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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2407.20934 |
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| _version_ | 1866913452802441216 |
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| author | Reardon-Smith, Oliver |
| author_facet | Reardon-Smith, Oliver |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates Reardon-Smith, Oliver Quantum Physics 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. |
| title | The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.20934 |