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Foundation models applied to bio-molecular space hold promise to accelerate drug discovery. Molecular representation is key to building such models. Previous works have typically focused on a single representation or view of the molecules. Here, we develop a multi-view foundation model approach, that integrates molecular views of graph, image and text. Single-view foundation models are each pre-trained on a dataset of up to 200M molecules and then aggregated into combined representations. Our multi-view model is validated on a diverse set of 18 tasks, encompassing ligand-protein binding, molecular solubility, metabolism and toxicity. We show that the multi-view models perform robustly and are able to balance the strengths and weaknesses of specific views. We then apply this model to screen compounds against a large (>100 targets) set of G Protein-Coupled receptors (GPCRs). From this library of targets, we identify 33 that are related to Alzheimer's disease. On this subset, we employ our model to identify strong binders, which are validated through structure-based modeling and identification of key binding motifs., Comment: 34 pages including supplement. 9 figures, 4 tables

Application of Unmanned Aerial Vehicles (UAVs) in search and rescue, emergency management, and law enforcement has gained traction with the advent of low-cost platforms and sensor payloads. The emergence of hybrid neural and symbolic AI approaches for complex reasoning is expected to further push the boundaries of these applications with decreasing levels of human intervention. However, current UAV simulation environments lack semantic context suited to this hybrid approach. To address this gap, HAMERITT (Hybrid Ai Mission Environment for RapId Training and Testing) provides a simulation-based autonomy software framework that supports the training, testing and assurance of neuro-symbolic algorithms for autonomous maneuver and perception reasoning. HAMERITT includes scenario generation capabilities that offer mission-relevant contextual symbolic information in addition to raw sensor data. Scenarios include symbolic descriptions for entities of interest and their relations to scene elements, as well as spatial-temporal constraints in the form of time-bounded areas of interest with prior probabilities and restricted zones within those areas. HAMERITT also features support for training distinct algorithm threads for maneuver vs. perception within an end-to-end mission run. Future work includes improving scenario realism and scaling symbolic context generation through automated workflow., Comment: 6 pages, 5 figures, 1 table

The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing channels and analyze their error correctability in the thermodynamic limit. We show that (i) there is a finite decoding threshold if and only if the minimal nonzero scaling dimension in the fusion algebra generated by the jump operator of the channel is larger than $1/2$ and (ii) the number of protected logical qubits $k \geq \Omega( \log \log n)$, where $n$ is the number of physical qubits. As an application, we show that the one-dimensional quantum critical Ising model has a finite threshold for certain types of dephasing noise. Our general results also imply that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes., Comment: 5+12 pages, 7 figures

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is `strongly symmetric', i.e. it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS), and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g. $SU(2)$), the bipartite entanglement of formation for the MMIS scales logarithmically $\sim \log N$ with the number of qudits $N$., Comment: 17+8 pages, 7 figures

Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space coordinates, averages of electrodynamic quantities at a single time will in general depend upon the inertial frame, and will differ between inertial frames. Here we illustrate how the use of continuous charge and current distributions rather than point-charge distributions can lead to physically mystifying and even inaccurate results for electromagnetic quantities and physical phenomena. The discrepancy noted between the average electric field values in different inertial frames is particularly striking because it is first order in the relative velocity between the frames., Comment: 20 pages

A derivation of the Planck spectrum for thermal radiation is given based upon wave fluctuations within relativistic classical physics. The derivation depends crucially on thermal fluctuations existing above the fundamental inertial-frame-independent fluctuations of classical zero-point radiation. Such frame-independent zero-point fluctuations exist only in a relativistic wave theory and cannot exist in a nonrelativistic wave theory. Thus such a classical derivation of the Planck spectrum exists in a Lorentz-covariant classical theory, such as classical electrodynamics, but not in a Galilean-covariant theory where all waves are based upon material media. Classical zero-point radiation provides a purely classical alternative to quanta in the analysis of the Planck spectrum., Comment: 23 pages

