Minimal entanglement for injecting diagonal gates

Fuente: arXiv
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Main Authors: Kliuchnikov, Vadym, Schoute, Eddie
Format: Preprint
Published: 2024
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author Kliuchnikov, Vadym
Schoute, Eddie
author_facet Kliuchnikov, Vadym
Schoute, Eddie
contents Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then be consumed by a stabilizer circuit to implement non-Clifford operations. We show that the connectivity between the computational space and magic state factories forms a fundamental bottleneck on the rate at which non-Clifford operations can be implemented. We show that the nullity of the magic state, $ν(|D\rangle)$ for diagonal gate $D$, characterizes the non-local resources required to implement $D$ in the computational space. As part of our proof, we construct local stabilizer circuits that use only $ν(|D\rangle)$ ebits to implement $D$ in the computational space that may be useful to reduce the non-local resources required to inject non-Clifford gates. Another consequence is that the edge-disjoint path compilation algorithm [arXiv:2110.11493] produces minimum-depth circuits for implementing single-qubit diagonal gates.
format Preprint
id arxiv_https___arxiv_org_abs_2403_18900
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Minimal entanglement for injecting diagonal gates
Kliuchnikov, Vadym
Schoute, Eddie
Quantum Physics
Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then be consumed by a stabilizer circuit to implement non-Clifford operations. We show that the connectivity between the computational space and magic state factories forms a fundamental bottleneck on the rate at which non-Clifford operations can be implemented. We show that the nullity of the magic state, $ν(|D\rangle)$ for diagonal gate $D$, characterizes the non-local resources required to implement $D$ in the computational space. As part of our proof, we construct local stabilizer circuits that use only $ν(|D\rangle)$ ebits to implement $D$ in the computational space that may be useful to reduce the non-local resources required to inject non-Clifford gates. Another consequence is that the edge-disjoint path compilation algorithm [arXiv:2110.11493] produces minimum-depth circuits for implementing single-qubit diagonal gates.
title Minimal entanglement for injecting diagonal gates
topic Quantum Physics
url https://arxiv.org/abs/2403.18900