Qudits and high-dimensional quantum computing

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.

This is a review article. This version is the final published version

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Cited by in corpus (230)

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• Universal quantum multi-qubit entangling gates with auxiliary spaces
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• Variational quantum simulation of U(1) lattice gauge theories with qudit systems
• FEqa: Finite Element Computations on Quantum Annealers
• Asymptotically Improved Circuit for $d$-ary Grover's Algorithm with Advanced Decomposition of $n$-qudit Toffoli Gate
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• Visualizing Entanglement in multi-Qubit Systems
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• Construction of efficient Schmidt number witnesses for high-dimensional quantum states
• Realizing nonadiabatic holonomic quantum computation beyond the three-level setting
• Data re-uploading with a single qudit
• Crosstalk-Robust Quantum Control in Multimode Bosonic Systems
• Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors
• On the role of entanglement in qudit-based circuit compression
• Qutrit and Qubit Circuits for Three-Flavor Collective Neutrino Oscillations
• Deterministic generation of qudit photonic graph states from quantum emitters
• Programmable quantum circuits in a large-scale photonic waveguide array
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• Robust Macroscopic Schrödinger's Cat on a Nucleus
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts
• Resonant Multilevel Amplitude Damping Channels
• Hyperfine spectroscopy and fast, all-optical arbitrary state initialization and readout of a single, ten-level ${}^{73}$Ge vacancy nuclear spin qudit in diamond
• $q$-analog qudit Dicke states
• Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit
• Dancing the Quantum Waltz: Compiling Three-Qubit Gates on Four Level Architectures
• Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus
• A hybrid-qudit representation of digital RGB images
• Quasienergy operators and generalized squeezed states for systems of trapped ions
• Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits
• Programmable photonic time circuits for highly scalable universal unitaries
• Qudit States in Noisy Quantum Channels
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• Implementation of Shor's Algorithm with a Single Photon in 32 Dimensions
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• Synthetic high angular momentum spin dynamics in a microwave oscillator
• Noise-adapted qudit codes for amplitude-damping noise
• The noisy Werner-Holevo channel and its properties
• Building Qutrit Diagonal Gates from Phase Gadgets
• High-dimensional maximally entangled photon pairs in parametric down-conversion
• Degenerate Local-dimension-invariant Stabilizer Codes and an Alternative Bound for the Distance Preservation Condition
• Pre-detection squeezing as a resource for high-dimensional Bell-state measurements
• Heralding Higher-Dimensional Bell and Greenberger-Horne-Zeilinger States Using Multiport Splitters
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• Weyl channels for multipartite systems
• Scaling W state circuits in the qudit Clifford hierarchy
• Mixed discrete variable Gaussian states
• Robust Quantum Arithmetic Operations with Intermediate Qutrits in the NISQ-era
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• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Bipartite Bound Entanglement
• Outcome determinism in measurement-based quantum computation with qudits
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• Qudit vs. Qubit: Simulated performance of error correction codes in higher dimensions
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• Generation of C-NOT, SWAP, and C-Z Gates for Two Qubits Using Coherent and Incoherent Controls and Stochastic Optimization
• Synthesis and Arithmetic of Single Qutrit Circuits
• The Complexity of Being Entangled
• Multi-Valued Quantum Neurons
• Complete ZX-calculi for the stabiliser fragment in odd prime dimensions
• Dissipative phase transition: from qubits to qudits
• Simulating electronic structure on bosonic quantum computers
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Extension of the Morris-Shore transformation to arbitrary time-dependent driving fields
• Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories
• N-qubit universal quantum logic with a photonic qudit and O(N) linear optics elements
• Efficient fidelity estimation: Alternative derivation and related applications
• Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits
• Absolute dimensionality of quantum ensembles
• Experimental simulation of quantum superchannels
• Monitoring the energy of a cavity by observing the emission of a repeatedly excited qubit
• Barren plateaus are amplified by the dimension of qudits
• Classifying Entanglement by Algebraic Geometry
• Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability
• Persistent Tensors and Multiqudit Entanglement Transformation
• Engineering of Anyons on M5-Probes via Flux Quantization
• Unitary Transformations using Robust Optimal Control on a Cold Atom Qudit
• Two-local modifications of SYK model with quantum chaos
• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures
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• Quantum generative modeling for financial time series with temporal correlations
• Engineering of maximally entangled orbital angular momentum states via path identity
• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
• Qudit low-density parity-check codes
• Experimental Demonstration of Swift Analytical Universal Control over Nearby Transitions
• SU(2) hyper-clocks: quantum engineering of spinor interferences for time and frequency metrology
• A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
• Self-guided tomography of time-frequency qudits
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• Finite-Function-Encoding Quantum States
• Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications
• Measurement-based quantum computing with qudit stabilizer states
• Nonlinearity of the Fidelity in Open Qudit Systems: Gate and Noise Dependence in High-dimensional Quantum Computing
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
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• Heralded High-Dimensional Photon-Photon Quantum Gate
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• Honest-binding quantum bit commitment from separable operations
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• Simple ways of preparing qudit Dicke states
• Single photonic qutrit in a collective Rydberg polariton
• Symmetry-enhanced Counterdiabatic Quantum Algorithm for Qudits
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• On The Stabilizer Formalism And Its Generalization
• Robust Quantum Circuit for Clique Problem with Intermediate Qudits
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• Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
• Encoder Circuit Optimization for Non-Binary Quantum Error Correction Codes in Prime Dimensions: An Algorithmic Framework
• Gaussian Amplitude Amplification for Quantum Pathfinding
• Quantum dynamics of spin-J particles in static and rotating magnetic fields: Entanglement resonances and kinks
• Sum rule for non-adiabatic geometric phases
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• Arbitrary high-dimensional entanglement purification with the superposition of paths
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Quantum computational resources for lattice QCD in the strong-coupling limit
• Qudit-native measurement protocol for dynamical correlations using Hadamard tests
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• Parafermionic representation of Potts-based cluster chain
• Obscure qubits and membership amplitudes
• Creating two-qudit maximally entangled quantum link through bulk
• Assessing the feasibility of quantum learning algorithms for noisy linear problems
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• Spin-$s$ $U(1)$-eigenstate preparation
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• Qudit encoding in Rydberg blockaded arrays of atoms
• Conditions for Time-Independence of N-level Systems under the Rotating Wave Approximation (RWA) and Dipole Selection Rules
• Linear Optical Schemes to Postselect High-Dimensional Dicke States
• Synthesis of Single Qutrit Circuits from Clifford+R
• CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems
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• Congestion-free routing on quantum chips
• Physically motivated decompositions of single-qutrit gates
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• Constructing all qutrit controlled Clifford+T gates in Clifford+T
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
• Time-inhomogeneous Quantum Markov Chains with Decoherence on Finite State Spaces
• Entanglement swapping for partially entangled qudits and the role of quantum complementarity
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