Qudits for decomposing multiqubit gates and realizing quantum algorithms

Abstract

The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially interesting in the quantum-mechanical domain. In this Colloquium several ideas are reviewed that indicate how multilevel quantum systems, also known as qudits, can be used for efficient realization of quantum algorithms, which are represented via standard qubit circuits. The focus in the Colloquium is on techniques for leveraging qudits for simplifying decomposition of multiqubit gates and for compressing quantum information by encoding multiple qubits in a single qudit. As discussed in the Colloquium, these approaches can be efficiently combined. This allows a reduction in the number of entangling (two-body) operations and the number of quantum information carriers used compared to straightforward qubit realizations. These theoretical schemes can be implemented with quantum computing platforms of various natures, such as trapped ions, neutral atoms, superconducting junctions, quantum light, spin systems, and molecules. The Colloquium concludes by summarizing a set of open problems whose resolution will be an important further step toward employing universal qudit-based processors for running qubit algorithms.

24 pages, 21 figures

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Cited by in corpus (15)

• Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits
• Demonstration of Discrete-Time Quantum Walks and Observation of Topological Edge States in a Superconducting Qutrit Chain
• Qudit low-density parity-check codes
• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures
• Engineering Non-Gaussian Bosonic Gates through Quantum Signal Processing
• Quantum circuits for simulating neutrino propagation in matter
• Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
• Generalized pulse design in Floquet engineering: Application to interacting spin systems
• A Graphical Calculus for Quantum Computing with Multiple Qudits using Generalized Clifford Algebras
• Efficient circuit compression by multiqudit entangling gates in linear optical quantum computation
• Applying Grover-mixer quantum alternating operator ansatz algorithm to higher-order unconstrained binary optimization problems
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Quantum-optical reset with classical memory
• Scalable platform for qudit-based quantum computing using polar molecules