Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization

We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how the bases are digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.Comment: 10 pages, 9 figures. v3: Journal version. A few added remarks and plots regarding qubit cost

Breaking the Symmetry of a Circular System of Coupled Harmonic Oscillators

First we compute the natural frequencies of vibration of four identical particles coupled by ideal, massless harmonic springs. The four particles are constrained to move on a fixed circle. The initial computations are simplified by a transformation to symmetry coordinates. Then the symmetry of the vibrating system is broken by changing the mass of a single particle by a very small amount. We observe the effect of applying the symmetry transformation to the now slightly nonsymmetric system. We compute the new frequencies and compare them with the frequencies of the original symmetric system of oscillators. Results of similar calculations for 2,3,5, and 6particles are given

SU(N) Coherent States and Irreducible Schwinger Bosons

We exploit the SU(N) irreducible Schwinger boson to construct SU(N) coherent states. This construction of SU(N) coherent state is analogous to the construction of the simplest Heisenberg-Weyl coherent states. The coherent states belonging to irreducible representations of SU(N) are labeled by the eigenvalues of the $(N-1)$ SU(N) Casimir operators and are characterized by $(N-1)$ complex orthonormal vectors describing the SU(N) group manifold.Comment: 12 pages, 3 figure

Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks

Towards the goal of quantum computing for lattice quantum chromodynamics, we present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. This novel framework was previously developed for an SU(2) lattice gauge theory in $d\leq3$ spatial dimensions and its advantages for classical and quantum algorithms have thus far been demonstrated in $d=1$. The LSH approach uses gauge invariant degrees of freedoms such as loop segments, string ends, and on-site hadrons, it is free of all nonabelian gauge redundancy, and it is described by a Hamiltonian containing only local interactions. In this work, the SU(3) LSH framework is systematically derived from the reformulation of Hamiltonian lattice gauge theory in terms of irreducible Schwinger bosons, including the addition of staggered quarks. Furthermore, the superselection rules governing the LSH dynamics are identified directly from the form of the Hamiltonian. The SU(3) LSH Hamiltonian with open boundary conditions has been numerically confirmed to agree with the completely gauge-fixed Hamiltonian, which contains long-range interactions and does not generalize to either periodic boundary conditions or to $d>1$.Comment: 35 pages plus references, 5 figures. v2 includes typo corrections, trivial adjustments to text sectioning, and added reference

Four Anharmonic Oscillators on a Circle

Four identical, uniformly separated particles interconnected by ideal anharmonic springs are constrained to move on a fixed, frictionless circular track. The Lagrangian for the system is written and then transformed by matrix operations suggested by the symmetry of the arrangement of springs and particles. The equations of motion derived from the transformed Lagrangian yield four natural frequencies of motion

Metabolic labeling of RNA uncovers principles of RNA production and degradation dynamics in mammalian cells

available in PMC 2011 November 01.Cellular RNA levels are determined by the interplay of RNA production, processing and degradation. However, because most studies of RNA regulation do not distinguish the separate contributions of these processes, little is known about how they are temporally integrated. Here we combine metabolic labeling of RNA at high temporal resolution with advanced RNA quantification and computational modeling to estimate RNA transcription and degradation rates during the response of mouse dendritic cells to lipopolysaccharide. We find that changes in transcription rates determine the majority of temporal changes in RNA levels, but that changes in degradation rates are important for shaping sharp 'peaked' responses. We used sequencing of the newly transcribed RNA population to estimate temporally constant RNA processing and degradation rates genome wide. Degradation rates vary significantly between genes and contribute to the observed differences in the dynamic response. Certain transcripts, including those encoding cytokines and transcription factors, mature faster. Our study provides a quantitative approach to study the integrative process of RNA regulation.Human Frontier Science Program (Strasbourg, France)Howard Hughes Medical InstituteBurroughs Wellcome Fund (Career Award at the Scientific Interface

Phosphocaveolin-1 is a mechanotransducer that induces caveola biogenesis via Egr1 transcriptional regulation

