Recoverable quantum computation: An information-centric paradigm for quantum computing with errors

Quantum computing promises transformative advances in computation, communication, sensing, and machine learning. Yet, the realization of large-scale fault-tolerant quantum computers remains hindered by the enormous overhead required for quantum error correction. This challenge raises a fundamental question: Must useful quantum computing wait until fully fault-tolerant quantum hardware becomes available? In this Perspective, we propose recoverable quantum computation (RQC), an information-centric paradigm for quantum computing with errors. Rather than requiring faithful preservation of the complete quantum state, RQC focuses on preserving the computational information required to accomplish a given task. A noisy quantum computation is task-level recoverable when its specified output can be inferred with prescribed accuracy and confidence using a finite, quantifiable recovery procedure. RQC may preserve quantum advantages if its overall computational cost is still lower than that of the best known classical method. We characterize recoverability through recovery overhead, task error, success probability, and end-to-end resource cost. We illustrate the framework using quantum Fourier transform period estimation on IBM quantum hardware and a conceptual example from quantum machine learning, demonstrating that useful computational information may remain recoverable despite significant physical errors. Building on these examples, we propose a preliminary classification of quantum applications according to their expected recoverability and outline a research roadmap toward a predictive theory of recoverability. RQC complements fault-tolerant quantum computing, error mitigation, quantum utility, and application-oriented benchmarking by separating the recovery of task-relevant information from the stronger claim of computational advantage.