dorsal/arxiv
View SchemaSimulating lattice gauge theories on a quantum computer
| Authors | Tim Byrnes, Yoshihisa Yamamoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510027 |
| URL | https://arxiv.org/abs/quant-ph/0510027 |
| DOI | 10.1103/PhysRevA.73.022328 |
| Journal | Phys.Rev. A73 (2006) 022328 |
Abstract
We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.
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"abstract": "We examine the problem of simulating lattice gauge theories on a universal\nquantum computer. The basic strategy of our approach is to transcribe lattice\ngauge theories in the Hamiltonian formulation into a Hamiltonian involving only\nPauli spin operators such that the simulation can be performed on a quantum\ncomputer using only one and two qubit manipulations. We examine three models,\nthe U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a\nspin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the\nlattice. The number of qubits required for storing a particular state is found\nto have a linear dependence with the total number of lattice sites. The number\nof qubit operations required for performing the time evolution corresponding to\nthe Hamiltonian is found to be between a linear to quadratic function of the\nnumber of lattice sites, depending on the arrangement of qubits in the quantum\ncomputer. We remark that our results may also be easily generalized to higher\nSU(N) gauge theories.",
"arxiv_id": "quant-ph/0510027",
"authors": [
"Tim Byrnes",
"Yoshihisa Yamamoto"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.022328",
"journal_ref": "Phys.Rev. A73 (2006) 022328",
"title": "Simulating lattice gauge theories on a quantum computer",
"url": "https://arxiv.org/abs/quant-ph/0510027"
},
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