Generalized Toffoli gates using qudit catalysis

TL;DR

This paper introduces quantum networks that implement generalized Toffoli gates using a qudit ancilla as a catalyst, minimizing two-body interactions and applicable to quantum algorithms and error correction.

Contribution

It presents a new method for constructing controlled gates with qudit catalysis, reducing the number of two-particle gates needed for multi-qubit operations.

Findings

Minimum two-particle gates for n-qubit controlled gates

Implementation via dispersive Jaynes-Cummings Hamiltonian

Applicable to quantum algorithms and error correction

Abstract

We present quantum networks for a n-qubit controlled gate C^{n-1}(U) which use a higher dimensional (qudit) ancilla as a catalyser. In its simplest form the network has only n two-particle gates (qubit-qudit) -- this is the minimum number of two-body interactions needed to couple all n+1 subsystems (n qubits plus one ancilla). This class of controlled gates includes the generalised Toffoli gate C^{n-1}(X) on n qubits, which plays an important role in several quantum algorithms and error correction. A particular example implementing this model is given by the dispersive limit of a generalised Jaynes-Cummings Hamiltonian of an effective spin-s interacting with a cavity mode.