Quantum resource distillation is a fundamental task in quantum information science and technology. Minimizing the overhead of distillation is crucial for the realization of quantum computation and other technologies. Here we explicitly demonstrate how, for general quantum resources, suitably designed quantum catalysts (i.e., auxiliary systems that remain unchanged before and after the process) can lift the multi-shot or asymptotic average distillation overhead to the one-shot setting. This can enable one-shot distillation with constant overhead, thereby overcoming the established logarithmic lower bound. In particular, for magic state distillation, our catalysis method paves a path for tackling the diverging batch size problem associated with code-based low-overhead protocols by enabling arbitrary reduction of the protocol size for any desired accuracy. Notably, this yields constant-overhead magic state distillation with controllable protocol size. Furthermore, we demonstrate a tunable spacetime trade-off between overhead and success probability enabled by catalysts which offers significant versatility for practical implementation. Finally, we extend catalysis techniques to dynamical quantum resources and show that channel mutual information determines one-shot catalytic channel transformation, thereby advancing our understanding for both dynamical catalysis and information theory. In quantum information processing, distilling pure quantum states from noisy ones in the practical one-shot setting imposes a high overhead. Here, Fang and Liu propose a one-shot distillation scheme that exploits catalysis to arbitrarily reduce distillation overhead, and apply this to magic state distillation to improve over existing results.

Nature is a scientific journal publishing research articles, reviews, and commentary across a wide range of scientific disciplines. Readers can find articles on topics such as biology, chemistry, physics, and environmental science. Additionally, they can learn about  research, scientific discoveries, and advances in understanding the natural world.

Nature

A new theoretical framework demonstrates how quantum catalysts — auxiliary systems unchanged before and after a process — can reduce the overhead of one-shot quantum resource distillation to a constant, overcoming the established logarithmic lower bound. Applied to magic state distillation, the catalysis method addresses the diverging batch size problem in code-based low-overhead protocols, enabling arbitrary reduction of protocol size for any desired accuracy. The work also reveals a tunable spacetime trade-off between overhead and success probability, and extends catalysis techniques to dynamical quantum resources, showing that channel mutual information governs one-shot catalytic channel transformation.

One-shot distillation with constant overhead using catalysts