Simplifying quantum logic using higher-dimensional Hilbert spaces

By B. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, Timothy C. Ralph, Kevin J. Resch, G. Pryde, Jeremy Lloyd O'Brien, A. Gilchrist, A. White. 2009

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Realization of a Quantum Integer-Spin Chain with Controllable Interactions (2014, methodology): “By adiabatically ramping a global field, we produce ground states of the XY model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase.”
Photonic quantum information processing: A concise review (2019, methodology): “271).”
Qudits and High-Dimensional Quantum Computing (2020, background): “In a qubit system, Toffoli gate is a three-qubit gate that flips the logical state of the target qubit conditional on the logical states of the two control qubits [64].”
Implementation of a Toffoli gate with superconducting circuits (2011, methodology): “The Toffoli gate has been implemented in nuclear magnetic resonance [3], linear optics [8] and ion trap systems [9].”
A universal qudit quantum processor with trapped ions (2021, background): “Using auxiliary levels as a cache memory for quantum information has enabled the implementation of highly complex quantum algorithms [8] and dissipative processes [1], as well as improved decomposition of multi-qubit gates [6].”