Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- N c Expansion

Ciavarella, Anthony N.; Bauer, Christian W.

doi:10.1103/PhysRevLett.133.111901

Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- $N_{c}$ Expansion

Journal Article · Mon Sep 09 00:00:00 EDT 2024 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.133.111901· OSTI ID:2440129

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Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we show how the Hilbert space and interactions can be expanded in inverse powers of $N_{c}$ . At leading order in this expansion, the Hamiltonian simplifies dramatically, both in the required size of the Hilbert space as well as the type of interactions involved. Adding a truncation of the resulting Hilbert space in terms of local energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits. This formulation allows a simulation of the real time dynamics of a SU(3) lattice gauge theory on a $5 \times 5$ and $8 \times 8$ lattice on ibm_torino with a CNOT depth of 113.

Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-05CH11231; AC05-00OR22725

OSTI ID:: 2440129

Alternate ID(s):: OSTI ID: 2504271

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 11 Vol. 133; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- $N_{c}$ Expansion