Minimum Toffoli depth for the multi-controlled Toffoli gate via teleportation

• URL: http://arxiv.org/abs/2604.25861v1
• Date: Tue, 28 Apr 2026 16:58:57 GMT
• Title: Minimum Toffoli depth for the multi-controlled Toffoli gate via teleportation
• Abstract summary: We introduce a teleportation-based decomposition that implements an arbitrary MCT gate with unit Toffoli depth, independent of the number of controls.<n>This is achieved at the cost of a linear overhead in ancilla qubits and the ability to distribute entangled pairs across distant qubits.
• Score: 2.125587952284545
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The decomposition of complex quantum operations into experimentally feasible gate sets has been a central challenge since the early development of quantum computing. The multi-controlled Toffoli (MCT) gate is a key example, with applications across a wide range of quantum algorithms, whose decomposition into smaller gates, however, typically leads to deep circuits. In this work, we introduce a teleportation-based decomposition that implements an arbitrary MCT gate with unit Toffoli depth, independent of the number of controls, while maintaining a relatively low Toffoli count compared to existing approaches. This is achieved at the cost of a linear overhead in ancilla qubits and the ability to distribute entangled pairs across distant qubits, a capability already available in several quantum computing platforms. We further demonstrate the advantages of this implementation in circuits that rely on MCT gates, such as the adder operator, quantum read-only memory, quantum neurons, and quantum decision trees.

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