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

TL;DR

This paper presents a teleportation-based method to implement multi-controlled Toffoli gates with constant depth, significantly reducing circuit depth for complex quantum operations.

Contribution

It introduces a novel decomposition technique that achieves unit Toffoli depth regardless of control count, with manageable ancilla overhead and distributed entanglement.

Findings

Achieves constant Toffoli depth for MCT gates independent of control number.

Reduces circuit depth in quantum algorithms like adders and quantum memory.

Maintains low Toffoli count compared to existing methods.

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.