1,455 research outputs found
Should The U.S. Seriously Contemplate Initiating A Value-Added Tax? What Are Other Countries Doing With This Type Of Tax?
The U. S. Tax System needs extensive changes. As Congress addresses these modifications, should it consider a value-added system? To what extent are other countries using the value-added tax
General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
With a focus on universal quantum computing for quantum simulation, and
through the example of lattice gauge theories, we introduce rather general
quantum algorithms that can efficiently simulate certain classes of
interactions consisting of correlated changes in multiple (bosonic and
fermionic) quantum numbers with non-trivial functional coefficients. In
particular, we analyze diagonalization of Hamiltonian terms using a
singular-value decomposition technique, and discuss how the achieved diagonal
unitaries in the digitized time-evolution operator can be implemented. The
lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions
coupled to one flavor of staggered fermions, for which a complete
quantum-resource analysis within different computational models is presented.
The algorithms are shown to be applicable to higher-dimensional theories as
well as to other Abelian and non-Abelian gauge theories. The example chosen
further demonstrates the importance of adopting efficient theoretical
formulations: it is shown that an explicitly gauge-invariant formulation using
loop, string, and hadron (LSH) degrees of freedom simplifies the algorithms and
lowers the cost compared with the standard formulations based on
angular-momentum as well as the Schwinger-boson degrees of freedom. The LSH
formulation further retains the non-Abelian gauge symmetry despite the
inexactness of the digitized simulation, without the need for costly controlled
operations. Such theoretical and algorithmic considerations are likely to be
essential in quantum simulating other complex theories of relevance to nature.Comment: 59+17+7 pages, 16 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
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
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