Contextuality bounds the efficiency of classical simulation of quantum processes

TL;DR

This paper establishes that contextuality imposes a lower bound on the classical memory needed to simulate quantum processes, with the bound scaling quadratically for qubit stabilizer sub-theories, highlighting its role as a computational resource.

Contribution

It provides a quantitative link between contextuality and classical simulation complexity, specifically showing the memory bounds for simulating quantum sub-theories.

Findings

Contextuality requires quadratic classical memory scaling for multi-qubit systems.

In the qubit stabilizer sub-theory, classical simulation memory scales quadratically with qubits.

Qudit systems can be simulated with linear memory scaling, unlike qubits.

Abstract

Contextuality has been conjectured to be a super-classical resource for quantum computation, analogous to the role of non-locality as a super-classical resource for communication. We show that the presence of contextuality places a lower bound on the amount of classical memory required to simulate any quantum sub-theory, thereby establishing a quantitative connection between contextuality and classical simulability. We apply our result to the qubit stabilizer sub-theory, where the presence of state-independent contextuality has been an obstacle in establishing contextuality as a quantum computational resource. We find that the presence of contextuality in this sub-theory demands that the minimum number of classical bits of memory required to simulate a multi-qubit system must scale quadratically in the number of qubits; notably, this is the same scaling as the Gottesman-Knill algorithm. We contrast this result with the (non-contextual) qudit case, where linear scaling is possible.