Abstract
Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity, simplification of the experimental setup and enhancement of the algorithm efficiency. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. We first discuss the qudit gate universality and a variety of qudit gates including the pi/8 gate, the SWAP gate, and the multi-level controlled-gate. We then present the qudit version of several representative quantum algorithms including the Deutsch-Jozsa algorithm, the quantum Fourier transform, and the phase estimation algorithm. Finally we discuss various physical realizations for qudit computation such as the photonic platform, iron trap, and nuclear magnetic resonance.
Highlights
Qudit technology, with a qudit being a quantum version of d-ary digits for d > 2 [23]; is emerging as an alternative to qubit for quantum computation and quantum information science
The qudit nature of so-called superconduting qubits, i.e., the higher-dimensional aspects of the objects serving as qubits, is not just a negative feature manifesting as leakage error; remarkable two-qubit gate performance is achieved by exploiting adiabatic evolution involving avoided crossings with higher levels [10, 110] with this exploitation for fast, high-fidelity quantum gates extendable to three-qubit gates and beyond by exploiting intermediate qudit dynamics and avoided level crossings [160, 161]
6.1 Summary of the Advantages of Qudit Systems Compared to Qubit Systems
Summary
With a qudit being a quantum version of d-ary digits for d > 2 [23]; is emerging as an alternative to qubit for quantum computation and quantum information science. Due to its multilevel nature, qudit provides a larger state space to store and process information and the ability to do multiple control operations simultaneously [106] These features play an important role in the reduction of the circuit complexity, the simplification of the experimental setup and the enhancement of the algorithm efficiency [100, 106, 108, 109].
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