Transforming collections of Pauli operators into equivalent collections of Pauli operators over minimal registers

Transformations which convert between fermionic modes and qubit operations have become a ubiquitous tool in quantum algorithms for simulating systems. Similarly, collections of Pauli operators might be obtained from solutions of nonlocal games and satisfiability problems. Drawing on ideas from entanglement-assisted quantum error-correcting codes and quantum convolutional codes, we prove the obtainable lower bound for the number of qubits needed to represent such Pauli operations which are equivalent to the initial ones and provide a procedure for determining such a set of minimal register Pauli operations.

Automated summary

Transformations between fermionic modes and qubit operations are widely used in quantum algorithms for system simulation. Collections of Pauli operators can be obtained from nonlocal games and satisfiability problems. Building on concepts from entanglement-assisted quantum error-correcting codes and quantum convolutional codes, we prove the lower bound for the number of qubits required to represent equivalent Pauli operations and provide a method for determining minimal register Pauli operations.