Table 1 Resources for a Suzuki–Trotter step

From: A universal framework for the quantum simulation of Yang–Mills theory

 

Number of qubits

# T gates in \(V(\hat{x})\) term

# T gates in \({\hat{p}}^{2}\) term

Scalar QFT

VlatticeQ

\({V}_{{{\rm{lattice}}}}\left(\begin{array}{c}Q\\ 4\end{array}\right)\)

VlatticeQ(Q − 1)

Matrix Model

dN2Q

d(d − 1)N4Q4

dN2Q(Q − 1)

Orbifold YM

2dN2VlatticeQ

d2VlatticeN4Q4

N2dVlatticeQ(Q − 1)

  1. The table summarizes qubit counts and T gate counts for Hamiltonian time evolution of the considered theories, which share the universal Hamiltonian form. Detailed derivations are provided in the section “Resource estimate for Suzuki–Trotter time evolution”.
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