Exponential Suppression Research Articles

High-field 1/f noise in hBN-encapsulated graphene transistors

$1/f$ electronic noise is a conductance fluctuation, expressed in terms of a mobility ``$\ensuremath{\alpha}$-noise'' by Hooge and Kleinpenning. Understanding this noise in graphene is key for high-performance electronics. Early investigations pointed out a deviation from the standard Hooge formula, with the free-carrier density substituted by a constant density ${n}_{\mathrm{\ensuremath{\Delta}}}\ensuremath{\sim}{10}^{12}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Here we investigate hBN-encapsulated graphene transistors where high mobility gives access to the velocity-saturation regime. We show that $\ensuremath{\alpha}$-noise is still accounted for by the Hooge formula on substituting conductance by differential conductance $G$, resulting in a bell-shaped dependence of flicker noise with bias voltage. The same analysis holds in the Zener regime at even larger bias, with two main differences. The first one is a strong enhancement of the Hooge parameter reflecting the hundred-times larger coupling of interband excitations to the hyperbolic phonon-polariton (HPhP) modes of the midinfrared Reststrahlen (RS) bands of hBN, which is supported by microwave noise thermometry measurements. The second is an exponential suppression of this coupling at large fields, which we attribute to decoherence effects. The phenomenology of $1/f$ noise in graphene supports a quantum-coherent bremsstrahlung interpretation of $\ensuremath{\alpha}$-noise.

Suppression exponent for multiparticle production in λϕ4 theory

We compute the probability of producing n particles from few colliding particles in the unbroken (3 + 1)-dimensional λϕ4 theory. To this end we numerically implement semiclassical method of singular solutions which works at n ≫ 1 in the weakly coupled regime λ ≪ 1. For the first time, we obtain reliable results in the region of exceptionally large final-state multiplicities n ≫ λ−1 where the probability decreases exponentially with n, mathcal{P}left(textrm{few}to nright)sim exp left{{f}_{infty}left(varepsilon right)nright} , and its slope f∞ < 0 depends on the mean kinetic energy ε of produced particles. In the opposite case n ≪ λ−1 our data match well-known tree-level result, and they interpolate between the two limits at n ~ λ−1. Overall, this proves exponential suppression of the multiparticle production probability at n ≫ 1 and arbitrary ε in the unbroken theory. Using numerical solutions, we critically analyze the mechanism for multiple Higgs boson production suggested in the literature. Application of our technique to the scalar theory with spontaneously broken symmetry can eradicate (or confirm) it in the nearest future.

Unitarity cuts of the worldsheet

We compute the imaginary parts of genus-one string scattering amplitudes. Following Witten’s i\varepsiloniε prescription for the integration contour on the moduli space of worldsheets, we give a general algorithm for computing unitarity cuts of the annulus, Möbius strip, and torus topologies exactly in \alpha'α′. With the help of tropical analysis, we show how the intricate pattern of thresholds (normal and anomalous) opening up arises from the worldsheet computation. The result is a manifestly-convergent representation of the imaginary parts of amplitudes, which has the analytic form expected from Cutkosky rules in field theory, but bypasses the need for performing laborious sums over the intermediate states. We use this representation to study various physical aspects of string amplitudes, including their behavior in the (s,t)(s,t) plane, exponential suppression, decay widths of massive strings, total cross section, and low-energy expansions. We find that planar annulus amplitudes exhibit a version of low-spin dominance: at any finite energy, only a finite number of low partial-wave spins give an appreciable contribution to the imaginary part.

Unified multivariate trace estimation and quantum error mitigation

Calculating the trace of the product of $m\phantom{\rule{4pt}{0ex}}n$-qubit density matrices (multivariate trace) is a crucial subroutine in quantum error mitigation and information measure estimation. We propose a unified multivariate trace estimation (UMT) which conceptually unifies the previous qubit-optimal and depth-optimal approaches with tunable quantum circuit depth and number of qubits. The constructed circuits have $\ensuremath{\lceil}(m\ensuremath{-}1)/s\ensuremath{\rceil}$ or $n\ensuremath{\lceil}(m\ensuremath{-}1)/s\ensuremath{\rceil}$ depth corresponding to $(s+m)n$ or $s+mn$ qubits for $s\ensuremath{\in}{1,\ensuremath{\cdots},\ensuremath{\lfloor}m/2\ensuremath{\rfloor}}$, respectively. Such flexible circuit structures enable people to choose suitable circuits for different hardware devices. We apply UMT to virtual distillation to achieve exponential error suppression and design a family of concrete circuits to calculate the trace of the product of eight and nine $n$-qubit density matrices. A numerical example shows that the additional circuits still mitigate the noise expectation value under the global depolarizing channel.

