The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates

Oliver Reardon-Smith

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arXiv · 2407.20934

The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates

Oliver Reardon-Smith

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Abstract

The Fermionic linear optical (FLO) extent is a quantity that serves two roles, firstly it serves as a measure of the "quantumness" (or non-classicality) of quantum circuits. Secondly it controls the runtime of a class of classical simulation algorithms, which are state-of-the-art for simulating quantum circuits formed mostly of FLO unitaries and promoted to universality by the addition of ``magic states''. It is therefore interesting to understand the scaling behaviour of the extent as magic states are added to a circuit. In this work we solve this problem for the case of $4$-qubit parity eigenstates. We show that the FLO extent of a tensor product of any pure state and a $4$ qubit parity eigenstate is the product of the extents of the two tensor factors. Applying this result recursively one proves a conjecture that the extent is multiplicative for arbitrary tensor products of $4$ qubit magic states.

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Oliver Reardon-Smith. 2024-07-30. The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates. https://arxiv.org/abs/2407.20934

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