Benchmarking Adversarially Robust Quantum Machine Learning at Scale

Machine learning (ML) methods such as artificial neural networks are rapidly becoming ubiquitous in modern science, technology and industry. Despite their accuracy and sophistication, neural networks can be easily fooled by carefully designed malicious inputs known as adversarial attacks. While such vulnerabilities remain a serious challenge for classical neural networks, the extent of their existence is not fully understood in the quantum ML setting. In this work, we benchmark the robustness of quantum ML networks, such as quantum variational classifiers (QVC), at scale by performing rigorous training for both simple and complex image datasets and through a variety of high-end adversarial attacks. Our results show that QVCs offer a notably enhanced robustness against classical adversarial attacks by learning features which are not detected by the classical neural networks, indicating a possible quantum advantage for ML tasks. Contrarily, and remarkably, the converse is not true, with attacks on quantum networks also capable of deceiving classical neural networks. By combining quantum and classical network outcomes, we propose a novel adversarial attack detection technology. Traditionally quantum advantage in ML systems has been sought through increased accuracy or algorithmic speed-up, but our work has revealed the potential for a new kind of quantum advantage through superior robustness of ML models, whose practical realisation will address serious security concerns and reliability issues of ML algorithms employed in a myriad of applications including autonomous vehicles, cybersecurity, and surveillance robotic systems.Comment: 10 pages, 5 Figure

Drastic Circuit Depth Reductions with Preserved Adversarial Robustness by Approximate Encoding for Quantum Machine Learning

Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver quantum advantage, but its realisation for practical applications remains impeded by challenges. Amongst those, a key barrier is the computationally expensive task of encoding classical data into a quantum state, which could erase any prospective speed-ups over classical algorithms. In this work, we implement methods for the efficient preparation of quantum states representing encoded image data using variational, genetic and matrix product state based algorithms. Our results show that these methods can approximately prepare states to a level suitable for QML using circuits two orders of magnitude shallower than a standard state preparation implementation, obtaining drastic savings in circuit depth and gate count without unduly sacrificing classification accuracy. Additionally, the QML models trained and evaluated on approximately encoded data display an increased robustness to adversarially generated input data perturbations. This partial alleviation of adversarial vulnerability, possible due to the "drowning out" of adversarial perturbations while retaining the meaningful large-scale features of the data, constitutes a considerable benefit for approximate state preparation in addition to lessening the requirements of the quantum hardware. Our results, based on simulations and experiments on IBM quantum devices, highlight a promising pathway for the future implementation of accurate and robust QML models on complex datasets relevant for practical applications, bringing the possibility of NISQ-era QML advantage closer to reality.Comment: 14 pages, 8 figure

pi-pi scattering in a QCD based model field theory

A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyse the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking, asymptotic freedom and quark confinement, allows one to calculate $f_\pi$, $m_\pi$, $r_\pi$ and the partial wave amplitudes in $\pi$-$\pi$ scattering and obtain good agreement with the experimental data, with the latter being well described up to energies \mbox{$E\simeq 700$ MeV}.Comment: 23 Pages, 4 figures in PostScript format, PHY-7512-TH-93, REVTEX Available via anonymous ftp in /pub: login anonymou get pipi93.tex Fig1.ps Fig2.ps Fig3.ps Fig4.p

Precision Pion-Proton Elastic Differential Cross Sections at Energies Spanning the Delta Resonance

A precision measurement of absolute pi+p and pi-p elastic differential cross sections at incident pion laboratory kinetic energies from T_pi= 141.15 to 267.3 MeV is described. Data were obtained detecting the scattered pion and recoil proton in coincidence at 12 laboratory pion angles from 55 to 155 degrees for pi+p, and six angles from 60 to 155 degrees for pi-p. Single arm measurements were also obtained for pi+p energies up to 218.1 MeV, with the scattered pi+ detected at six angles from 20 to 70 degrees. A flat-walled, super-cooled liquid hydrogen target as well as solid CH2 targets were used. The data are characterized by small uncertainties, ~1-2% statistical and ~1-1.5% normalization. The reliability of the cross section results was ensured by carrying out the measurements under a variety of experimental conditions to identify and quantify the sources of instrumental uncertainty. Our lowest and highest energy data are consistent with overlapping results from TRIUMF and LAMPF. In general, the Virginia Polytechnic Institute SM95 partial wave analysis solution describes our data well, but the older Karlsruhe-Helsinki PWA solution KH80 does not.Comment: 39 pages, 22 figures (some with quality reduced to satisfy ArXiv requirements. Contact M.M. Pavan for originals). Submitted to Physical Review

The pi -> pi pi process in nuclei and the restoration of chiral symmetry

The results of an extensive campaign of measurements of the pi -> pi pi process in the nucleon and nuclei at intermediate energies are presented. The measurements were motivated by the study of strong pi pi correlations in nuclei. The analysis relies on the composite ratio C_{pi pi}^A, which accounts for the clear effect of the nuclear medium on the (pi pi) system. The comparison of the C_{pi pi}^A distributions for the (pi pi)_{I=J=0} and (pi pi)_{I=0,J=2} systems to the model predictions indicates that the C_{pi pi}^A behavior in proximity of the 2m_pi threshold is explainable through the partial restoration of chiral symmetry in nuclei.Comment: accepted for publication in Nucl. Phys.

Microscopic calculation of proton capture reactions in mass 60-80 region and its astrophysical implications

Microscopic optical potentials obtained by folding the DDM3Y interaction with the densities from Relativistic Mean Field approach have been utilized to evaluate S-factors of low-energy $(p,\gamma)$ reactions in mass 60-80 region and to compare with experiments. The Lagrangian density FSU Gold has been employed. Astrophysical rates for important proton capture reactions have been calculated to study the behaviour of rapid proton nucleosynthesis for waiting point nuclei with mass less than A=80

Low energy (p,γp,\gamma) reactions in Ni and Cu nuclei using microscopic optical model

Radiative capture reactions for low energy protons have been theoretically studied for Ni and Cu isotopes using the microscopic optical model. The optical potential has been obtained in the folding model using different microscopic interactions with the nuclear densities from Relativistic Mean Field calculations. The calculated total cross sections as well as the cross sections for individually low lying levels have been compared with measurements involving stable nuclear targets. Rates for the rapid proton capture process have been evaluated for astrophysically important reactions.Comment: To appear in Physical Review

Low Energy Analyzing Powers in Pion-Proton Elastic Scattering

Analyzing powers of pion-proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS as well as a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for pi+ p scattering, and at 67.3 and 87.2 MeV for pi- p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.Comment: 15 pages, 4 figure

Baryon polarization in low-energy unpolarized meson-baryon scattering

We compute the polarization of the final-state baryon, in its rest frame, in low-energy meson--baryon scattering with unpolarized initial state, in Unitarized BChPT. Free parameters are determined by fitting total and differential cross-section data (and spin-asymmetry or polarization data if available) for $pK^-$, $pK^+$ and $p\pi^+$ scattering. We also compare our results with those of leading-order BChPT

Working group on ππ\pi\pi and π\piN interactions - Summary

This is the summary of the working group on $\pi\pi$ and $\pi$N interactions of the Chiral Dynamics Workshop in Mainz, September 1-5, 1997. Each talk is represented by an extended one page abstract. Some additional remarks by the convenors are addedComment: 20 pp, LaTeX2e, uses epsf, 1 fi