Probabilistic error cancellation is an attempt to reverse the effect of dissipative noise channels on quantum computers by applying unphysical channels after the execution of a quantum algorithm on noisy hardware. We investigate on general grounds the properties of such unphysical quantum channels by considering a random matrix ensemble modeling noisy quantum algorithms. We show that the complex spectra of denoiser channels inherit their structure from random Lindbladians. Additional structure imposed by the locality of noise channels of the quantum computer emerges in terms of a hierarchy of timescales.

The celebrated theorem of Perron and Frobenius implies that spectra of classical Markov operators, represented by stochastic matrices, are restricted to the unit disk. This property holds also for spectra of quantum stochastic maps (quantum channels), which describe quantum Markovian evolution in discrete time. Moreover, the spectra of stochastic N × N matrices are additionally restricted to a subset of the unit disk, called Karpelevic̆ region, the shape of which depends on N. We address the question of whether the spectra of generators, which induce Markovian evolution in continuous time, can be bound in a similar way. We propose a rescaling that allows us to answer this question affirmatively. The eigenvalues of the rescaled classical generators are confined to the modified Karpelevic̆ regions, whereas the eigenvalues of the rescaled quantum generators fill the entire unit disk.

We report an improved measurement of the valence u and d quark distributions from the forward-backward asymmetry in the Drell-Yan process using 8.6 fb(-1) of data collected with the D0 detector in p (p) over bar collisions at root s = 1.96. This analysis provides the values of new structure parameters that are directly related to the valence up and down quark distributions in the proton. In other experimental results measuring the quark content of the proton, d quark contributions are mixed with those from other quark flavors. In this measurement, the u and d quark contributions are separately extracted by applying a factorization of the QCD and electroweak portions of the forward-backward asymmetry.

We introduce different ensembles of random Lindblad operators [Formula: see text], which satisfy quantum detailed balance condition with respect to given stationary state [Formula: see text] of size [Formula: see text], and investigate their spectral properties. Such operators are known as ‘Davies generators’ and their eigenvalues are real; however, their spectral densities depend on [Formula: see text]. We propose different structured ensembles of random matrices, which allow us to tackle the problem analytically in the extreme cases of Davies generators corresponding to random [Formula: see text] with a nondegenerate spectrum or the maximally mixed stationary state, [Formula: see text]. Interestingly, in the latter case the density can be reasonably well approximated by integrating out the imaginary component of the spectral density characteristic to the ensemble of random unconstrained Lindblad operators. The case of asymptotic states with partially degenerated spectra is also addressed. Finally, we demonstrate that similar universal properties hold for the detailed balance-obeying Kolmogorov generators obtained by applying superdecoherence to an ensemble of random Davies generators. In this way we construct an ensemble of random classical generators with imposed detailed balance condition.

A bstract A search for the exclusive decays of the Higgs and Z bosons to a ϕ or ρ meson and a photon is performed with a pp collision data sample corresponding to an integrated luminosity of up to 35 . 6 fb −1 collected at $$ \sqrt{s}=13 $$ s = 13 TeV with the ATLAS detector at the CERN Large Hadron Collider. These decays have been suggested as a probe of the Higgs boson couplings to light quarks. No significant excess of events is observed above the background, as expected from the Standard Model. Upper limits at 95% confidence level were obtained on the branching fractions of the Higgs boson decays to ϕ γ and ρ γ of 4 . 8 × 10 −4 and 8 . 8 × 10 −4 , respectively. The corresponding 95% confidence level upper limits for the Z boson decays are 0 . 9 × 10 −6 and 25 × 10 −6 for ϕ γ and ρ γ, respectively.

