MIT Center for Theoretical Physics — a Leinweber Institute Publications

We study infinite limits of neural network quantum states (\(\infty\)-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of Renyi entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For \(\infty\)-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an \(\infty\)-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. \(\infty\)-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

We study the universal behavior of quantum information-theoretic quantities in thermalized isolated quantum many-body systems and evaporating black holes. In particular, we study a genuine mixed-state entanglement measure called the logarithmic negativity, other correlation measures including the Renyi negativities and the mutual information, and a signature of multipartite entanglement called the reflected entropy. We also probe the feasibility of recovering quantum information from subsystems of a thermalized quantum many-body system or from the radiation of an evaporating black hole, using quantities such as relative entropy and Petz map fidelity. A recently developed technique called the equilibrium approximation allows us to probe these quantities at finite temperature. We find striking qualitative differences from the infinite temperature case, which has been the topic of previous studies using Haar-random states. In particular, we find regimes where the logarithmic negativity is extensive but the mutual information is sub-extensive, indicating a large amount of undistillable, bound entanglement in thermalized states. For evaporating black holes at finite temperature, both the logarithmic negativity and the Petz map fidelity reveal an important new time scale \(t_b\), which is earlier than the Page time \(t_p\) by a finite fraction of the total evaporation time. We find that \(t_b\), as opposed to \(t_p\), is the time scale at which quantum entanglement between different parts of the radiation becomes extensive, and the fidelity of information recovery for a large diary thrown into the black hole starts to grow.

We investigate numerically different techniques to extract scattering amplitudes from the Euclidean Lattice ϕ4 theory with two fields, having different masses. We present an exploratory study of the recently proposed method by Bruno and Hansen for extracting the scattering length from a four-point function (cf 10.1007/JHEP06(2021)043), and a study of the two- and three-particle quantization condition.

Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. As a novel approach, quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations and may eventually outperform classical computers. However, current quantum devices still suffer from inherent quantum noise. In this work, we propose an error mitigation scheme suitable for parametric quantum circuits. This scheme is based on projecting a general quantum noise channel onto depolarization errors. Our method can efficiently reduce errors in quantum computations, which we demonstrate by carrying out simulations both on classical and IBM’s quantum devices. In particular, we test the performance of the method by computing the mass gap of the transverse-field Ising model using the variational quantum eigensolver algorithm.

We show that the vacuum-subtracted maximal volume, the proposed holographic dual to complexity of formation, can be negative when contributions from compact directions are included. We construct explicit solutions with arbitrarily negative complexity of formation in asymptotically AdS\(_{4}\times S^{7}\) SUGRA. These examples rely critically on the compact directions, specifically the fact that the full eleven-dimensional spacetime is not asymptotically AdS\(_{11}\). While there is some ambiguity in the extension of the holographic complexity proposal to the compact directions, we show that the two natural candidates can both have arbitrarily negative complexity of formation in SUGRA solutions. We further find examples in which complexity can even decrease at late times, including cases of both single-sided geometries and two-sided wormholes. In particular, we construct a cosmological wormhole with simultaneously negative and decreasing complexity of formation (as computed by volume) at late times. We find a distinguished role for relevant primaries in these constructions and comment on possible interpretations.

Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear systems is the conjugate gradient (CG) approach. In this work we present an implementation of CG that can be executed on different devices, including CPUs, GPUs, and FPGAs. This is achieved by using the SYCL/DPC++ framework, which allows the execution of the same source code on heterogeneous systems.

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. In this article, we discuss the calculation of the second and fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion. The resulting value for the second Mellin moment is \( \langle{ \xi^2 }\rangle(\mu = 2~\text{GeV})= 0.210 \pm 0.013\text{ (stat.)} \pm 0.034\text{ (sys.)}\). This result is compatible with those from previous determinations of this quantity.

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude \(\mathcal{K}_\text{df,3}\) into the matrix basis used in the quantization condition, including both \(s\) and \(p\) waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to \(\mathcal{O}(1/L^5)\); and we calculate the leading-order predictions in chiral perturbation theory for \(\mathcal{K}_\text{df,3}\) in the \(\pi^+\pi^+K^+\) and \(\pi^+K^+K^+\) systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of \(\pi^+\pi^+K^+\) levels using the two- and three-particle interactions predicted by chiral perturbation theory.