For quantum phases of Hamiltonian ground states, the energy gap plays a central role in ensuring the stability of the phase as long as the gap remains finite. We propose Markov length, the length scale at which the quantum conditional mutual information (CMI) decays exponentially, as an equally essential quantity characterizing mixed-state phases and transitions. For a state evolving under a local Lindbladian, we argue that if its Markov length remains finite along the evolution, then it remains in the same phase, meaning there exists another quasi-local Lindbladian evolution that can reverse the former one. We apply this diagnostic to toric code subject to decoherence and show that the Markov length is finite everywhere except at its decodability transition, at which it diverges. CMI in this case can be mapped to the free energy cost of point defects in the random bond Ising model. This implies that the mixed state phase transition coincides with the decodability transition and also suggests a quasi-local decoding channel., Comment: 5 + 7 pages, 3 main figures; v2: simpler derivation of quasi-local decoder

We study presentations of $C^*(X)$ that are evaluative over a presentation of $X$ in that $(f,p) \mapsto f(p)$ is computable. We prove existence-uniqueness theorems for such presentations. We use our methods to prove an effective Banach-Stone Theorem for unital commutative $C^*$ algebras. We also apply our results to the computable categoricity of $C^*$ algebras and compact Polish spaces.

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.

Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. To establish that two mixed states are in the same phase, as defined by their two-way connectivity via local quantum channels, we use the renormalization group (RG) and decoders of quantum error correcting codes. We introduce a real-space RG scheme for mixed states based on local channels which ideally preserve correlations with the complementary system, and we prove this is equivalent to the reversibility of the channel's action. As an application, we demonstrate an exact RG flow of finite temperature toric code in two dimensions to infinite temperature, thus proving it is in the trivial phase. In contrast, for toric code subject to local dephasing, we establish a mixed state toric code phase using local channels obtained by truncating an RG-type decoder and the minimum weight perfect matching decoder. We also discover a precise relation between mixed state phase and decodability, by proving that local noise acting on toric code cannot destroy logical information without bringing the state out of the toric code phase.

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (not too entangled) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at large bond dimension. Through this statistical-mechanics lens, we argue that: i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. These results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states

A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle moving in a circular orbit with counter-propagating plane waves providing the power which balances the energy radiated away by the accelerating charge. It is emphasized that only an electromagnetic arrangement, such as a Coulomb potential or a constant magnetic field, can provide the relativistic central force for the particle motion., Comment: 14 pages

We show how distinct phases of matter can be generated by performing random single-qubit measurements on a subsystem of toric code. Using a parton construction, such measurements map to random Gaussian tensor networks, and in particular, random Pauli measurements map to a classical loop model in which watermelon correlators precisely determine measurement-induced entanglement. Measuring all but a 1d boundary of qubits realizes hybrid circuits involving unitary gates and projective measurements in 1+1 dimensions. We find that varying the probabilities of different Pauli measurements can drive transitions in the un-measured boundary between phases with different orders and entanglement scaling, corresponding to short and long loop phases in the classical model. Furthermore, by utilizing single-site boundary unitaries conditioned on the bulk measurement outcomes, we generate mixed state ordered phases and transitions that can be experimentally diagnosed via linear observables. This demonstrates how parton constructions provide a natural framework for measurement-based quantum computing setups to produce and manipulate phases of matter.

