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arXiv:2602.02344

Large Nc Truncations for SU(Nc) Lattice Yang-Mills Theory with Fermions

Neel S. Modi, Anthony N. Ciavarella, Jad C. Halimeh, Christian W. Bauer

hep-lathep-phquant-phSubmitted Feb 2, 2026• Announced Feb 3, 2026• 0 citations• Revised May 12, 2026 (v2)
v1 · Feb 2, 2026v2 · May 12, 2026
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Abstract

Quantum simulations of quantum chromodynamics (QCD) require a representation of gauge fields and fermions on the finitely many degrees of freedom available on a quantum computer. We introduce a truncation of lattice QCD coupled to staggered fermions that includes (i) a local Krylov truncation that generates allowed basis states; (ii) a maximum allowed electric energy per link; (iii) a limit on the number of fermions per site; and (iv) a truncation in the large N_c scaling of Hamiltonian matrix elements. Explicit truncated Hamiltonians for 1+1D and 2+1D lattices are given, and numerical simulations of string-breaking dynamics are performed.

Comments
37 pages, 33 figures, 5 appendices

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Quantum simulations of quantum chromodynamics (QCD) require a representation of gauge fields and fermions on the finitely many degrees of freedom available on a quantum computer. We introduce a truncation of lattice QCD coupled to staggered fermions that includes (i) a local Krylov truncation that generates allowed basis states; (ii) a maximum allowed electric energy per link; (iii) a limit on the number of fermions per site; and (iv) a truncation in the large N_c scaling of Hamiltonian matrix elements. Explicit truncated Hamiltonians for 1+1D and 2+1D lattices are given, and numerical simulations of string-breaking dynamics are performed.
Quantum simulations of lattice gauge theories offer the potential to directly study the nonperturbative dynamics of quantum chromodynamics, but naive analyses suggest that they require large computational resources. Large N c expansions are performed to order 1 / N c to simplify the Hamiltonian of pure SU ( N c ) lattice gauge theories. A reformulation of the electric basis is introduced with a truncation strategy based on the construction of local Krylov subspaces with plaquette operators. Numerical simulations show that these truncated Hamiltonians are consistent with traditional lattice calculations at relatively small couplings. It is shown that the computational resources required for quantum simulation of time evolution generated by these Hamiltonians is 17–19 orders of magnitude smaller than previous approaches, provided that the truncations in this work can reach lattice spacings in three-dimensional simulations comparable to the two-dimensional simulations performed.
We develop a framework for quantum simulations of lattice SU(NcN_cNc​) gauge theory with quarks. Staggered and Wilson lattice fermions are considered in two and three spatial dimensions and a theta angle is included in three dimensions. The physical, gauge-invariant Hilbert space is formulated in a representation basis, where gauge and fermionic degrees of freedom are encoded by irreducible representations of SU(NcN_cNc​) that tensor at each lattice site to contain a singlet. We discuss algorithms for simulating time evolution on quantum computers and carry out noiseless simulations of lattice quantum chromodynamics (Nc=3N_c=3Nc​=3) on small lattices with up to 32 qubits, showcasing theta angle effects, hadronic states, string dynamics, and a baryon chemical potential for the first time in three spatial dimensions.
Quantum simulations of lattice gauge theories are anticipated to directly probe the real time dynamics of QCD, but scale unfavorably with the required truncation of the gauge fields. Improved Hamiltonians are derived to correct for the effects of gauge field truncations on the SU(3) Kogut-Susskind Hamiltonian. It is shown in 1+1D1+1D1+1D that this enables low chromoelectric field truncations to quantitatively reproduce features of the untruncated theory over a range of couplings and quark masses. In 3+1D3+1D3+1D, an improved Hamiltonian is derived for lattice QCD with staggered massless fermions. It is shown in the strong coupling limit that the spectrum qualitatively reproduces aspects of two flavor QCD and simulations of a small system are performed on IBM's Perth quantum processor.
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 5×5 and 8×8 lattice on ibm_torino with a CNOT depth of 113.
Quantum simulations of lattice gauge theories with continuous gauge groups require a choice of basis (how states of the gauge theory map to the qubit computational basis) and truncation scheme (which of the infinitely many gauge theory basis states should be omitted in the map to the finite dimensional qubit Hilbert space.) The most common choices are adapted to an electric basis for the gauge theory, where the basis states for each link are associated with irreducible representations of the gauge group. Electric bases and truncations are generally advantageous for preserving gauge symmetries and simulating the strong coupling regime, but their effectiveness in the weak coupling regimes of physical interest are less well understood. In this work, we compute relative probabilities p(R′)/p(R)p(R')/p(R)p(R′)/p(R) for finding a link in the irreps R,R′R,R'R,R′ in the ground state of SU(3) lattice gauge theory using Euclidean Monte Carlo methods and weak-coupling lattice perturbation theory. The observables that compute these relative probabilities are constructed by introducing seams into an anisotropic lattice, and by a similar construction we are also able to measure relative probabilities of different site singlets (ways that electric flux braids together into a gauge singlet) at each vertex. With these methods we can quantify, for example, the importance of higher electric flux states in the weak coupling ground state. These results directly inform what truncations are needed to accurately capture non-abelian gauge dynamics near the continuum limit.
A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of the non-perturbative dynamics of QCD. 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. 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 electric energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits to leading order in large N.