MIT Center for Theoretical Physics — a Leinweber Institute Publications

Readout errors are among the most dominant errors on current noisy intermediate-scale quantum devices. Recently, an efficient and scaleable method for mitigating such errors has been developed, based on classical bit-flip correction. In this talk, we compare the performance of this method for IBM's and Rigetti's quantum devices, demonstrating how the method improves the noisy measurements of observables obtained on the quantum hardware. Moreover, we examine the variance amplification to the data after applying of our mitigation procedure, which is common to all mitigation strategies. We derive a new expression for the variance of the mitigated Pauli operators in terms of the corrected expectation values and the noisy variances.Our hardware results show good agreement with the theoretical prediction, and we demonstrate that the increase of the variance due to the mitigation procedure is only moderate.

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter \(\xi^2\) that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in \(\xi^2\) reduces the action to a local two-derivative theory with a \(\xi^2\)-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

Quantum and tensor network simulations have emerged as prominent sign-problem free approaches to lattice gauge theories. Unlike conventional Markov chain Monte Carlo methods, they are based on the Hamiltonian formulation. In this talk, we fill a gap in the literature and present the first derivation of the Hamiltonian 3+1D \(\theta\)-term -- which is an important sign-problem afflicted term -- for Abelian and non-Abelian lattice gauge theories. Furthermore, we perform exact diagonalization for a 3+1D U(1) lattice gauge theory including the \(\theta\)-term on a unit periodic cube. Our numerical results reveal a novel phase transition at fixed values of \(\theta\) in the strong-coupling regime. The transition is evidenced by an avoided level crossing in the ground state energy, as well as sudden changes in the plaquette expectation value, the electric energy density, and the topological charge density. Extensions of our work to larger lattices can be readily performed using state-of-the-art tensor network simulations. Moreover, our work provides a concrete starting point for an eventual quantum simulation of the \(\theta\)-dependent phase structure and dynamics of lattice gauge theories in 3+1D. This talk is mainly based on~\cite{kan2021investigating}. We expand beyond~\cite{kan2021investigating} by including a derivation of the (non-)Abelian fixed-length Higgs term in the Hamiltonian formulation for future studies of (non-)Abelian-Higgs models with a \(\theta\)-term.

Particles may be emitted efficiently from the solar interior if they are sufficiently light and weakly coupled to the solar plasma. In a narrow region of phase space, they are emitted with velocities smaller than the escape velocity of the solar system, thereby populating a gravitationally bound density that can accumulate over the solar lifetime, referred to as a "solar basin." Detection strategies that can succeed in spite of (or even be enhanced by) the low particle velocities are therefore poised to explore new regions of parameter space when taking this solar population into account. Here we identify "direct deflection" as a powerful method to detect such a population of millicharged particles. This approach involves distorting the local flow of gravitationally bound millicharges with an oscillating electromagnetic field and measuring these distortions with a resonant LC circuit. Since it is easier to distort the flow of slowly moving particles, the signal is parametrically enhanced by the small solar escape velocity near Earth. The proposed setup can probe couplings an order of magnitude smaller than other methods for millicharge masses ranging from 100 meV to 100 eV and can operate concurrently as a search for sub-GeV millicharged dark matter. The signal power scales as the millicharge coupling to the eighth power, meaning that even with conservative assumptions, direct deflection could begin to explore new regions of parameter space. We also highlight novel features of millicharge solar basins, including those associated with the phase space distribution and the possibility for the occupation number to vastly exceed that of a thermal distribution.

For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory, both in the continuum and in a modified Villain lattice model. The duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides. We further construct the duality defect in non-abelian gauge theories and the \(\mathbb{Z}_N\) lattice gauge theory.

We study the relation between approximate horizon symmetries of AdS black branes and approximately conserved currents in their dual hydrodynamic description. We argue that the existence of an approximately conserved enstrophy current unique to \(2+1\) dimensional fluid flow implies that AdS\({}_4\) black branes possess a special class of approximate supertranslations (which we identify).

A vanishing Yukawa coupling of the up quark could in principle solve the strong CP problem. To render this solution consistent with current algebra results, the up quark must receive an alternative mass contribution that conserves CP symmetry. Such a contribution could be provided by QCD through non-perturbative topological effects, including instantons. In this talk, we present the first direct lattice computation of this topological mass contribution, using gauge configurations generated by the Extended Twisted Mass collaboration. We use the Iwasaki gauge action, Wilson twisted mass fermions at maximal twist, and dynamical up, down, strange and charm quarks. Our result for the topological mass contribution is an order of magnitude too small to account for the phenomenologically required up-quark mass. This rules out the "massless" up-quark solution to the strong CP problem, in accordance with previous results relying on \(\chi\)PT fits to lattice data. The talk is based on [Alexandrou et al., PRL 125, 232001 (2020)], where more details can be found.

