Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers

TL;DR

This paper establishes a lower bound on the number of qubits needed to represent collections of equivalent Pauli operators and provides a method to find minimal register representations, aiding quantum simulation and error correction.

Contribution

It introduces a new lower bound for minimal register size and a procedure to transform collections of Pauli operators into equivalent minimal-register forms.

Findings

Derived a lower bound for qubits needed in Pauli operator representations

Provided a systematic procedure for minimal register transformation

Applicable to quantum algorithms and error-correcting codes

Abstract

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 non-local 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 and provide a procedure for determining such a set of minimal register Pauli operations.