Qu8its for Quantum Simulations of Lattice Quantum Chromodynamics

Qu8its for Quantum Simulations of Lattice Quantum Chromodynamics

July 17, 2024 | Marc Illa, Caroline E. P. Robin, and Martin J. Savage
This paper explores the use of d=8 qudits, or qu8its, for simulating the dynamics of 1+1D SU(3) lattice quantum chromodynamics (QCD). The authors propose a mapping of quarks and antiquarks to qu8its, which allows for more efficient time evolution and reduces the number of entangling gates required compared to qubit-based simulations. The qu8it representation enables a more compact description of the quantum states, with each quark flavor mapped to three qubits, and each antiquark flavor mapped to another qu8it. This approach significantly reduces the number of two-qudit entangling gates needed for time evolution, by a factor of more than five, compared to qubit-based simulations. The authors also demonstrate that the use of qu8its can lead to more efficient quantum circuits and lower circuit depths, which is crucial for achieving high-fidelity quantum simulations. The paper provides a detailed analysis of the Kogut-Susskind Hamiltonian for QCD, and shows how it can be mapped to qu8its, with a focus on the kinetic, mass, and chromo-electric terms. The authors also discuss the implications of using qu8its for quantum simulations of QCD, including the potential for improved performance on emerging quantum hardware. The results suggest that qu8its could provide a significant advantage in simulating non-Abelian lattice gauge theories, particularly in terms of gate count and circuit depth. The paper concludes with a discussion of the broader implications of using qudits for quantum simulations, including the potential for more efficient simulations of quantum field theories in higher dimensions.This paper explores the use of d=8 qudits, or qu8its, for simulating the dynamics of 1+1D SU(3) lattice quantum chromodynamics (QCD). The authors propose a mapping of quarks and antiquarks to qu8its, which allows for more efficient time evolution and reduces the number of entangling gates required compared to qubit-based simulations. The qu8it representation enables a more compact description of the quantum states, with each quark flavor mapped to three qubits, and each antiquark flavor mapped to another qu8it. This approach significantly reduces the number of two-qudit entangling gates needed for time evolution, by a factor of more than five, compared to qubit-based simulations. The authors also demonstrate that the use of qu8its can lead to more efficient quantum circuits and lower circuit depths, which is crucial for achieving high-fidelity quantum simulations. The paper provides a detailed analysis of the Kogut-Susskind Hamiltonian for QCD, and shows how it can be mapped to qu8its, with a focus on the kinetic, mass, and chromo-electric terms. The authors also discuss the implications of using qu8its for quantum simulations of QCD, including the potential for improved performance on emerging quantum hardware. The results suggest that qu8its could provide a significant advantage in simulating non-Abelian lattice gauge theories, particularly in terms of gate count and circuit depth. The paper concludes with a discussion of the broader implications of using qudits for quantum simulations, including the potential for more efficient simulations of quantum field theories in higher dimensions.
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