We numerically study the Hamiltonian lattice formulation of the two-flavor Schwinger model using matrix product states. Keeping the mass of the first flavor at a fixed positive value, we tune the mass of the second flavor through a range of negative values, thus exploring a regime where conventional Monte Carlo methods suffer from the sign problem and may run into instabilities due to zero modes. Our results indicate a phase transition at the point where the absolute value of the second flavor mass approaches the first flavor mass. The phase transition is accompanied by the formation of a fermion condensate, a steep drop of the average electric field, and a peak in the bipartite entanglement entropy. Our data hints at a second order transition, which is the 1+1D analog of the CP-violating Dashen phase transition in QCD.

We study the Large \(N_\text{c}\) scaling of pion-pion scattering amplitudes for \(N_\text{f}=4\) degenerate quark flavors. We focus on the standard isospin-2 channel and the adjoint-antisymmetric (AA) representation. The latter only exists for \(N_\text{f}\geq 4\) and a representative state is \(\frac{1}{\sqrt{2}}(|D_s^+\pi^+\rangle-|D^+ K^+\rangle)\). We compare the results obtained for two regularizations (Wilson and twisted-mass fermions) and three values of the lattice spacing, and observe significant discretization effects in the AA channel. Finally, we match our results to NLO SU(4) and NNLO U(4) Chiral Perturbation Theory and constrain the \(N_\text{c}\) scaling of the relevant low-energy couplings.

Finite-density QCD and many other field theories with sign problems have a \(\mathcal{PT}\)-type symmetry. After a brief introduction to \(\mathcal{PT}\)-symmetric field theories, a real dual representation for \(\mathcal{PT}\)-symmetric scalar field theories with complex actions is derived. We show that \(\mathcal{PT}\)-symmetric field theories can exhibit exotic behavior, including sinusoidally modulated propagators, disorder lines, and spatially inhomogeneous pattern-forming phases. We discuss the interplay of duality, \(\mathcal{PT}\)-symmetry and pattern formation using a \(\phi^4\) model and \(Z(N)\) spin model with sign problems as examples. These behaviors may occur in finite-density QCD and related models.

Axions are a theoretically promising dark matter (DM) candidate. In the presence of radiation from bright astrophysical sources at radio frequencies, nonrelativistic DM axions can undergo stimulated decay to two nearly back-to-back photons, meaning that bright sources of radio waves will have a counterimage (''gegenschein'') in nearly the exact opposite spatial direction. The counterimage will be spectrally distinct from backgrounds, taking the form of a narrow radio line centered at \(\nu = m_a/4\pi\) with a width determined by Doppler broadening in the DM halo, \(\Delta \nu/\nu \sim 10^{-3}\). In this work, we show that the axion decay-induced echoes of supernova remnants may be bright enough to be detectable. Their non-detection may be able to set the strongest limits to date on axion DM in the \(\sim 1-10 \, \mu\)eV mass range where there are gaps in coverage from existing experiments.

We introduce a global analysis of relativistic heavy ion collisions using Trajectum of a significantly higher precision and including a new option to vary the normalization of the centrality estimator. We use the posterior distribution of our parameters to generate a set of high statistics samples that allows us to make precise predictions including statistical and systematic uncertainties estimated from the model parameter distribution. The results are systematically compared with experiment whereby we also include many observables not included in the global analysis. This includes in particular (extremely) ultracentral anisotropic flow and mean transverse momentum, whereby we find satisfactory agreement with experiment where data is available. Lastly, we compute spectra and anisotropic flow for oxygen-oxygen collisions performed at RHIC and to be performed at the LHC and comment on how these collisions may inform us on properties of the Quark-Gluon-Plasma.

We study the impact of selection biases on jet structure and substructure observables and separate these effects from effects caused by jet quenching. We use the angular separation \(\Delta R\) of the hardest splitting in a jet as the primary example observable. We first conduct a simplified Monte Carlo study in which it is possible to identify the same jet after quenching in a heavy ion collision and as it would have been if it had formed in vacuum. We select a sample of jets by placing a cut on their quenched \(p_T\) and, as is possible only in a Monte Carlo study, compare to the same jets unquenched, and see that the \(\Delta R\) distribution seems to be unmodified. However, if we select a sample of jets formed in vacuum by placing a cut on their unquenched \(p_T\) and compare to those same jets after quenching, we see a significant enhancement in the number of jets with large \(\Delta R\), primarily due to the soft particles in the jet that originate from the wake in the droplet of quark-gluon plasma excited by the parton shower. We confirm that the jets contributing to this enhancement are those jets which lost the most energy, which were not included in the sample selected after quenching; jets selected after quenching are those which lose a small fraction of their energy. Next, we employ a method that is available to experimentalists: in a sample of jets with a recoiling \(Z\) boson, we show that selecting jets based on the jet \(p_T\) after quenching yields a \(\Delta R\) distribution that appears unmodified while selecting a sample of jets produced in association with a \(Z\) boson whose (unmodified) \(p_T\) is above some cut yields a significant enhancement in the number of jets with large \(\Delta R\). We again confirm that this is due to particles from the wake, and that the jets contributing to this enhancement are those which have lost a significant fraction of their energy.

