Minimal entanglement for injecting diagonal gates

• URL: http://arxiv.org/abs/2403.18900v1
• Date: Wed, 27 Mar 2024 18:00:03 GMT
• Title: Minimal entanglement for injecting diagonal gates
• Authors: Vadym Kliuchnikov, Eddie Schoute,
• Abstract summary: 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 construct local stabilizer circuits that use only $nu(|Drangle)$ ebits to implement $D$ in the computational space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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, $\nu(|D\rangle)$ 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 $\nu(|D\rangle)$ 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.

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