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Quantum codes for quantum simulation of fermions on a square lattice of qubits

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Figure

FIG. 1. Visualizing an auxiliary qubit mapping (AQM) as a con- con-catenation of the Jordan-Wigner transform and a particular quantum code
TABLE I. All fermion-to-qubit mappings discussed in this work. We consider a N = ( 1 ×  2 ) square lattice block of fermionic modes, and compare the number of auxiliary qubits, or more generally the total number of qubits minus N
FIG. 2. Simulation of Pauli strings in a system with limited connectivity. (a) Qubit connectivity graph: the vertices are qubits
FIG. 3. Skipping several qubits in a CNOT -chain. Here we consider the effect of the circuits on a computational basis state (
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