Hamiltonian simulation is a fundamental problem at the heart of quantum computation, and the associated simulation algorithms are useful building blocks for designing larger quantum algorithms. In order to be successfully concatenated into a larger quantum algorithm, a Hamiltonian simulation algorithm must succeed with arbitrarily high success probability \(1-\delta\) while only requiring a single copy of the initial state, a property which we call fully-coherent. Although optimal Hamiltonian simulation has been achieved by quantum signal processing (QSP), with query complexity linear in time \(t\) and logarithmic in inverse error \(\ln(1/\epsilon)\), the corresponding algorithm is not fully-coherent as it only succeeds with probability close to \(1/4\). While this simulation algorithm can be made fully-coherent by employing amplitude amplification at the expense of appending a \(\ln(1/\delta)\) multiplicative factor to the query complexity, here we develop a new fully-coherent Hamiltonian simulation algorithm that achieves a query complexity additive in \(\ln(1/\delta)\): \(\Theta\big( \|\mathcal{H}\| |t| + \ln(1/\epsilon) + \ln(1/\delta)\big)\). We accomplish this by compressing the spectrum of the Hamiltonian with an affine transformation, and applying to it a QSP polynomial that approximates the complex exponential only over the range of the compressed spectrum. We further numerically analyze the complexity of this algorithm and demonstrate its application to the simulation of the Heisenberg model in constant and time-dependent external magnetic fields. We believe that this efficient fully-coherent Hamiltonian simulation algorithm can serve as a useful subroutine in quantum algorithms where maintaining coherence is paramount.

Recent FPGA accelerator cards promise large acceleration factors for some specific computational tasks. In the context of Lattice QCD calculations, we investigate the possible gain of moving the \(SU(3)\) gauge field smearing routine to such accelerators. We study Xilinx Alveo U280 cards and use the associated Vitis high-level synthesis framework. We discuss the possible pros and cons of such a solution based on the gathered benchmarks.

We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding bulk is therefore a non-trivial subsystem symmetry protected topological (SSPT) phase. We demonstrate these phenomena in several examples with continuous and discrete subsystem global symmetries, as well as time-reversal symmetry. For each example we describe the boundary anomaly, and present classical continuum actions for the corresponding bulk SSPT phases, which describe the response of background gauge fields associated with the subsystem symmetries. Interestingly, we show that the anomaly does not uniquely specify the bulk SSPT phase. In general, the latter may also depend on how the symmetry and the associated foliation structure on the boundary are extended into the bulk.

We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and \(\mathcal{PT}\)-symmetric QFTs. Finite-density QCD is symmetric under the combined operation of the charge and complex conjugation operators \(\mathcal{CK}\), which falls into the class of so-called generalized \(\mathcal{PT}\) symmetries. We show that \(\mathcal{PT}\)-symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy quark model at nonzero chemical potential that displays patterning behavior for a range of parameters. We derive a simple approximate criterion for the formation of these patterns, which can be used with lattice results.

The nature of the Fermi gamma-ray Galactic Center Excess (GCE) has remained a persistent mystery for over a decade. Although the excess is broadly compatible with emission expected due to dark matter annihilation, an explanation in terms of a population of unresolved astrophysical point sources e.g., millisecond pulsars, remains viable. The effort to uncover the origin of the GCE is hampered in particular by an incomplete understanding of diffuse emission of Galactic origin. This can lead to spurious features that make it difficult to robustly differentiate smooth emission, as expected for a dark matter origin, from more "clumpy" emission expected for a population of relatively bright, unresolved point sources. We use recent advancements in the field of simulation-based inference, in particular density estimation techniques using normalizing flows, in order to characterize the contribution of modeled components, including unresolved point source populations, to the GCE. Compared to traditional techniques based on the statistical distribution of photon counts, our machine learning-based method is able to utilize more of the information contained in a given model of the Galactic Center emission, and in particular can perform posterior parameter estimation while accounting for pixel-to-pixel spatial correlations in the gamma-ray map. This makes the method demonstrably more resilient to certain forms of model misspecification. On application to Fermi data, the method generically attributes a smaller fraction of the GCE flux to unresolved point sources when compared to traditional approaches. We nevertheless infer such a contribution to make up a non-negligible fraction of the GCE across all analysis variations considered, with at least \(38^{+9}_{-19}\%\) of the excess attributed to unresolved points sources in our baseline analysis.

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. This identification has many puzzles, including the boundary descriptions of the event horizons, the interiors of the black hole, and the singularities. Compounding these mysteries is the fact that, while there is no interaction between the CFTs, observers from them can fall into the black hole and interact. We address these issues in this paper. In particular, (i) we reformulate the meeting-behind-the-horizon puzzle by introducing a concept called causal connectability for any two quantum systems (which can in principle interact with each other), and show that this simple bulk experiment cannot be described by the boundary system at finite \(N\); (ii) we present a resolution of the puzzle by arguing there are emergent type III\(_1\) von Neumann subalgebras in the operator algebra of the boundary system in the large \(N\) limit; (iii) the type III\(_1\) structure leads to an explicit construction in the boundary theory of the evolution operator for a bulk in-falling observer, making manifest the emergence of the black hole horizons, the interiors, and the associated causal structure.

We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g., when variational quantum eigensolvers are used.