Search for Efficient Formulations for Hamiltonian Simulation of
non-Abelian Lattice Gauge Theories
- URL: http://arxiv.org/abs/2009.11802v1
- Date: Thu, 24 Sep 2020 16:44:39 GMT
- Title: Search for Efficient Formulations for Hamiltonian Simulation of
non-Abelian Lattice Gauge Theories
- Authors: Zohreh Davoudi, Indrakshi Raychowdhury, Andrew Shaw
- Abstract summary: Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation.
It remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories.
This paper is a first step toward addressing this question in the case of non-Abelian LGTs.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural
framework for the purpose of quantum simulation, an area of research that is
growing with advances in quantum-computing algorithms and hardware. It,
therefore, remains an important task to identify the most accurate, while
computationally economic, Hamiltonian formulation(s) in such theories,
considering the necessary truncation imposed on the Hilbert space of gauge
bosons with any finite computing resources. This paper is a first step toward
addressing this question in the case of non-Abelian LGTs, which further require
the imposition of non-Abelian Gauss's laws on the Hilbert space, introducing
additional computational complexity. Focusing on the case of SU(2) LGT in 1+1 D
coupled to matter, a number of different formulations of the original
Kogut-Susskind framework are analyzed with regard to the dependence of the
dimension of the physical Hilbert space on boundary conditions, system's size,
and the cutoff on the excitations of gauge bosons. The impact of such
dependencies on the accuracy of the spectrum and dynamics is examined, and the
(classical) computational-resource requirements given these considerations are
studied. Besides the well-known angular-momentum formulation of the theory, the
cases of purely fermionic and purely bosonic formulations (with open boundary
conditions), and the Loop-String-Hadron formulation are analyzed, along with a
brief discussion of a Quantum Link Model of the same theory. Clear advantages
are found in working with the Loop-String-Hadron framework which implements
non-Abelian Gauss's laws a priori using a complete set of gauge-invariant
operators. Although small lattices are studied in the numerical analysis of
this work, and only the simplest algorithms are considered, a range of
conclusions will be applicable to larger systems and potentially to higher
dimensions.
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