The design of parametric quantum circuits (PQCs) for efficient use in variational quantum simulations (VQS) is subject to two competing factors. On one hand, the set of states that can be generated by the PQC has to be large enough to contain the solution state. Otherwise, one may at best find the best approximation of the solution restricted to the states generated by the chosen PQC. On the other hand, the PQC should contain as few parametric quantum gates as possible to minimize noise from the quantum device. Thus, when designing a PQC one needs to ensure that there are no redundant parameters. The dimensional expressivity analysis discussed in these proceedings is a means of addressing these counteracting effects. Its main objective is to identify independent and redundant parameters in the PQC. Using this information, superfluous parameters can be removed and the dimension of the space of states that are generated by the PQC can be computed. Knowing the dimension of the physical state space then allows us to deduce whether or not the PQC can reach all physical states. Furthermore, the dimensional expressivity analysis can be implemented efficiently using a hybrid quantum-classical algorithm. This implementation has relatively small overhead costs both for the classical and quantum part of the algorithm and could therefore be used in the future for on-the-fly circuit construction. This would allow for optimized circuits to be used in every loop of a VQS rather than the same PQC for the entire VQS. These proceedings review and extend work in [1, 2].

We study general freeze-out scenarios where an arbitrary number of initial and final dark matter particles participate in the number-changing freeze-out interaction. We consider a simple sector with two particle species undergoing such a thermal freeze-out; one of the relics is stable and gives rise to the dark matter today, while the other one decays to the Standard Model, injecting significant entropy into the thermal bath that dilutes the dark matter abundance. We show that this setup can lead to a stable relic population that reproduces the observed dark matter abundance without requiring weak scale masses or couplings. The final dark matter abundance is estimated analytically. We carry out this calculation for arbitrary temperature dependence in the freeze-out process and identify the viable dark matter mass and cross section ranges that explain the observed dark matter abundance. This setup can be used to open parameter space for both heavy (above the unitarity bound) or light (sub-GeV) dark matter candidates. We point out that the best strategy for probing most parts of our parameter space is to look for signatures of an early matter-dominant epoch.

Estimating the free energy, as well as other thermodynamic observables, is a key task in lattice field theories. Recently, it has been pointed out that deep generative models can be used in this context. Crucially, these models allow for the direct estimation of the free energy at a given point in parameter space. This is in contrast to existing methods based on Markov chains which generically require integration through parameter space. In this contribution, we will review this novel machine-learning-based estimation method. We will in detail discuss the issue of mode collapse and outline mitigation techniques which are particularly suited for applications at finite temperature.

We present an error mitigation scheme which corrects readout errors on Noisy Intermediate-Scale Quantum (NISQ) computers [1,2]. After a short review of applying the method to one qubit, we proceed to discuss the case when correlations between different qubits occur. We demonstrate how the readout error can be mitigated in this case. By performing experiments on IBMQ hardware, we show that such correlations do not have a strong effect on the results, justifying to neglect them.

Standard sampling algorithms for lattice QCD suffer from topology freezing (or critical slowing down) when approaching the continuum limit, thus leading to poor sampling of the distinct topological sectors. I will present a modified Hamiltonian Monte Carlo (HMC) algorithm that triggers topological sector jumps during the assembly of Markov chain of lattice configurations. We study its performance in the 2D Schwinger model and compare it to alternative methods, such as fixing topology or master field. We then briefly discuss the difficulties of the algorithm in a SU(2) gauge model in 4D.

We present results for \(B_{(s)}\)- and \(D_{(s)}\)-meson semileptonic decays from ongoing calculations by the Fermilab Lattice and MILC Collaborations. Our calculation employs the highly improved staggered quark (HISQ) action for both sea and valence quarks and includes several ensembles with physical-mass up, down, strange, and charm quarks and lattice spacings ranging from \(a\approx0.15\) fm down to 0.06 fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The use of the highly improved action, combined with the MILC Collaboration’s gauge ensembles with lattice spacings down to \(a\approx0.042\) fm, allows heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows (in some cases) for absolutely normalized currents, bypassing the need for perturbative matching, which has been a leading source of uncertainty in previous calculations of \(B\)-meson decay form factors by our collaboration. All preliminary form-factor results are blinded.

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).