A general scheme is presented for simulating gauge theories, with matter fields, on a digital quantum computer. A Trotterized time-evolution operator that respects gauge symmetry is constructed, and a procedure for obtaining time-separated, gauge-invariant correlators is detailed. We demonstrate the procedure on small lattices, including the simulation of a 2+1D non-Abelian gauge theory.

Parton distribution functions and hadronic tensors may be computed on a universal quantum computer without many of the complexities that apply to Euclidean lattice calculations. We detail algorithms for computing parton distribution functions and the hadronic tensor in the Thirring model. Their generalization to QCD is discussed, with the conclusion that the parton distribution function is best obtained by fitting the hadronic tensor, rather than direct calculation. As a side effect of this method, we find that lepton-hadron cross sections may be computed relatively cheaply. Finally, we estimate the computational cost of performing such a calculation on a digital quantum computer, including the cost of state preparation, for physically relevant parameters.

Monolayers of cis-unsaturated fatty acids have been investigated at the air/water interface by using surface pressure (π)−molecular area (A) isotherms and Brewster angle microscopic (BAM) observation. The film materials used are oleic, gondoic, erucic, and nervonic acid. Elaidic acid, a trans-isomer of the oleic acid, is also employed for comparison. The measurements have been performed in a wide temperature range. Oleic and gondoic acid always take expanded phases on the water surface even at near 0 °C. However, first-order phase transitions from expanded to condensed phases have been observed for erucic and nervonic monolayers in certain temperature ranges, accompanied by nonequilibrium growth of condensed phase domains in homogeneous fluid phases. The shape of the emerging domains in the erucic acid monolayers is sixfold and highly dendritic, like snowflakes. The nervonic acid forms also sixfold but rather rounded, flowerlike domains on the water surface. In contrast to the nonequilibrium patterns observed for the cis-unsaturated fatty acid monolayers, elaidic acid monolayers exhibit growth of circular domains in phase transition regions during compression. Formation of the branched structures is interpreted as a consequence of higher supersaturation arising from the packing directivity of cis-long chain into two-dimensional crystal aggregates. For erucic acid monolayers, the shape relaxation of dendrites after compression is stopped is followed by BAM, where the highly branched nonequilibrium structures gradually transform into nearly rounded equilibrium domains with elapsed time.

It is for the first time that quantum simulation for High Energy Physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in Quantum Information Sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This community whitepaper is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

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