All you need is controlled-V: universality of a standard two-qubit gate by catalytic embedding

• URL: http://arxiv.org/abs/2509.07578v2
• Date: Sat, 27 Sep 2025 22:09:58 GMT
• Title: All you need is controlled-V: universality of a standard two-qubit gate by catalytic embedding
• Authors: Robin Kaarsgaard,
• Abstract summary: Gate sets that contain disproportionately powerful instructions obscuring source of quantum computational power.<n>Controlled-$V$ gate, a simple two-qubit interaction, suffices on its own to perform universal quantum universality.<n>Our construction, based on catalytic embedding and a procedure to generate the necessary resource states, simulates standard universal gate sets with constant overhead.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A central pursuit in quantum computing is to identify the minimal resources required to achieve universality. Within the quantum circuit model, this is studied by considering the gate sets that provide the fundamental instructions from which quantum algorithms are built. However, standard gate sets such as Clifford+$T$ contain some instructions that are disproportionately powerful, obscuring the precise source of quantum computational power. While single-gate universal sets are known, these rely on rotation angles that are irrational multiples of $2\pi$, requiring fine-tuned control that is difficult to achieve on quantum hardware today. Here, we show the surprising result that the controlled-$V$ (or controlled-$\sqrt{X}$) gate, a simple two-qubit interaction previously described as "semi-classical" and already widely used in reversible logic synthesis and directly realisable on leading hardware platforms, suffices on its own to perform universal quantum computation. Our construction, based on catalytic embedding and a procedure to generate the necessary resource states, simulates standard universal gate sets with constant overhead, highlighting how the full power of quantum computation can emerge from unexpectedly simple ingredients.

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