Qutrit Magic State Distillation

Abstract

Magic state distillation (MSD) is a purification protocol that plays a central role in fault tolerant quantum computation. Repeated iteration of the steps of a MSD protocol, generates pure single non-stabilizer states, or magic states, from multiple copies of a mixed resource state using stabilizer operations only. Thus mixed resource states promote the stabilizer operations to full universality. Magic state distillation was introduced for qubit-based quantum computation, but little has been known concerning MSD in higher dimensional qudit-based computation. Here, we describe a general approach for studying MSD in higher dimensions. We use it to investigate the features of a qutrit MSD protocol based on the 5-qutrit stabilizer code. We show that this protocol distills non-stabilizer magic states, and identify two types of states, that are attractors of this iteration map. Finally, we show how these states may be converted, via stabilizer circuits alone, into a state suitable for state injected implementation of a non-Clifford phase gate, enabling non-Clifford unitary computation.

13 pages, 5 figures

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• Implementation of Clifford gates in the Ising-anyon topological quantum computer
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Cited by in corpus (64)

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• Universal quantum computation with weakly integral anyons
• Efficient Decoders for Qudit Topological Codes
• Quantum Computing with Parafermions
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Towards low overhead magic state distillation
• A fast fault-tolerant decoder for qubit and qudit surface codes
• Uniqueness of noncontextual models for stabilizer subtheories
• Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions
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• Pseudomagic Quantum States
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• Qutrit Magic State Distillation Tight in Some Directions
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• Qutrit and Ququint Magic States
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Order 3 Symmetry in the Clifford Hierarchy
• Magic State Distillation with the Ternary Golay Code
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• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits
• Designing the Quantum Channels Induced by Diagonal Gates
• Resource Optimized Quantum Architectures for Surface Code Implementations of Magic-State Distillation
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• Local Dimension Invariant Qudit Stabilizer Codes
• Interplay of entanglement structures and stabilizer entropy in spin models
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• Parafermion stabilizer codes
• Climbing the Diagonal Clifford Hierarchy
• Realisation of Qudits in Coupled Potential Wells
• Building Qutrit Diagonal Gates from Phase Gadgets
• Magic state distillation with punctured polar codes
• Small Codes for Magic State Distillation
• Exact Synthesis of Multiqutrit Clifford-Cyclotomic Circuits
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• Normalizer Circuits and Quantum Computation
• On the Power of Reusable Magic States
• A note on many valued quantum computational logics
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• Low Overhead Qutrit Magic State Distillation
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• Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
• General entropic constraints on CSS codes within magic distillation protocols
• Quantum-Assisted Graph Clustering and Quadratic Unconstrained D-ary Optimisation
• Censorship of quantum resources against catalytic account sharing
• The robustness of magic state distillation against errors in Clifford gates
• Quantifying magic via quantum $(\alpha ,\beta )$ Jensen-Shannon divergence
• Entanglement swapping for partially entangled qudits and the role of quantum complementarity
• Encoder Circuit Optimization for Non-Binary Quantum Error Correction Codes in Prime Dimensions: An Algorithmic Framework
• Transversal AND in Quantum Codes