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

• URL: http://arxiv.org/abs/2402.10265v4
• Date: Mon, 26 Aug 2024 20:57:20 GMT
• Title: Quantum Simulation of SU(3) Lattice Yang Mills Theory at Leading Order in Large N
• Authors: Anthony N. Ciavarella, Christian W. Bauer,
• Abstract summary: We show how the Hilbert space and interactions can be expanded in inverse powers of N_c. 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 5x5 and 8x8 lattice on ibm_torino with a CNOT depth of 113.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 5x5 and 8x8 lattice on ibm_torino with a CNOT depth of 113.

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