Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates II: Single-Copy Measurements
This addresses a practical limitation in quantum state tomography for researchers in quantum computing, offering a more feasible experimental approach, though it is incremental as it builds on prior work with similar efficiency.
The paper tackles the problem of learning quantum states prepared with few non-Clifford gates, achieving trace distance ε using poly(n,2^t,1/ε) resources, but with a novel algorithm that relies only on single-copy measurements instead of entangled measurements across two copies.
Recent work has shown that $n$-qubit quantum states output by circuits with at most $t$ single-qubit non-Clifford gates can be learned to trace distance $ε$ using $\mathsf{poly}(n,2^t,1/ε)$ time and samples. All prior algorithms achieving this runtime use entangled measurements across two copies of the input state. In this work, we give a similarly efficient algorithm that learns the same class of states using only single-copy measurements.