The paper presents the results of calculations of the sampling fluctuations in Pb–LAr electromagnetic sandwich calorimeters. The GEANT4 package was used to generate showers initiated by electrons with energies E0 from 20 to 500 GeV. It is shown that the dependence of the sampling fluctuations on E0 and the thickness of the lead absorber x can be described by the formula kxb/ $$\sqrt {{{E}_{0}}} $$ . The exponent b weakly depends on the LAr gap width d and is close to 2/3 and k = 0.1985−0.0363lnd[mm].

Similar to its classical version, quantum Markovian evolution can be either time-discrete or time-continuous. Discrete quantum Markovian evolution is usually modeled with completely positive trace-preserving maps, while time-continuous evolution is often specified with superoperators referred to as "Lindbladians." Here, we address the following question: Being given a quantum map, can we find a Lindbladian that generates an evolution identical-when monitored at discrete instances of time-to the one induced by the map? It was demonstrated that the problem of getting the answer to this question can be reduced to an NP-complete (in the dimension N of the Hilbert space, the evolution takes place in) problem. We approach this question from a different perspective by considering a variety of machine learning (ML) methods and trying to estimate their potential ability to give the correct answer. Complimentarily, we use the performance of different ML methods as a tool to validate a hypothesis that the answer to the question is encoded in spectral properties of the so-called Choi matrix, which can be constructed from the given quantum map. As a test bed, we use two single-qubit models for which the answer can be obtained using the reduction procedure. The outcome of our experiment is that, for a given map, the property of being generated by a time-independent Lindbladian is encoded both in the eigenvalues and the eigenstates of the corresponding Choi matrix.

Bent silicon crystals mounted on high-accuracy angular actuators were installed in the CERN Super Proton Synchrotron (SPS) and extensively tested to assess the feasibility of crystal-assisted collimation in circular hadron colliders. The adopted layout was exploited and regularly upgraded for about a decade by the UA9 Collaboration. The investigations provided the compelling evidence of a strong reduction of beam losses induced by nuclear inelastic interactions in the aligned crystals in comparison with amorphous orientation. A conceptually similar device, installed in the betatron cleaning insertion of CERN Large Hadron Collider (LHC), was operated through the complete acceleration and storage cycle and demonstrated a large reduction of the background leaking from the collimation region and radiated into the cold sections of the accelerator and the experimental detectors. The implemented layout and the relevant results of the beam tests performed in the SPS and in the LHC with stored proton and ion beams are extensively discussed.

We describe an analysis comparing the pp[over ¯] elastic cross section as measured by the D0 Collaboration at a center-of-mass energy of 1.96 TeV to that in pp collisions as measured by the TOTEM Collaboration at 2.76, 7, 8, and 13 TeV using a model-independent approach. The TOTEM cross sections, extrapolated to a center-of-mass energy of sqrt[s]=1.96  TeV, are compared with the D0 measurement in the region of the diffractive minimum and the second maximum of the pp cross section. The two data sets disagree at the 3.4σ level and thus provide evidence for the t-channel exchange of a colorless, C-odd gluonic compound, also known as the odderon. We combine these results with a TOTEM analysis of the same C-odd exchange based on the total cross section and the ratio of the real to imaginary parts of the forward elastic strong interaction scattering amplitude in pp scattering for which the significance is between 3.4σ and 4.6σ. The combined significance is larger than 5σ and is interpreted as the first observation of the exchange of a colorless, C-odd gluonic compound.

This letter presents a search for narrow, high-mass resonances in the Zγ final state with the Z boson decaying into a pair of electrons or muons. The s=13 TeV pp collision data were recorded by the ATLAS detector at the CERN Large Hadron Collider and have an integrated luminosity of 140 fb−1. The data are found to be in agreement with the Standard Model background expectation. Upper limits are set on the resonance production cross section times the decay branching ratio into Zγ. For spin-0 resonances produced via gluon–gluon fusion, the observed limits at 95% confidence level vary between 65.5 fb and 0.6 fb, while for spin-2 resonances produced via gluon–gluon fusion (or quark–antiquark initial states) limits vary between 77.4 (76.1) fb and 0.6 (0.5) fb, for the mass range from 220 GeV to 3400 GeV.

