تقرير
Efficient Pauli channel estimation with logarithmic quantum memory
| العنوان: | Efficient Pauli channel estimation with logarithmic quantum memory |
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| المؤلفون: | Chen, Sitan, Gong, Weiyuan |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics Quantum Physics Statistics |
| مصطلحات موضوعية: | Quantum Physics, Computer Science - Computational Complexity, Computer Science - Information Theory, Computer Science - Machine Learning, Mathematics - Statistics Theory |
| الوصف: | Here we revisit one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating every eigenvalue of an $n$-qubit Pauli noise channel to error $\epsilon$. Prior work (Chen et al., 2022) proved no-go theorems for this task in the practical regime where one has a limited amount of quantum memory, e.g. any protocol with $\le 0.99n$ ancilla qubits of quantum memory must make exponentially many measurements, provided it is non-concatenating. Such protocols can only interact with the channel by repeatedly preparing a state, passing it through the channel, and measuring immediately afterward. This left open a natural question: does the lower bound hold even for general protocols, i.e. ones which chain together many queries to the channel, interleaved with arbitrary data-processing channels, before measuring? Surprisingly, in this work we show the opposite: there is a protocol that can estimate the eigenvalues of a Pauli channel to error $\epsilon$ using only $O(\log n/\epsilon^2)$ ancilla qubits and $\tilde{O}(n^2/\epsilon^2)$ measurements. In contrast, we show that any protocol with zero ancilla, even a concatenating one, must make $\Omega(2^n/\epsilon^2)$ measurements, which is tight. Our results imply, to our knowledge, the first quantum learning task where logarithmically many qubits of quantum memory suffice for an exponential statistical advantage. Comment: 57 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.14326 |
| رقم الأكسشن: | edsarx.2309.14326 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |