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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.07578 |
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Table of Contents:
- We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely tuned irrational rotations, making them difficult to realize on near-term devices. We find that the controlled-$V$ gate, an elementary two-qubit interaction directly implementable on leading hardware, is universal and capable of simulating standard universal gate sets with minimal overhead. Specifically, we use catalytic embeddings to develop a constant-overhead algorithm that simulates standard universal gate sets, including Clifford$+T$ and Clifford$+$Toffoli. We combine this simulation algorithm with existing synthesis results to yield exact and approximate synthesis algorithms for unitaries with and without number-theoretic restrictions. The results highlight how full quantum computational power, complete with algorithms for synthesis and simulation, can emerge from unexpectedly simple ingredients.