MIT Center for Theoretical Physics — a Leinweber Institute Publications

Studying the dynamics of open quantum systems holds the potential to enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Due to the high-dimensional nature of the problem, customized deep generative neural networks have been instrumental in modeling the high-dimensional density matrix \(\rho\), which is the key description for the dynamics of such systems. However, the complex-valued nature and normalization constraints of \(\rho\), as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding probability distribution \(Q\), the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow evolution governed by high-dimensional PDEs, based on the Euler method and the application of the time-dependent variational principle. We name the resulting approach Q-Flow and demonstrate the scalability and efficiency of Q-Flow on open quantum system simulations, including the dissipative harmonic oscillator and the dissipative bosonic model. Q-Flow is superior to conventional PDE solvers and state-of-the-art physics-informed neural network solvers, especially in high-dimensional systems.

To compute the string one-loop correction to the Kahler potential of moduli fields of string compactifications in Einstein-frame, one must compute: the string one-loop correction to the Einstein-Hilbert action, the string one-loop correction to the moduli kinetic terms, the string one-loop correction to the definition of the holomorphic coordinates. In this note, we compute the string one-loop correction to the Einstein-Hilbert action of type II string theory compactified on orientifolds of Calabi-Yau threefolds. We find that the one-loop correction is determined by the new supersymmetric index studied by Cecotti, Fendley, Intriligator, and Vafa. As a simple application, we apply our results to estimate the size of the one-loop corrections around a conifold point in the Kahler moduli space.

We investigate the performance of the variational quantum eigensolver (VQE) for the optimal flight gate assignment problem. This problem is a combinatorial optimization problem that aims at finding an optimal assignment of flights to the gates of an airport, in order to minimize the passenger travel time. To study the problem, we adopt a qubit-efficient binary encoding with a cyclic mapping, which is suitable for a digital quantum computer. Using this encoding in conjunction with the Conditional Value at Risk (CVaR) as an aggregation function, we systematically explore the performance of the approach by classically simulating the CVaR-VQE. Our results indicate that the method allows for finding a good solution with high probability, and the method significantly outperforms the naive VQE approach. We examine the role of entanglement for the performance, and find that ansätze with entangling gates allow for better results than pure product states. Studying the problem for various sizes, our numerical data show that the scaling of the number of cost function calls for obtaining a good solution is not exponential for the regimes we investigate in this work.

By explicit counterexample, we show that the “reflected entropy” defined by Dutta and Faulkner is not monotonically decreasing under partial trace, and so is not a measure of physical correlations. In fact, our counterexamples show that none of the Rényi reflected entropies \(S_{R}^{(\alpha)}\) for \(0 < \alpha < 2\) is a correlation measure; the usual reflected entropy is realized as the \(\alpha=1\) member of this family. The counterexamples are given by quantum states that correspond to classical probability distributions, so reflected entropy fails to measure correlations even at the classical level.

In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. In this paper, we prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all \(4\)-body interactions as a perturbation to a random free-fermion model.

The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time and evolving the system using a space transfer matrix. The infinite-volume limit is then described by the fixed points of this operator, also known as influence matrices. To evaluate the potential of this method as a numerical scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. It is then natural to wonder what is the scaling of their entanglement, dubbed temporal entanglement, as a function of time. In this work we study space evolution in chaotic quantum circuits. First, we extend the concept of space-evolution to include evolution in any generic space-like direction, which enables us to use influence matrices on a generic time-like surface, or path, to describe any two-point function. Then we study their entanglement, finding that it scales linearly with time for all paths but with two interesting marginal cases: (i) vertical paths in generic chaotic systems (ii) any path in dual-unitary circuits. In these cases Rényi entropies with index larger than one are sub-linear in time, while the von Neumann entanglement entropy is linear but grows at a slower rate compared to regular state entanglement. We attribute this behaviour to the existence of a product state with large overlap with the influence matrices, similarly to what has been observed for regular entanglement in systems with conservation laws.

Topological magnetic structures are promising candidates for resilient information storage. An elementary example are spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schrödinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. We find two classes of quantum spin helices that can reach and even exceed ground-state stability: Spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered “phantom helices”. Beyond that, we show that the helicity itself (left- or right-rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon towards stabilizing helical quantum structures, e.g., in ultracold atoms and solid state systems. We also identify an – up to our knowledge – previously unknown new type of phantom helices.