Caveolin-1 (Cav1) is an essential component of caveolae whose Src kinase-dependent phosphorylation on tyrosine 14 (Y14) is associated with regulation of focal adhesion dynamics. However, the relationship between these disparate functions remains to be elucidated. Caveola biogenesis requires expression of both Cav1 and cavin-1, but Cav1Y14 phosphorylation is dispensable. In this paper, we show that Cav1 tyrosine phosphorylation induces caveola biogenesis via actin-dependent mechanotransduction and inactivation of the Egr1 (early growth response-1) transcription factor, relieving inhibition of endogenous Cav1 and cavin-1 genes. Cav1 phosphorylation reduces Egr1 binding to Cav1 and cavin-1 promoters and stimulates their activity. In MDA-231 breast carcinoma cells that express elevated levels of Cav1 and caveolae, Egr1 regulated Cav1, and cavin-1 promoter activity was dependent on actin, Cav1, Src, and Rho-associated kinase as well as downstream protein kinase C (PKC) signaling. pCav1 is therefore a mechanotransducer that acts via PKC to relieve Egr1 transcriptional inhibition of Cav1 and cavin-1, defining a novel feedback regulatory loop to regulate caveola biogenesis

Breaking the symmetry of a circular system of coupled harmonic oscillators

First we compute the natural frequencies of vibration of four identical particles coupled by ideal, massless harmonic springs. The four particles are constrained to move on a fixed circle. The initial computations are simplified by a transformation to symmetry coordinates. Then the symmetry of the vibrating system is broken by changing the mass of a single particle by a very small amount. We observe the effect of applying the symmetry transformation to the now slightly nonsymmetric system. We compute the new frequencies and compare them with the frequencies of the original symmetric system of oscillators. Results of similar calculations for 2,3,5, and 6 particles are given

Characterization of Na+-permeable cation channels in LLC-PK1 renal epithelial cells

In this study, the presence of Na+-permeable cation channels was determined and characterized in LLC-PK1 cells, a renal tubular epithelial cell line with proximal tubule characteristics derived from pig kidney. Patch-clamp analysis under cell-attached conditions indicated the presence of spontaneously active Na+-permeable cation channels. The channels displayed nonrectifying single channel conductance of 11 pS, substates, and an ∼3:1 Na+/K+ permeability-selectivity ratio. The Na+-permeable cation channels were inhibited by pertussis toxin and reactivated by G protein agonists. Cation channel activity was observed in quiescent cell-attached patches after vasopressin stimulation. The addition of protein kinase A and ATP to excised patches also induced Na+ channel activity. Spontaneous and vasopressin-induced Na+ channel activity were inhibited by extracellular amiloride. To begin assessing potential molecular candidates for this cation channel, both reverse transcription-PCR and immunocytochemical analyses were conducted in LLC-PK1 cells. Expression of porcine orthologs of the αENaC and ApxL genes were found in LLC-PK1 cells. The expression of both gene products was confirmed by immunocytochemical analysis. Although αENaC labeling was mostly intracellular, ApxL labeled to both the apical membrane and cytoplasmic compartments of subconfluent LLC-PK1 cells. Vasopressin stimulation had no effect on αENaC immunolabeling but modified the cellular distribution of ApxL, consistent with an increased membrane-associated ApxL. The data indicate that proximal tubular LLC-PK1 renal epithelial cells express amiloride-sensitive, Na+-permeable cation channels, which are regulated by the cAMP pathway, and G proteins. This channel activity may implicate previously reported epithelial channel proteins, although this will require further experimentation. The evidence provides new clues as to potentially relevant Na+ transport mechanisms in the mammalian proximal nephron.Fil: Raychowdhury, Malay K.. Harvard Medical School; Estados Unidos. Massachusetts General Hospital East; Estados UnidosFil: Ibarra, Cristina Adriana. Universidad de Buenos Aires. Facultad de Medicina; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Departamento de Química Analítica y Fisicoquímica. Cátedra de Química General e Inorgánica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Damiano, Alicia Ermelinda. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Departamento de Química Analítica y Fisicoquímica. Cátedra de Química General e Inorgánica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Jackson Jr., George R.. Massachusetts General Hospital East; Estados UnidosFil: Smith, Peter R.. University of Alabama at Birmingahm; Estados UnidosFil: McLaughlin, Margaret. Massachusetts General Hospital East; Estados UnidosFil: Prat, Adriana G.. Massachusetts General Hospital East; Estados Unidos. Universidad de Buenos Aires. Facultad de Medicina; ArgentinaFil: Ausiello, Dennis A.. Harvard Medical School; Estados Unidos. Massachusetts General Hospital East; Estados UnidosFil: Lader, Alan S.. Harvard Medical School; Estados Unidos. Massachusetts General Hospital East; Estados UnidosFil: Cantiello, Horacio Fabio. Massachusetts General Hospital East; Estados Unidos. Harvard Medical School; Estados Unidos. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Departamento de Química Analítica y Fisicoquímica. Cátedra de Química General e Inorgánica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin