Measurement-Driven Adaptive Low-Overhead Implementation of Multi-Controlled Toffoli Gates

TL;DR

This paper introduces adaptive, measurement-driven techniques for implementing multi-controlled Toffoli gates that significantly reduce resource overhead while maintaining fault-tolerance, leveraging dynamic circuit capabilities.

Contribution

It presents novel dynamic decomposition strategies that exploit adaptive execution and ancilla assistance to optimize multi-controlled Toffoli gate implementation.

Findings

Reduces entangling-gate count, T-count, and T-depth compared to static methods.

Uses measurement-conditioned corrections for scalable, resource-efficient circuits.

Demonstrates improved depth and resource efficiency through analytical and experimental evaluation.

Abstract

The Toffoli gate is a fundamental building block for quantum arithmetic and reversible logic, yet its efficient realization remains a major challenge in both near-term and fault-tolerant quantum architectures. Recent advances in dynamic quantum circuit capabilities, including mid-circuit measurement and classical feedforward, provide new opportunities for reducing the resource overhead of non-Clifford operations. In this work, we propose a set of dynamic decomposition strategies for multi-controlled Toffoli gates that exploit adaptive circuit execution and ancilla-assisted constructions. Our methods systematically reduce entangling-gate count, T-count, and T-depth compared with conventional static decompositions, while preserving fault-tolerance guarantees. Through analytical cost models and experimental evaluation, we demonstrate that relative-phase primitives and measurement-conditioned corrections enable scalable implementations with improved depth and resource efficiency.