Atmospheric aerosols facilitate reactions between ambient gases and dissolved species. Here, we review our efforts to interrogate the uptake of these gases and the mechanisms of their reactions both theoretically and experimentally. We highlight the fascinating behavior of $\mathrm{N}_2\mathrm{O}_5$ in solutions ranging from pure water to complex mixtures, chosen because its aerosol-mediated reactions significantly impact global ozone, hydroxyl, and methane concentrations. As a hydrophobic, weakly soluble, and highly reactive species, $\mathrm{N}_2\mathrm{O}_5$ is a sensitive probe of the chemical and physical properties of aerosol interfaces. We employ contemporary theory to disentangle the fate of $\mathrm{N}_2\mathrm{O}_5$ as it approaches pure and salty water, starting with adsorption and ending with hydrolysis to HNO$_3$, chlorination to $\mathrm{ClNO}_2$, or evaporation. Flow reactor and gas-liquid scattering experiments probe even greater complexity as added ions, organic molecules, and surfactants alter interfacial composition and reaction rates. Together, we reveal a new perspective on multiphase chemistry in the atmosphere., Comment: Posted with permission from the Annual Review of Physical Chemistry, Volume 75, copyright 2024 Annual Reviews, http://www.annualreviews.org

The interaction of a solenoid with a passing charged particle can be treated within classical or quantum physics. If charged particles pass around both sides of a solenoid, there is an experimentally-observed Aharonov-Bohm deflection of the double-slit particle interference pattern between charges passing on opposite sides. Such a deflection can be obtained by a classical force calculation. Although the magnitude of the angular deflection agrees between the classical force calculation and the quantum topological theory, the direction of the predicted deflection is opposite. Here we point out the simple basis for the direction of the deflection based upon classical electrodynamics and based upon quantum theory, and we mention analogues, both the electrostatic deflection of the particle interference pattern and the optical analogue of the classical calculation. The deflection direction involves an experimental question which is addressed rarely if ever., Comment: 12 pages

Super-resolution microscopy, or nanoscopy, enables the use of fluorescent-based molecular localization tools to study molecular structure at the nanoscale level in the intact cell, bridging the mesoscale gap to classical structural biology methodologies. Analysis of super-resolution data by artificial intelligence (AI), such as machine learning, offers tremendous potential for discovery of new biology, that, by definition, is not known and lacks ground truth. Herein, we describe the application of weakly supervised paradigms to super-resolution microscopy and its potential to enable the accelerated exploration of the nanoscale architecture of subcellular macromolecules and organelles., Comment: 26 pages, 4 figures

We propose a general framework for using local measurements, local unitaries, and non-local classical communication to construct quantum channels which can efficiently prepare mixed states with long-range quantum order or quantum criticality. As an illustration, symmetry-protected topological (SPT) phases can be universally converted into mixed-states with long-range entanglement, which can undergo phase transitions with quantum critical correlations of local operators and a logarithmic scaling of the entanglement negativity, despite coexisting with volume-law entropy. Within the same framework, we present two applications using fermion occupation number measurement to convert (i) spinful free fermions in one dimension into a quantum-critical mixed state with enhanced algebraic correlations between spins and (ii) Chern insulators into a mixed state with critical quantum correlations in the bulk. The latter is an example where mixed-state quantum criticality can emerge from a gapped state of matter in constant depth using local quantum operations and non-local classical communication., Comment: 25 pages, 11 figures; updated to the published version

Adaptive quantum circuits employ unitary gates assisted by mid-circuit measurement, classical computation on the measurement outcome, and the conditional application of future unitary gates based on the result of the classical computation. In this paper, we experimentally demonstrate that even a noisy adaptive quantum circuit of constant depth can achieve a task that is impossible for any purely unitary quantum circuit of identical depth: the preparation of long-range entangled topological states with high fidelity. We prepare a particular toric code ground state with fidelity of at least $76.9\pm 1.3\%$ using a constant depth ($d=4$) adaptive circuit, and rigorously show that no unitary circuit of the same depth and connectivity could prepare this state with fidelity greater than $50\%$., Comment: 5 pages, 3 figures

The situation of a charged particle passing down the symmetry axis through a magnetic toroid presents a relativity paradox; different inertial frames suggest different forces on the charge and on the toroid due to the unperturbed systems. We review the charge-toroid interaction and suggest that the magnetic Aharonov-Bohm situation is misunderstood because of unfamiliarity with the acceleration fields following from the Darwin Lagrangian, which go unmentioned in recent textbooks of classical electromagnetism., Comment: 16 pages