I discuss several novel and unexpected aspects of quantum chromodynamics. These include: (a) the nonperturbative origin of intrinsic strange, charm and bottom quarks in the nucleon at large x; the breakdown of pQCD factorization theorems due to the lensing effects of initialand final-state interactions; (b) important corrections to pQCD scaling for inclusive reactions due to processes in which hadrons are created at high transverse momentum directly in the hard processes and their relation to the baryon anomaly in high-centrality heavy-ion collisions; and (c) the nonuniversality of quark distributions in nuclei. I also discuss some novel theoretical perspectives in QCD: (a) lightfront holography – a relativistic color-confining first approximation to QCD based on the AdS/CFT correspondence principle; (b) the principle of maximum conformality – a method which determines the renormalization scale at finite order in perturbation theory yielding scheme independent results; (c) the replacement of quark and gluon vacuum condensates by “in-hadron condensates” and how this helps to resolves the conflict between QCD vacuum and the cosmological constant.

Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of N-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence. In analogy with the mechanism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolution). We inspect spectra of random Lindblad operators undergoing superdecoherence and demonstrate that, in the limit of complete superdecoherence, the resulting operators exhibit spectral density typical to random Kolmogorov operators. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification that is a generalization of the scheme used to construct a quantum state out of a classical one. Finally, we study microscopic correlation between neighboring eigenvalues through the complex spacing ratios and observe the horseshoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives both superdecoherence and supercoherification.

Floquet engineering of isolated systems is often based on the concept of the effective time-independent Floquet Hamiltonian, which describes the stroboscopic evolution of a periodically driven quantum system in steps of the driving period and which is routinely obtained analytically using high-frequency expansions. The generalization of these concepts to open quantum systems described by aMarkovian master equation of Lindblad type turns out to be nontrivial: On the one hand, already for a two-level system two different phases can be distinguished, where the effective time-independent Floquet generator (describing the stroboscopic evolution) is either again Markovian and of Lindblad type or not. On the other hand, even though in the high-frequency regime a Lindbladian Floquet generator (Floquet Lindbladian) is numerically found to exist, this behavior is, curiously, not correctly reproduced within analytical high-frequency expansions. Here, we demonstrate that a proper Floquet Lindbladian can still be obtained from a high-frequency expansion, when treating the problem in a suitably chosen rotating frame. Within this approach, we can then also describe the transition to a phase at lower driving frequencies, where no Floquet Lindbladian exists, and show that the emerging non-Markovianity of the Floquet generator can entirely be attributed to the micromotion of the open driven system.

We present a study of the normalized transverse momentum distribution of W bosons produced in p ¯ p collisions, using data corresponding to an integrated luminosity of 4 . 35 fb − 1 collected with the D0 detector at the Fermilab Tevatron collider at ffiffiffi s p ¼ 1 . 96 TeV. The measurement focuses on the transverse momentum region below 15 GeV, which is of special interest for electroweak precision measurements; it relies on the same detector calibration methods which were used for the precision measurement of the W boson mass. The measured distribution is compared to different QCD predictions and a procedure is given to allow the comparison of any further theoretical models to the D0 data.

The first measurement of longitudinal decorrelations of harmonic flow amplitudes v_{n} for n=2-4 in Xe+Xe collisions at sqrt[s_{NN}]=5.44  TeV is obtained using 3  μb^{-1} of data with the ATLAS detector at the LHC. The decorrelation signal for v_{3} and v_{4} is found to be nearly independent of collision centrality and transverse momentum (p_{T}) requirements on final-state particles, but for v_{2} a strong centrality and p_{T} dependence is seen. When compared with the results from Pb+Pb collisions at sqrt[s_{NN}]=5.02  TeV, the longitudinal decorrelation signal in midcentral Xe+Xe collisions is found to be larger for v_{2}, but smaller for v_{3}. Current hydrodynamic models reproduce the ratios of the v_{n} measured in Xe+Xe collisions to those in Pb+Pb collisions but fail to describe the magnitudes and trends of the ratios of longitudinal flow decorrelations between Xe+Xe and Pb+Pb. The results on the system-size dependence provide new insights and an important lever arm to separate effects of the longitudinal structure of the initial state from other early and late time effects in heavy-ion collisions.

