Propagation of generalized Pauli errors in qudit Clifford circuits

Abstract

It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum circuits composed of qudit Clifford gates. Our framework is compatible with qudit stabilizer quantum error-correcting codes. We show how the error probability tensor can be applied in the most general case, and we demonstrate an error analysis of bipartite qudit repeaters with quantum error correction. We provide an exact analytical solution of the error statistics of the state distributed by such a repeater. For a fixed number of degrees of freedom, we observe that higher-dimensional qudits can outperform qubits in terms of distributed entanglement.

arXiv comment15 pages, 8 figures

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• Asymptotic Improvements to Quantum Circuits via Qutrits
• Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED
• Resource-Efficient Quantum Computing by Breaking Abstractions
• Controlling error orientation to improve quantum algorithm success rates
• Dancing the Quantum Waltz: Compiling Three-Qubit Gates on Four Level Architectures
• GraphStateVis: Interactive Visual Analysis of Qubit Graph States and their Stabilizer Groups
• Imperfect quantum networks with tailored resource states
• Combating quantum errors: an integrated approach
• Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters
• Shor-Laflamme distributions of graph states and noise robustness of entanglement
• Weyl channels for multipartite systems
• Error-immune quantum communication
• Qudit Noisy Stabilizer Formalism