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Efficient implementation of multicontrolled quantum gates

Ben Zindorf* and Sougato Bose

  • *Contact author: ben.zindorf.19@ucl.ac.uk
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Phys. Rev. Applied 24, 044030 – Published 9 October, 2025

DOI: https://doi.org/10.1103/8blx-nfcr

Abstract

We present an implementation of multicontrolled (mc) quantum gates that provides significant reductions of cost compared to state-of-the-art methods. The operator applied on the target qubit is a unitary, special unitary, or the Pauli X operator (multicontrolled Toffoli), and requires one clean ancilla, no ancilla, or one dirty ancilla, respectively. We generalize our methods for any number of target qubits, and provide further cost reductions if additional ancilla qubits are available. For each type of mc gate, we provide implementations for unrestricted (all-to-all) connectivity and for linear-nearest-neighbor (LNN) connectivity. All of the methods use a linear cost of gates from the Clifford+T (fault-tolerant) set. In the context of LNN architecture, the cost and depth of our circuits scale linearly irrespective of the position of the qubits on which the gate is applied. Our methods directly improve the compilation process of many quantum algorithms, providing optimized circuits. Given the scale of our improvements, for example, the quadratic-to-linear controlled-not count for LNN, they will naturally result in a large reduction of errors.

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Phys. Rev. Applied 24, 044030– Published 9 October, 2025
  • Received 21 August 2024
  • Revised 11 September 2025
  • Accepted 15 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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