129 research outputs found
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 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
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
spatial dimensions and its advantages for classical and quantum
algorithms have thus far been demonstrated in . 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 .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
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
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 SU(N) Casimir operators and are characterized by
complex orthonormal vectors describing the SU(N) group manifold.Comment: 12 pages, 3 figure
Prepotential formulation of SU(3) lattice gauge theory
The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential
harmonic oscillators. This reformulation has enlarged gauge invariance under which the prepotential operators transform
like matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to
be equivalent to the Hilbert space of the prepotential formulation satisfying
certain color invariant Sp(2,R) constraints. The SU(3) irreducible prepotential
operators which solve these Sp(2,R) constraints are used to construct SU(3)
gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge
invariant vertex operators. The electric fields and the link operators are
reconstructed in terms of these SU(3) irreducible prepotential operators. We
show that all the SU(3) Mandelstam constraints become local and take very
simple form within this approach. We also discuss the construction of all
possible linearly independent SU(3) loop states which solve the Mandelstam
constraints. The techniques can be easily generalized to SU(N).Comment: 25 pages, 10 figures, LaTeX, Minor modifications done. Version to
appear in J. Phys. A: Mathematical and General, 43 (2010
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
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