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This research presents analytical stochastic Schrödinger equations that enable real-time quantum state recovery without variational techniques, offering a closed-form solution for reversing noise in monitored quantum trajectories. By dynamically steering states back to their initial configurations, these equations provide a foundational framework for noise-resilient quantum gates, generative modeling, and potential paradigms for quantum error correction. The work bridges theoretical quantum dynamics with practical applications in tomography and gate fidelity, establishing a new analytical approach to handling irreversibility at the trajectory level.
Stochastic Schr\"odinger Equations for Quantum Reverse Diffusion
arXiv:2511.15919v5 Announce Type: replace Abstract: The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic Schr\"odinger equations for quantum reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. We show that the reverse processes generalize the forward dynamics by combining the noise effects of the forward processes with an additional stochastic drift that dynamically steers a quantum state back to its initial configuration. Consequently, the exact reverse stochastic Schr\"odinger equations admit closed-form solutions that can be implemented in real-time without the need for variational techniques. Our findings establish an analytical framework for quantum state recovery, noise-resilient quantum gates, quantum generative modelling, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.
Abstract:The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic Schrödinger equations for quantum reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. We show that the reverse processes generalize the forward dynamics by combining the noise effects of the forward processes with an additional stochastic drift that dynamically steers a quantum state back to its initial configuration. Consequently, the exact reverse stochastic Schrödinger equations admit closed-form solutions that can be implemented in real-time without the need for variational techniques. Our findings establish an analytical framework for quantum state recovery, noise-resilient quantum gates, quantum generative modelling, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.
arXiv:2511.15919 [quant-ph]
(or arXiv:2511.15919v5 [quant-ph] for this version)
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