The Aharonov-Bohm phase shift in a particle interference pattern when electrons pass a long solenoid is identical in form with the optical interference pattern shift when a piece of retarding glass is introduced into one path of a two-beam optical interference pattern. The particle interference-pattern deflection is a relativistic effect of order 1/c^2, though this relativity aspect is rarely mentioned in the literature. Here we give a thorough analysis of the classical electromagnetic aspects of the interaction between a solenoid or toroid and a charged particle. We point out the magnetic Lorentz force which the solenoid or toroid experiences due to a passing charge. Although analysis in the rest frame of the solenoid or toroid will involve back Faraday fields on the charge, the analysis in the inertial frame in which the charge is initially at rest involves forces due to only electric fields where forces are equal in magnitude and opposite in direction. The classical analysis is made using the Darwin Lagrangian. We point out that the classical analysis suggests an angular deflection independent of Planck's constant where the deflection magnitude is identical with that given by the traditional quantum analysis, but where the deflection direction is unambiguous., Comment: 34 pages

We analyze the effect of decoherence, modelled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "$g$-function" in conformal field theory (CFT), allowing us to define a notion of renormalization group (RG) flow (or "phase transitions") between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the CFT. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods., Comment: 7+14 pages, 4+11 figures, published version

Projective measurement, a basic operation in quantum mechanics, can induce seemingly nonlocal effects. In this work, we analyze such effects in many-body systems by studying the non-equilibrium dynamics of weakly monitored quantum circuits, focusing on entanglement generation and information spreading. We find that, due to measurements, the entanglement dynamics in monitored circuits is indeed "faster" than that of unitary ones in several ways. Specifically, we find that a pair of well-separated regions can become entangled in a time scale $\ell^{2/3}$, sub-linear in their distance $\ell$. For the case of Clifford monitored circuits, this originates from super-ballistically growing stabilizer generators of the evolving state. In addition, we find initially local information can spread super-ballistically as $t^{3/2}$. Furthermore, by viewing the dynamics as a dynamical encoding process, we show that the super-ballistic growing length scale relates to an encoding time that is sublinear in system size. To quantify the information dynamics, we develop a formalism generalizing operator spreading to non-unitary dynamics, which is of independent interest., Comment: 19 pages

Within the framework of computable infinitary continuous logic, we develop a system of hyperarithmetic numerals. These numerals are infinitary sentences in a metric language $L$ that have the same truth value in every interpretation of $L$. We prove that every hyperarithmetic real can be represented by a hyperarithmetic numeral at the same level of complexity.

Although the expressions for energy densities involving electric and magnetic fields are exactly analogous, the connections to forces and electromagnetic potentials are vastly different. For electrostatic situations, the changes in the \textit{electric} energy can be related directly to \textit{electric} forces and to the electrostatic potential. The situation involving magnetic forces and energy changes involves two fundamentally different situations. For charged particles moving with constant velocities, the changes in both electric and magnetic field energies are provided by the external forces that keep the particles' velocities constant; there are no Faraday acceleration electric fields in this situation. However, for particles that change speed, the changes in \textit{magnetic} energy density are related to acceleration-dependent Faraday \textit{electric} fields. Current undergraduate and graduate textbooks deal only with highly symmetric situations where the Faraday electric fields are easily calculated from the time-changing magnetic flux. However, in situations that lack high symmetry, such as the magnetic Aharonov-Bohm situation, the back (Faraday) acceleration electric fields of point charges seem unfamiliar. In this article, we present a simple unsymmetric example and analyze it using the Darwin Lagrangian. In \textit{all} cases involving changing velocities of the current carriers, it is the work done by the back (Faraday) acceleration \textit{electric} fields that balances the \textit{magnetic} energy changes., Comment: 15 pages