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Quantum Simulation of QCD in Axial Gauge · arXivDesk

2608.16783Aug 17, 202631 pages

Quantum Simulation of QCD in Axial Gauge

Xiaojun Yao

Lattice Phenomenology Theory Nuclear Theory Quantum Physics

Abstract

We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in $3+1$ dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees of freedom and a lattice regulated Green's function. The axial gauge condition is trivially maintained in time evolution, even under Trotterization. The gauge field degrees of freedom are expressed in the local field basis and can be efficiently transformed into the canonical conjugate momentum basis by local quantum Fourier transforms. We prove the number of qubits needed for describing all states up to an energy $E$ with an accuracy $ε$ on a lattice of volume $V$ at bare coupling

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g

is bounded as

16n_A V + 12n_f V

, where

n_A \approx \log_2 (\frac{64 E' V^{4/3}}{π^2ε} + \frac{32\sqrt{2}g n_f E'^{1/2} V^{7/6}}{\sqrt{3}π^3ε^{1/2}} )

is the number of qubits needed for each independent gauge field per site with a shifted energy

E'

, and

n_f

denotes the number of fermion flavors. We then analyze a quantum algorithm for time evolution that is based on Trotterization, quantum Fourier transform, and Jordan-Wigner transformation, for which quantum circuits can be explicitly constructed under arbitrary gauge field truncation and digitization. We find the numbers of CNOT and single-qubit rotation gates both scale as

O(n_A^4 V^{4/3}) + O(V^{5/3})

per Trotter step for fixed

n_f\leq 6

. We conclude that quantum resources needed for simulating real-time dynamics of lattice QCD scale polynomially with volume, energy, time, accuracy, and bare Hamiltonian parameters.

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