Lévy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a new unidirectional motion event either in the positive or in the negative direction. We consider two-dimensional generalization of Lévy walks in the form of the so-called XY model. It describes a particle moving with a constant velocity along one of the four basic directions and randomly switching between them when starting a new motion event. We address the ballistic regime and derive solutions for the asymptotic density profiles. The solutions have a form of first-order integrals which can be evaluated numerically. For specific values of parameters we derive an exact expression. The analytic results are in agreement with the results of finite-time numerical samplings.

The stroboscopic evolution of a time-periodically driven isolated quantum system can always be described by an effective time-independent Hamiltonian. Whether this concept can be generalized to open Floquet systems, described by a Markovian Lindblad master equation with a time-periodic generator (Lindbladian), remains an open question. By using a two-level system as a model, we explicitly show the existence of two well-defined parameter regions. In one region the stroboscopic evolution can be described by a Markovian master equation with a time-independent Floquet Lindbladian. In the other it cannot; but here the one-cycle evolution operator can be reproduced with an effective non-Markovian master equation that is homogeneous but nonlocal in time. Interestingly, we find that the boundary between the phases depends on when during the period the evolution is stroboscopically monitored. This reveals the nontrivial role played by the micromotion in the dynamics of open Floquet systems.

We present various properties of the production of the X(3872) and psi(2S) states based on 10.4 fb(-1) collected by the D0 experiment in Tevatron p (p) over bar collisions at root s = 1.96 TeV. For both states, we measure the nonprompt fraction f(NP) of the inclusive production rate due to decays of b-flavored hadrons. We find the f(NP) values systematically below those obtained at the LHC. The f(NP) fraction for psi(2S) increases with transverse momentum, whereas for the X(3872) it is constant within large uncertainties, in agreement with the LHC results. The ratio of prompt to nonprompt psi(2S) production, ( 1 - f(NP))/f(NP), decreases only slightly going from the Tevatron to the LHC, but for the X(3872), this ratio decreases by a factor of about 3. We test the soft-pion signature of the X(3872) modeled as a weakly bound charm-meson pair by studying the production of the X(3872) as a function of the kinetic energy of the X(3872) and the pion in the X(3872)pi center-of-mass frame. For a subsample consistent with prompt production, the results are incompatible with a strong enhancement in the production of the X(3872) at the small kinetic energy of the X(3872) and the pi in the X(3872)pi center-of-mass frame expected for the X + soft-pion production mechanism. For events consistent with being due to decays of b hadrons, there is no significant evidence for the soft-pion effect, but its presence at the level expected for the binding energy of 0.17 MeV and the momentum scale Lambda = M(pi) is not ruled out.

With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master equations describing the evolution of the system density operators. In this paper, we address master equations of the Lindblad form, which are a popular theoretical tools in quantum optics, cavity quantum electrodynamics, and optomechanics. By using the generalized Gell–Mann matrices as a basis, any Lindblad equation can be transformed into a system of ordinary differential equations with real coefficients. Recently, we presented an implementation of the transformation with the computational complexity, scaling as O(N5logN) for dense Lindbaldians and O(N3logN) for sparse ones. However, infeasible memory costs remains a serious obstacle on the way to large models. Here, we present a parallel cluster-based implementation of the algorithm and demonstrate that it allows us to integrate a sparse Lindbladian model of the dimension N=2000 and a dense random Lindbladian model of the dimension N=200 by using 25 nodes with 64 GB RAM per node.