These notes provide an explanation of the type classification of von Neumann algebras, which has made many appearances in recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature between resources that are too technical for the non-expert reader, and resources that seek to explain the broad intuition of the theory without giving precise definitions. Reading these notes will provide you with: (i) an argument for why “factors” are the fundamental von Neumann algebras that one needs to study; (ii) an intuitive explanation of the type classification of factors in terms of renormalization schemes that turn unnormalizable positive operators into “effective density matrices;” (iii) a mathematical explanation of the different types of renormalization schemes in terms of the allowed traces on a factor; (iv) an intuitive characterization of type I and II factors in terms of their “standard forms;” and (v) a list of some interesting connections between type classification and modular theory, including the argument for why type III\(_1\) factors are believed to be the relevant ones in quantum field theory. None of the material is new, but the pedagogy is different from other sources I have read; it is most similar in spirit to the recent work on gravity and the crossed product by Chandrasekaran, Longo, Penington, and Witten.

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.

We present an update of the Fermilab Lattice and MILC Collaborations project to compute the form factors for semileptonic \(B_{(s)}\)-meson decays. Our calculation uses the highly improved staggered quark (HISQ) action for sea and valence quarks, and ensembles with up, down, strange, and charm quarks in the sea. Using a highly improved action with the MILC Collaboration’s gauge ensembles with lattice spacings down to \(a\approx0.03\) fm, allows the heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows for absolutely normalized vector currents, bypassing the need for perturbative matching, which has been a source of uncertainty in previous calculations of \(B\)-meson decay form factors by our collaboration. All preliminary form-factor results are blinded.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by \(\epsilon < 1\) is introduced. It is shown that while Pauli \(Z\)-errors are not recoverable without additional resources, Pauli \(X\) and \(Y\) errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length \(O(2^k c^{k^2} d)\) is sufficient to correct any length-\(d\) QSP with \(c\) unique phases to \(k^{th}\)-order in error \(\epsilon\). Allowing an additional assumption, a lower bound of \(\Omega(cd)\) is shown, which is tight for \(k = 1\), on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

With the vast data-collecting capabilities of current and future high-energy collider experiments, there is an increasing demand for computationally efficient simulations. Generative machine learning models enable fast event generation, yet so far these approaches are largely constrained to fixed data structures and rigid detector geometries. In this paper, we introduce EPiC-GAN – equivariant point cloud generative adversarial network – which can produce point clouds of variable multiplicity. This flexible framework is based on deep sets and is well suited for simulating sprays of particles called jets. The generator and discriminator utilize multiple EPiC layers with an interpretable global latent vector. Crucially, the EPiC layers do not rely on pairwise information sharing between particles, which leads to a significant speed-up over graph- and transformer-based approaches with more complex relation diagrams. We demonstrate that EPiC-GAN scales well to large particle multiplicities and achieves high generation fidelity on benchmark jet generation tasks.

In this note, we prove that the one-loop pfaffian of the non-perturbative superpotential generated by Euclidean D-branes in type II compactifications on orientifolds of Calabi-Yau threefolds is determined by the moduli integral of the new supersymmetric index defined by Cecotti, Fendley, Intriligator, and Vafa. As this quantity can be computed via topological string theory, Chern-Simons theory, matrix models, or by solving the holomorphic anomaly equation, this result provides a method to directly compute the one-loop pfaffian of the non-perturbative superpotential. The relation between the one-loop pfaffian, threshold corrections to the gauge coupling, and the one-loop partition function of open topological string theory is discussed.

One of the greatest challenges in quantum chromodynamics is understanding the hadronization mechanism, which is also crucial for carrying out precision physics with jet substructure. In this Letter, we combine recent advancements in our understanding of the field theory-based nonperturbative structure of the soft drop jet mass with precise perturbative calculations of its multi-differential variants at next-to-next-to-leading logarithmic (NNLL) accuracy. This enables a systematic study of its hadronization power corrections in a completely model-independent way. We calibrate and test hadronization models and their interplay with parton showers by comparing our universality predictions with various event generators for quark and gluon initiated jets in both lepton-lepton and hadron-hadron collisions. We find that hadronization models perform better for quark jets relative to gluon jets. Our results provide the necessary toolkit for precision studies with the soft drop jet mass motivating future analyses using real world collider data. The nontrivial constraints derived in our framework are useful for improving the modeling of hadronization and its interface with parton showers in next generation event generators.

First-principles calculations of multi-hadron dynamics are a crucial goal in lattice QCD. Significant progress has been achieved in developing, implementing, and applying theoretical tools that connect finite-volume quantities to their infinite-volume counterparts. Here, I review some recent theoretical developments and numerical results regarding multi-particle quantities in a finite volume. These results include \(N\pi\) scattering, systems of two and three mesons at maximal isospin, three-body resonances in a toy model, and the formulation of effective theories in finite volume for multi-nucleon systems.

