Learning and Generating Mixed States Prepared by Shallow Channel Circuits
Learning quantum states from measurement data is a central problem in quantum information and computational complexity. In this work, we study the problem of learning to generate mixed states on a finite-dimensional lattice. Motivated by recent developments in mixed state phases of matter, we focus on arbitrary states in the trivial phase. A state belongs to the trivial phase if there exists a shallow preparation channel circuit under which local reversibility is preserved throughout the preparation. We prove that any mixed state in this class can be efficiently learned from measurement access alone. Specifically, given copies of an unknown trivial phase mixed state, our algorithm outputs...
| Authors | Fangjun Hu, Christian Kokail, Milan Kornjača et al. |
|---|---|
| Primary category | quant-ph |
| Published | 1 April 2026 |
| Last updated at source | 15 June 2026 |
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