Simulating dimensionally reduced 4D Yang-Mills theory on a quantum computer
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The construction of gauge-invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no knowledge of Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH formulation was recently generalized to SU(3), but limited to one spatial dimension. In this work, we generalize the LSH approach to constructing the basis of SU(3) gauge-invariant states at a trivalent vertex—the essential building block to multidimensional space. A direct generalization from the SU(2) vertex yields a legitimate basis; however, in certain sectors of the Hilbert space, the naive LSH basis vectors so defined suffer from being nonorthogonal. The issues with orthogonality are directly related to the “missing label” or “outer multiplicity” problem associated with SU(3) tensor products and may also be phrased in terms of Littlewood-Richardson coefficients or the need for a “seventh Casimir” operator. The states that are unaffected by the problem are orthonormalized in closed form. For the sectors that are afflicted, we discuss the nonorthogonal bases and their orthogonalization. A few candidates for seventh Casimir operators are readily constructed from the suite of LSH gauge-singlet operators. The diagonalization of a seventh Casimir represents one prescriptive solution toward obtaining a complete orthonormal basis, but a closed-form general solution remains to be found. Published by the American Physical Society 2025
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Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we show how the Hilbert space and interactions can be expanded in inverse powers of N c . At leading order in this expansion, the Hamiltonian simplifies dramatically, both in the required size of the Hilbert space as well as the type of interactions involved. Adding a truncation of the resulting Hilbert space in terms of local energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits. This formulation allows a simulation of the real time dynamics of a SU(3) lattice gauge theory on a 5 × 5 and 8 × 8 lattice on ibm_torino with a CNOT depth of 113.
Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in (d+2)-dimensional Minkowski spacetime for any d ≥ 2, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in (d+2)-dimensional spacetime.
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The foundation stone of atmospheric electricity is the existence of a Global Electric Circuit (GEC) influencing all of the planet. In fact, global thunderstorm activity acts as a voltage source that imposes a potential difference between the ionosphere (positively charged) and the Earth’s surface (negatively charged) of about ~300 kV. Such potential difference is discharged through the poorly conducting atmosphere in fair-weather regions, with atmospheric electric fields of ~100 V/m. First evidence of the GEC was gathered by scientists involved on the Carnegie vessel expeditions (early 20th Century), in which they describe a similar daily variation of the atmospheric electric field in different parts of the Pacific Ocean. Such variation become known as the Carnegie Curve (CC).
This project is directed at improving the efficiency and productivity of the existing installed US machine tool base by correcting a fundamental system-wide flaw in the existing programmable machine tool infrastructure. The project will catalyze a shift from a geometry-only mindset to a geometry -and-machine -performance mindset. The project will lead to a dramatic overhaul of the existing ecosystem for programming of Computer Numerically Controlled (CNC) machine tools, and will result in energy savings, cost savings, reduced scrap, and improved competitiveness of US manufacturers.
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This presentation will report the rational design and fabrication of NETL’s highly permeable non-aging thin film composite (TFC) membranes for CO2 capture from various industrial point sources. This talk will also cover the design, computational fluid dynamic simulation, 3D printing, and permeation testing of plate-and-frame membrane modules for an upcoming field demonstration at U. S. Steel’s Edgar Thomson Plant in Braddock, PA. The field test will demonstrate membrane-based CO2 capture from a blast furnace for decarbonization of steel manufacturing for the first time in the U.S. A mobile gas permeation test unit is currently under design and construction for the field test, which is scheduled to take place in 2025.
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The Industrial Technology Validation (ITV) program aims to identify and demonstrate the performance of new, emerging, and underutilized technologies in the industrial sector to help inform decisions towards accelerating commercialization and deployment. This initiative aims to identify, validate, and showcase new, emerging, and underutilized technologies in the industrial sector to expedite their commercialization and widespread deployment. By conducting thorough validations and demonstrating the efficacy of these technologies, the ITV program facilitates informed decision-making among industry stakeholders, contributing to the transition towards more sustainable and efficient industrial processes. This ITV demonstration involved the testing of an electrocoagulation (EC) treatment system at a steel plant in Ohio. The system was designed to treat oily wastewater generated from cold rolling operations.
Oily wastewater is a significant byproduct across various industries, including steel production, posing environmental and health risks. Steelmaking is particularly water-intensive, with an estimated 75,000 gallons required to produce 1 ton of steel, although recycling reduces this to 13,000–23,000 gallons per ton.1 Water serves multiple purposes in steelmaking, including equipment cooling, scale removal, steam generation, lubrication, and pollution control.