Fractional quantum fields with Le'vy paths
Le résumé fourni par la source
This is a novel approach to mitigating decoherence in quantum computing with "Fractional-Time Qubits: Leveraging Memory Kernels to Combat Decoherence in Quantum Computing." In this work, Erika Barker introduces fractional quantum dynamics by replacing the conventional time derivative in Schrödinger’s equation with a fractional derivative of order β. This modification incorporates long-range memory kernels—crucial for modeling 1/f noise and other non-Markovian effects—that fundamentally alter decoherence profiles and extend qubit lifetimes. Key highlights include: Expanded Hilbert Space Formalism: A novel framework that embeds fractional dynamics into a larger, unitary space, ensuring probability conservation and a generalized energy conservation law reminiscent of pseudo-Hermitian quantum mechanics. Noise Mitigation Strategies: Detailed analysis and numerical simulations demonstrate how fractional dynamics produce stretched-exponential and power-law decays, effectively countering decoherence in 1/f, Ohmic, and sub-Ohmic noise environments. Resource Efficiency: A comparative discussion on resource overhead reveals potential advantages over traditional quantum error correction, offering a promising pathway for near-term quantum devices with limited qubit counts. Interdisciplinary Impact: The paper also connects these techniques with broader theoretical frameworks in quantum gravity and fractal time, suggesting far-reaching implications for both practical quantum engineering and fundamental physics. This comprehensive study provides essential insights for researchers focused on quantum decoherence, advanced error mitigation techniques, and the development of robust quantum computing architectures. Keywords: quantum computing, decoherence, fractional dynamics, memory kernels, 1/f noise, non-Markovian, Hilbert space, quantum error correction.
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