The bumblebee field excitations in a cosmological braneworld

We investigate the effects of the spacetime curvature and extra dimensions on the excitations of the Lorentz violating bumblebee field B μ . By assuming the bumblebee field living in a five-dimensional AdS 5 bulk, we found an exponential suppression of the bumblebee self-interacting constant λ and of the bumblebee vacuum expectation value (VEV) b M along the fifth extra dimension. The fluctuations of the bumblebee field upon the VEV can be decomposed into transverse and longitudinal modes with respect to b M . For a spacelike b M along the extra dimension and assuming a thin FRW 3-brane embedded in the AdS 5, the transverse mode is localized on the brane. The bulk geometry leads to a propagating and unbound longitudinal mode along the extra dimension. On the brane, the cosmological expansion leads to the decay of the longitudinal mode in time, as Δt ≈ H −1.

Anomalous universal conductance as a hallmark of non-locality in a Majorana-hosted superconducting island

The non-local feature of topological states of matter is the key for the topological protection of quantum information and enables robust non-local manipulation in quantum information. Here we propose to manifest the non-local feature of a Majorana-hosted superconducting island by measuring the temperature dependence of Coulomb blockade peak conductance in different regimes. In the low-temperature regime, we discover a coherent double Majorana-assisted teleportation (MT) process, where any independent tunneling process always involves two coherent non-local MTs; and we also find an anomalous universal scaling behavior, i.e., a crossover from a {[max (T,eV)]}^{6} power-law to a {[max (T,eV)]}^{3} power-law conductance behavior when energy scale increases — in stark contrast to the usual exponential suppression due to certain local transport. In the high-temperature regime, the conductance is instead proportional to the temperature inverse, indicating a non-monotonic temperature-dependence of the conductance. Both the anomalous power law and non-monotonic temperature-dependence of the conductance can be distinguished from the conductance peak in the traditional Coulomb block, and therefore, together serve as a hallmark for the non-local feature in the Majorana-hosted superconducting island.

Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice

To simulate the dynamics of massless Dirac fermions in curved space-times with one, two, and three spatial dimensions, we construct tight-binding Hamiltonians with spatially varying hoppings. These models represent tilted Weyl semimetals where the tilting varies with position, in a manner similar to the light cones near the horizon of a black hole. We illustrate the gravitational analogies in these models by numerically evaluating the propagation of wave packets on the lattice and then comparing them to the geodesics of the corresponding curved space-time. We also show that the motion of electrons in these spatially varying systems can be understood through the conservation of energy and the quasiconservation of quasimomentum. This picture is confirmed by calculations of the scattering matrix, which indicate an exponential suppression of any noncontinuous change in the quasimomentum. Finally, we show that horizons in the lattice models can be constructed also at finite energies using specially designed tilting profiles.

Quantum dynamics in 1D lattice models with synthetic horizons

We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimics a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes. We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a horizon. Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon. We additionally observe a power-law localization of all eigenstates, each bordering a region of exponential suppression. These forbidden regions dictate the closest possible approach to the horizon of states with any given energy. These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.

Electron-magnon scattering in an anisotropic half-metallic ferromagnetic Weyl semimetal Co3Sn2S2

${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ is a magnetic Weyl semimetal, anisotropic ferromagnet, and half-metal in a single material. These qualities modify the spin dynamics and behavior of electron-magnon scattering. We have investigated this unconventional ferromagnet for modified electron-magnon scattering behavior using temperature and magnetic field dependent resistivity. ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ exhibits exponential suppression of spin-flip electron-magnon scattering below a characteristic crossover temperature which separates the regime of anomalous magnon scattering from one-magnon scattering. Interestingly, the Weyl fermion mediated spin dynamics with large magnetocrystalline anisotropy can also cause exponential suppression of electron-magnon scattering giving similar behavior in resistivity. The gap characterizing the suppression of electron-magnon scattering is 2.46(4) meV and increases linearly with magnetic field. The suppression of electron-magnon scattering could occur from half-metallic or anisotropic character but the presence of anomalous-magnon scattering at low temperatures evinces the half-metallic nature. A large anisotropy gap in magnon dispersion of half-metal can help prevent the deviation from 100% spin polarization at low temperatures.

Boundary chaos.

Scrambling in many-body quantum systems causes initially local observables to spread uniformly over the whole available Hilbert space under unitary dynamics, which in lattice systems causes exponential suppression of dynamical correlation functions with system size. Here, we present a perturbed free quantum circuit model, in which ergodicity is induced by an impurity interaction placed on the system's boundary, that allows for demonstrating the underlying mechanism. This is achieved by mapping dynamical correlation functions of local operators acting at the boundary to a partition function with complex weights defined on a two-dimensional lattice with a helical topology. We evaluate this partition function in terms of transfer matrices, which allow for numerically treating system sizes far beyond what is accessible by exact diagonalization and whose spectral properties determine the asymptotic scaling of correlations. Combining analytical arguments with numerical results, we show that for impurities which remain unitary under partial transpose correlations are exponentially suppressed with system size in a particular scaling limit. In contrast, for generic impurities or generic locations of the local operators, correlations show persistent revivals with a period given by the system size.

CD47-SIRPα Checkpoint Disruption in Metastases Requires Tumor-Targeting Antibody for Molecular and Engineered Macrophage Therapies.

Simple SummaryImmunotherapies offer broad potential to treat many diseases, including cancer. Macrophages are highly abundant immune cells, but are generally inhibited from eliminating tumor cells by ‘self’ signaling. Blocking this macrophage signaling checkpoint with antibodies has gone through clinical trials, which show that efficacy remains elusive especially for solid tumors. Here we show that CRISPR-based deletion of this inhibitory checkpoint is also insufficient to suppress solid metastatic tumors unless combined with a pro-phagocytic tumor-opsonizing antibody. Our tumor model is immunocompetent and resistant to T cell checkpoint blockade, which are typical characteristics of human cancer. We further demonstrate an equally effective cell therapy with antibody-engineered macrophages, and the approach also suppresses model metastatic human tumors.The macrophage checkpoint interaction CD47-SIRPα is an emerging target for cancer therapy, but clinical trials of monoclonal anti-CD47 show efficacy only in liquid tumors when combined with tumor-opsonizing IgG. Here, in challenging metastatic solid tumors, CD47 deletion shows no effect on tumor growth unless combined with otherwise ineffective tumor-opsonization, and we likewise show wild-type metastases are suppressed by SIRPα-blocked macrophages plus tumor-opsonization. Lung tumor nodules of syngeneic B16F10 melanoma cells with CD47 deletion show opsonization drives macrophage phagocytosis of B16F10s, consistent with growth versus phagocytosis calculus for exponential suppression of cancer. Wild-type CD47 levels on metastases in lungs of immunocompetent mice and on human metastases in livers of immunodeficient mice show that systemic injection of antibody-engineered macrophages also suppresses growth. Such in vivo functionality can be modulated by particle pre-loading of the macrophages. Thus, even though CD47-SIRPα disruption and tumor-opsonizing IgG are separately ineffective against established metastatic solid tumors, their combination in molecular and cellular therapies prolongs survival.

Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability.

We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate macroscopic weakly nonintegrable dynamics beyond the limits set by the KAM regime. We perform our analysis in two fundamentally distinct long-range and short-range integrable limits which stem from the type of nonintegrable perturbations. Long-range limits result in a single parameter scaling of the Lyapunov spectrum, with the inverse largest Lyapunov exponent being the only diverging control parameter and the rescaled spectrum approaching an analytical function. Short-range limits result in a dramatic slowing down of thermalization which manifests through the rescaled Lyapunov spectrum approaching a non-analytic function. An additional diverging length scale controls the exponential suppression of all Lyapunov exponents relative to the largest one.

The density of states method in Yang-Mills theories and first order phase transitions

Extensions of the standard model that lead to first-order phase transitions in the early universe can produce a stochastic background of gravitational waves, which may be accessible to future detectors. Thermodynamic observables at the transition, such as the latent heat, can be determined by lattice simulations, and then used to predict the expected signatures in a given theory. In lattice calculations, the emergence of metastabilities in proximity of the phase transition may make the precise determination of these observables quite challenging, and may lead to large uncontrolled numerical errors. In this contribution, we discuss as a prototype lattice calculation the first order deconfinement transition that arises in the strong SU(3) Yang-Mills sector. We adopt the novel logarithmic linear relaxation method, which can provide a determination of the density of states of the system with exponential error suppression. Thermodynamic observables can be reconstructed with a controlled error, providing a promising direction for accurate model predictions in the future.

Supersymmetric particle and Higgs boson masses from the landscape: Dynamical versus spontaneous supersymmetry breaking

Perturbative supersymmetry breaking on the landscape of string vacua is expected to favor large soft terms as a power-law or log distribution, but tempered by an anthropic veto of inappropriate vacua or vacua leading to too large a value for the derived weak scale -- a violation of the atomic principle. Indeed, scans of such vacua yield a statistical prediction for light Higgs boson mass m_h~ 125 GeV with sparticles (save possibly light higgsinos) typically beyond LHC reach. In contrast, models of dynamical SUSY breaking (DSB) -- with a hidden sector gauge coupling g^2 scanned uniformly -- lead to gaugino condensation and a uniform distribution of soft parameters on a log scale. Then soft terms are expected to be distributed as $m_{\rm soft}^{-1}$ favoring small values. A scan of DSB soft terms generally leads to $m_h\ll 125$ GeV and sparticle masses usually below LHC limits. Thus, the DSB landscape scenario seems excluded from LHC search results. An alternative is that the exponential suppression of the weak scale is set anthropically on the landscape via the atomic principle.

