Analyzing the Dynamics of Quantum Error Detection Codes via Stochastic Processes
Oral-In-person · Withdrawn
Abstract
Quantum error detection (QED) codes offer a resource-efficient alternative to full error correction by discarding errors rather than correcting them. We present a comprehensive framework for analyzing stabilizer QED codes through stochastic processes, revealing fundamental aspects of their dynamics and performance.
Using a transition matrix formalism, we demonstrate that stabilizer QED codes exhibit non-Markovian dynamics during the initial rounds of error detection. While this non-Markovian behavior is transient, it has important implications for practical applications such as quantum process tomography where short-time dynamics are crucial. We propose ways to account for these transient dynamics in tomography and demonstrate their efficacy in simulation.
We introduce "shot efficiency" as a QED-specific metric, inspired by applications in error mitigation. Unlike traditional metrics borrowed from quantum error correction, shot efficiency captures the unique operational constraints of detection-only protocols. We employ transition matrix methods to analytically derive how varying the frequency of error detection impacts shot efficiency. We also identify the types of stabilizer QED codes maximize shot efficiency, and show that codes optimized for QEC do not necessarily yield optimal shot efficiency when operated as QED codes.
Using a transition matrix formalism, we demonstrate that stabilizer QED codes exhibit non-Markovian dynamics during the initial rounds of error detection. While this non-Markovian behavior is transient, it has important implications for practical applications such as quantum process tomography where short-time dynamics are crucial. We propose ways to account for these transient dynamics in tomography and demonstrate their efficacy in simulation.
We introduce "shot efficiency" as a QED-specific metric, inspired by applications in error mitigation. Unlike traditional metrics borrowed from quantum error correction, shot efficiency captures the unique operational constraints of detection-only protocols. We employ transition matrix methods to analytically derive how varying the frequency of error detection impacts shot efficiency. We also identify the types of stabilizer QED codes maximize shot efficiency, and show that codes optimized for QEC do not necessarily yield optimal shot efficiency when operated as QED codes.
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Presenters
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Rohan Kumar
- Yale University