Efficient Pauli channel estimation with logarithmic quantum memory

演讲人: Weiyuan Gong Harvard University
时间: 2023-12-21 10:00-2023-12-21 12:00
地点:FIT 1-222

We revisit one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating every eigenvalue of an Pauli noise channel. Prior work 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 <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 using logarithmic ancilla qubits  and polynomially many measurements. In contrast, we show a tight lower bound that any protocol with zero ancilla, even a concatenating one, must make \Omega(2^n/\epsilon^2) measurements to estimate within error \epsilon. Our results imply, to our knowledge, the first quantum learning task where logarithmically many qubits of quantum memory suffice for an exponential statistical advantage.


Weiyuan Gong is a graduate student of computer science at Harvard, under the supervision of Prof. Sitan Chen. He received his Bachelor degree from IIIS, Tsinghua University in 2023.  His major research interests include quantum information, quantum machine learning, and quantum complexity theory.