Efficient classical simulation of quantum computation beyond Wigner positivity

TL;DR

This paper extends classical simulation techniques for quantum computation to odd-prime-dimensional qudits by generalizing the CNC formalism, enabling efficient simulation of a broader class of quantum circuits beyond stabilizer and Wigner function methods.

Contribution

The authors develop a new CNC-type phase space representation for odd-prime-dimensional qudits that preserves positivity under measurements and includes nonnegative Wigner functions as a subset.

Findings

Broader class of quantum circuits can be efficiently simulated classically.

New quasiprobability representation is covariant with the Clifford group.

Positivity-preserving under Pauli measurements.

Abstract

We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a quasiprobability representation for quantum computation which is covariant with respect to the Clifford group and positivity preserving under Pauli measurements, and whose nonnegative sector strictly contains the subtheory of quantum theory described by nonnegative Wigner functions. This allows for a broader class of magic state quantum circuits to be efficiently classically simulated than those covered by the stabilizer formalism and Wigner function methods.