We present lattice-QCD calculations of the hadronic form factors for the semileptonic decays \(D\to\pi\ell\nu\), \(D\to K\ell\nu\), and \(D_s\to K\ell\nu\). Our calculation uses the highly improved staggered quark (HISQ) action for all valence and sea quarks and includes \(N_f=2+1+1\) MILC ensembles with lattice spacings ranging from \(a\approx0.12\) fm down to \(0.042\) fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The HISQ action allows all the quarks to be treated with the same relativistic light-quark action, allowing for nonperturbative renormalization using partial conservation of the vector current. We combine our results with experimental measurements of the differential decay rates to determine \(|V_{cd}|^{D\to\pi}=0.2238(11)^{\rm Expt}(15)^{\rm QCD}(04)^{\rm EW}(02)^{\rm SIB}[22]^{\rm QED}\) and \(|V_{cs}|^{D\to K}=0.9589(23)^{\rm Expt}(40)^{\rm QCD}(15)^{\rm EW}(05)^{\rm SIB}[95]^{\rm QED}\) This result for \(|V_{cd}|\) is the most precise to date, with a lattice-QCD error that is, for the first time for the semileptonic extraction, at the same level as the experimental error. Using recent measurements from BES III, we also give the first-ever determination of \(|V_{cd}|^{D_s\to K}=0.258(15)^{\rm Expt}(01)^{\rm QCD}[03]^{\rm QED}\) from \(D_s\to K \ell\nu\). Our results also furnish new Standard Model calculations of the lepton flavor universality ratios \(R^{D\to\pi}=0.98671(17)^{\rm QCD}[500]^{\rm QED}\), \(R^{D\to K}=0.97606(16)^{\rm QCD}[500]^{\rm QED}\), and \(R^{D_s\to K}=0.98099(10)^{\rm QCD}[500]^{\rm QED}\), which are consistent within \(2\sigma\) with experimental measurements. Our extractions of \(|V_{cd}|\) and \(|V_{cs}|\), when combined with a value for \(|V_{cb}|\), provide the most precise test of second-row CKM unitarity, finding agreement with unitarity at the level of one standard deviation.

In this paper, we compare several event classification architectures defined on the point cloud representation of collider events. These approaches, which are based on the frameworks of deep sets and edge convolutions, circumvent many of the difficulties associated with traditional feature engineering. To benchmark our architectures against more traditional event classification strategies, we perform a case study involving Higgs boson decays to tau leptons. We find a 2.5 times increase in performance compared to a baseline ATLAS analysis with engineered features. Our point cloud architectures can be viewed as simplified versions of graph neural networks, where each particle in the event corresponds to a graph node. In our case study, we find the best balance of performance and computational cost for simple pairwise architectures, which are based on learned edge features.

We present a new way of deriving effective theories of dynamical electromagnetic fields in general media. It can be used to give a systematic formulation of magnetohydrodynamics (MHD) with strong magnetic fields, including systems with chiral matter and Adler-Bell-Jackiw (ABJ) anomaly. We work in the regime in which velocity and temperature fluctuations can be neglected. The resulting chiral anomalous MHD incorporates and generalizes the chiral magnetic effect, the chiral separation effect, the chiral electric separation effect, as well as recently derived strong-field MHD, all in a single coherent framework. At linearized level, the theory predicts that the chiral magnetic wave survives strong dynamical magnetic fields, and predicts the wave velocity. We also introduce a simple, but solvable nonlinear model to explore the fate of the chiral instability.

The Hamiltonian limit of lattice gauge theories can be found by extrapolating the results of anisotropic lattice computations, i.e., computations using lattice actions with different temporal and spatial lattice spacings (\(a_t\neq a_s\)), to the limit of \(a_t\to 0\). In this work, we present a study of this Hamiltonian limit for a Euclidean \(U(1)\) gauge theory in 2+1 dimensions (QED3), regularized on a toroidal lattice. The limit is found using the renormalized anisotropy \(\xi_R=a_t/a_s\), by sending \(\xi_R \to 0\) while keeping the spatial lattice spacing constant. We compute \(\xi_R\) in \(3\) different ways: using both the “normal” and the “sideways” static quark potential, as well as the gradient flow evolution of gauge fields. The latter approach will be particularly relevant for future investigations of combining quantum computations with classical Monte Carlo computations, which requires the matching of lattice results obtained in the Hamiltonian and Lagrangian formalisms.

The Heavy Quark Expansion (HQE) gives an expansion of inclusive decay rates of \(b\)-hadrons as a simultaneous series in \(\alpha_s\) and \(1/m_b\), in terms of perturbatively defined coefficients and non-perturbative matrix elements. Spectator effects arise from the dimension-\(6\) operators in the HQE in which along with the heavy quark, a light spectator quark from the hadron participates in the weak decay. In this work, we provide a lattice determination of the bare matrix elements that contribute to the spectator effects for the \(B^+\)-meson, \(B_d\)-meson and the \(\Lambda_b\)-baryon. The computations were performed on two separate lattice spacings of the RBC-UKQCD (2+1)-flavor Domain Wall Fermion ensembles. Renormalization and continuum extrapolation of the matrix elements have not yet been computed, and are left to future work.