactions in eight protic and aprotic solvents. It is revealed that the prediction of rate constants in organic solvents is not necessarily less challenging than in water and popular solvent models struggle to predict their rate constants to within 3 log units of experimental values. Among the continuum solvent models, the ADF-COSMO-RS model performed the best in predicting absolute rate contants while the SM12 model was best at predicting relative rate constants with an average accuracy of about 1.5 and 0.8 log units, respectively. The use of computationally more demanding MM explicit solvent models did not translate to improvements in absolute rate constants but was quite effective at predicting relative rate constants due to systematic error cancellation. Free energy barriers obtained from umbrella sampling with explicit solvent QM/MM simulations led to excellent agreement with experimental values, provided that a validated level of theory is used to treat the QM region.

Application-specific optimal model weighting of global climate models: A red tide example

Global climate models (GCMs) and Earth system models (ESMs) provide many climate services with environmental relevance. The High Resolution Model Intercomparison Project (HighResMIP) of the Coupled Model Intercomparison Project Phase 6 (CMIP6) provides model runs of GCMs and ESMs to address regional phenomena. Developing a parsimonious ensemble of CMIP6 requires multiple ensemble methods such as independent-model subset selection, prescreening-based subset selection, and model weighting. The work presented here focuses on application-specific optimal model weighting, with prescreening-based subset selection. As such, independent ensemble members are categorized, selected, and weighted based on their ability to reproduce physically-interpretable features of interest that are problem-specific. We discuss the strengths and caveats of optimal model weighting using a case study of red tide prediction in the Gulf of Mexico along the West Florida Shelf. Red tide is a common name of specific harmful algal blooms that occur worldwide, causing adverse socioeconomic and environmental impacts. Our results indicate the importance of prescreening-based subset selection as optimal model weighting can underplay robust ensemble members by optimizing error cancellation. Prescreening-based subset selection also provides insights about the validity of the model weights. By illustrating the caveats of using non-representative models when optimal model weighting is used, the findings and discussion of this study are pertinent to many other climate services.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory.

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.

Excitation spectra of fully correlated donor-acceptor complexes by density matrix renormalisation group

In this paper, we investigate the convergence properties of density matrix renormalisation group (DMRG) calculations for vertical electronic excitations performed on three bimolecular complexes motivated by Szalay's recent benchmark results [JCTC. 2020;16:7]. Besides the high-level coupled-cluster reference spectrum, the extrapolated truncation-free DMRG results are compared against several alternative solutions based on multireference configuration interaction and coupled-cluster theories. By taking advantage of the error cancellation effects, which are inherent in the state-averaged computational scheme, we demonstrate that the extrapolated solution based on only low bond-dimensional DMRG data could already provide quantitative predictions even for large active spaces. We also show that orbital optimisation improves further the accuracy of the DMRG results which systematically approach the excitation energies of coupled cluster single-double-triple at similar computational costs.

Sensitivity of coupled cluster electronic properties on the reference determinant: Can Kohn-Sham orbitals be more beneficial than Hartree-Fock orbitals?

Coupled cluster calculations are traditionally performed over Hartree-Fock reference orbitals (HF-CC methodology). However, in the literature it has been repeatedly raised whether the use of a Kohn-Sham reference (KS-CC methodology) might result in improved performance relative to HF-CC. In the present study, we re-examine the relation of HF-CC and KS-CC methods by comparing the results of widely applied truncated CC calculations (CCSD, CCSD(T), CCSDT) to the limit of full configuration interaction (FCI), which serves as an undebatable reference point of accuracy. Based on a series of CC calculations on diatoms and transition metal complexes, we demonstrate that no systematic improvement of coupled cluster electronic energies, densities and chemical reaction energies is expected when changing from HF to a KS reference. Nevertheless, fortuitous error cancellations might occasionally result in illusory improvement compared to HF-CC. Altogether, the application of KS-CC is not advantageous over HF-CC, but it is also not unreasonable as the choice of reference has negligible influence on the results at sufficiently high CC levels. In addition, KS-CC can be a particularly useful alternative if difficulties are encountered in HF or HF-CC convergence. It is also notable that KS-CC results are found to be practically independent of the chosen density functional, which implies that almost any KS-CC method can be used in place of HF-CC.

Assessment of the Second-Order Statically Screened Exchange Correction to the Random Phase Approximation for Correlation Energies.

With increasing interelectronic distance, the screening of the electron–electron interaction by the presence of other electrons becomes the dominant source of electron correlation. This effect is described by the random phase approximation (RPA) which is therefore a promising method for the calculation of weak interactions. The success of the RPA relies on the cancellation of errors, which can be traced back to the violation of the crossing symmetry of the 4-point vertex, leading to strongly overestimated total correlation energies. By the addition of second-order screened exchange (SOSEX) to the correlation energy, this issue is substantially reduced. In the adiabatic connection (AC) SOSEX formalism, one of the two electron–electron interaction lines in the second-order exchange term is dynamically screened (SOSEX(W, vc)). A related SOSEX expression in which both electron–electron interaction lines are statically screened (SOSEX(W(0), W(0))) is obtained from the G3W2 contribution to the electronic self-energy. In contrast to SOSEX(W, vc), the evaluation of this correlation energy expression does not require an expensive numerical frequency integration and is therefore advantageous from a computational perspective. We compare the accuracy of the statically screened variant to RPA and RPA+SOSEX(W, vc) for a wide range of chemical reactions. While both methods fail for barrier heights, SOSEX(W(0), W(0)) agrees very well with SOSEX(W, vc) for charged excitations and noncovalent interactions where they lead to major improvements over RPA.

Fundamental limits of quantum error mitigation

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental bounds concerning how error-mitigation algorithms can reduce the computation error as a function of their sampling overhead. Our bounds place universal performance limits on a general error-mitigation protocol class. We use them to show (1) that the sampling overhead that ensures a certain computational accuracy for mitigating local depolarizing noise in layered circuits scales exponentially with the circuit depth for general error-mitigation protocols and (2) the optimality of probabilistic error cancellation among a wide class of strategies in mitigating the local dephasing noise on an arbitrary number of qubits. Our results provide a means to identify when a given quantum error-mitigation strategy is optimal and when there is potential room for improvement.

On-chip simultaneous measurement of humidity and temperature using cascaded photonic crystal microring resonators with error correction.

We present the design, fabrication, and characterization of cascaded silicon-on-insulator photonic crystal microring resonators (PhCMRRs) for dual-parameter sensing based on a multiple resonances multiple modes (MRMM) technique. Benefitting from the slow-light effect, the engineered PhCMRRs exhibit unique optical field distributions with different sensitivities via the excitation of dielectric and air modes. The multiple resonances of two distinct modes offer new possibilities for enriching the sensing receptors with additional information about environmental changes while preserving all essential properties of traditional microring resonator based sensors. As a proof of concept, we demonstrate the feasibility of extracting humidity and temperature responses simultaneously with a single spectrum measurement by employing polymethyl methacrylate as the hydrophilic coating, obtaining a relative humidity (RH) sensitivity of 3.36 pm/%RH, 5.57 pm/%RH and a temperature sensitivity of 85.9 pm/°C, 67.1 pm/°C for selected dielectric mode and air mode, respectively. Moreover, the MRMM enriched data further forges the capability to perform mutual cancellation of the measurement error, which improves the sensing performance reflected by the coefficient of determination (R2-value), calculated as 0.97 and 0.99 for RH and temperature sensing results, respectively.

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.