Quantum Stabilizer Codes Embedding Qubits Into Qudits

Abstract

We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to protect the qubit against both amplitude and phase errors. The performance of such code is evaluated on Weyl channels by means of the entanglement fidelity as function of the error probability. A comparison with standard block codes, like five and seven qubit stabilizer codes, shows its superiority.

15 pages, 2 figures (improved version); accepted for publication in Phys. Rev. A

References in corpus (6)

• Introduction to Quantum Error Correction
• Asymmetric quantum error correction via code conversion
• Minimal qudit code for a qubit in the phase-damping channel
• Error correction optimisation in the presence of X/Z asymmetry
• On Weyl channels being covariant with respect to the maximum commutative group of unitaries
• Asymmetric and Symmetric Subsystem BCH Codes and Beyond

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• Counteracting dephasing in Molecular Nanomagnets by optimized qudit encodings
• Quantum error correction codes and absolutely maximally entangled states
• Geometric Algebra and Information Geometry for Quantum Computational Software
• Quantum error-correcting code for ternary logic
• Fault-Tolerant Computing with Single Qudit Encoding
• An Algebraic-Geometric Characterization of Tripartite Entanglement
• High-dimensional quantum state transfer in a noisy network environment
• Platonic dynamical decoupling sequences for interacting spin systems
• Stabilizer codes for Open Quantum Systems
• Dephasing-tolerant quantum sensing for transverse magnetic fields with spin qudits
• Mitigating decoherence in molecular spin qudits
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• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Persistent Tensors and Multiqudit Entanglement Transformation
• High cooperativity coupling to nuclear spins on a circuit QED architecture
• Classifying Entanglement by Algebraic Geometry
• Nonlinear quantum error correction
• Geometric Graph-Theoretic Aspects of Quantum Stabilizer Codes
• A simple comparative analysis of exact and approximate quantum error correction