Aspects of gravitational decoherence in neutrino lensing

We study decoherence effects in neutrino flavour oscillations in curved spacetime with particular emphasis on the lensing in a Schwarzschild geometry. Assuming Gaussian wave packets for neutrinos, we argue that the decoherence length derived from the exponential suppression of the flavour transition amplitude depends on the proper time of the geodesic connecting the events of the production and detection in general gravitational setting. In the weak gravity limit, the proper time between two events of given proper distance is smaller than that in the flat spacetime. Therefore, in presence of a Schwarzschild object, the neutrino wave packets have to travel relatively more physical distance in space to lapse the same amount of proper time before they decoher. For non-radial propagation applicable to the lensing phenomena, we show that the decoherence, in general, is sensitive to the absolute values of neutrino masses as well as the classical trajectories taken by neutrinos between the source and detector along with the spatial widths of neutrino wave packets. At distances beyond the decoherence length, the probability of neutrino flavour transition due to lensing attains a value which depends only on the leptonic mixing parameters. Hence, the observability of neutrino lensing significantly depends on these parameters and in-turn the lensing can provide useful information about them.

Tunable Anderson localization of dark states

Random scattering of photons in disordered one-dimensional solids gives rise to an exponential suppression of transmission, which is known as Anderson localization. Here, we experimentally study Anderson localization in a superconducting waveguide quantum electrodynamics system comprising eight individually tunable qubits coupled to a photonic continuum of a waveguide. Employing the qubit frequency control, we artificially introduce frequency disorder to the system and observe an exponential suppression of the transmission coefficient in the vicinity of its subradiant dark modes. The localization length decreases with the disorder strength, which we control in-situ by varying individual qubit frequencies. Employing a one-dimensional non-interacting model of coupled qubits and photons, we are able to support and complement the experimental results. The difference between our investigation and previous studies of localization in qubit arrays is the coupling via a common waveguide, allowing us to explore the localization of mediating photons in an intrinsically open system. The experiment opens the door to the study of various localization phenomena on a new platform, which offers a high degree of control and readout possibilities.

Black hole induced false vacuum decay from first principles

We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green’s function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.

Quantum Error Mitigation using Symmetry Expansion

Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to their limited scale. Therefore instead of relying on engineered code symmetry, symmetry verification was developed which uses the inherent symmetry within the physical problem we try to solve. In this article, we develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes beyond symmetry verification, enabling us to achieve different balances between the estimation bias and the sampling cost of the scheme. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification through cancellation between the biases due to the detectable and undetectable noise components. A practical way to search for such a small-bias scheme is introduced. By numerically simulating the Fermi-Hubbard model for energy estimation, the small-bias symmetry expansion we found can achieve an estimation bias 6 to 9 times below what is achievable by symmetry verification when the average number of circuit errors is between 1 to 2. The corresponding sampling cost for random shot noise reduction is just 2 to 6 times higher than symmetry verification. Beyond symmetries inherent to the physical problem, our formalism is also applicable to engineered symmetries. For example, the recent scheme for exponential error suppression using multiple noisy copies of the quantum device is just a special case of symmetry expansion using the permutation symmetry among the copies.

Exponential Error Suppression for Near-Term Quantum Devices

As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level $E$ at a cost in qubit-count $n$ that is merely poly-logarithmic in $1/E$. However in the NISQ era, the complexity and scale required to adopt even the smallest QEC is prohibitive. Instead, error mitigation techniques have been employed; typically these do not require an increase in qubit-count but cannot provide exponential error suppression. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms) one can indeed achieve an effective exponential suppression. We introduce the Error Suppression by Derangement (ESD) approach: by increasing the qubit count by a factor of $n\geq 2$, the error is suppressed exponentially as $Q^n$ where $Q<1$ is a suppression factor that depends on the entropy of the errors. The ESD approach takes $n$ independently-prepared circuit outputs and applies a controlled derangement operator to create a state whose symmetries prevent erroneous states from contributing to expected values. The approach is therefore `NISQ-friendly' as it is modular in the main computation and requires only a shallow circuit that bridges the $n$ copies immediately prior to measurement. Imperfections in our derangement circuit do degrade performance and therefore we propose an approach to mitigate this effect to arbitrary precision due to the remarkable properties of derangements. a) they decompose into a linear number of elementary gates -- limiting the impact of noise b) they are highly resilient to noise and the effect of imperfections on them is (almost) trivial. In numerical simulations validating our approach we confirm error suppression below $10^{-6}$ for circuits consisting of several hundred noisy gates (two-qubit gate error $0.5\%$) using no more than $n=4$ circuit copies.

Statistical Floquet prethermalization of the Bose-Hubbard model

The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, such exponential suppression of heating has been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.