Efficient Quantum State Sample Tomography with Basis-dependent
  Neural-networks
We use a meta-learning neural-network approach to analyse data from a
measured quantum state. Once our neural network has been trained it can be used
to efficiently sample measurements of the state in measurement bases not
contained in the training data. These samples can be used calculate expectation
values and other useful quantities. We refer to this process as "state sample
tomography". We encode the state's measurement outcome distributions using an
efficiently parameterized generative neural network. This allows each stage in
the tomography process to be performed efficiently even for large systems. Our
scheme is demonstrated on recent IBM Quantum devices, producing a model for a
6-qubit state's measurement outcomes with a predictive accuracy (classical
fidelity) > 95% for all test cases using only 100 random measurement settings
as opposed to the 729 settings required for standard full tomography using
local measurements. This reduction in the required number of measurements
scales favourably, with training data in 200 measurement settings yielding a
predictive accuracy > 92% for a 10 qubit state where 59,049 settings are
typically required for full local measurement-based quantum state tomography. A
reduction in number of measurements by a factor, in this case, of almost 600
could allow for estimations of expectation values and state fidelities in
practicable times on current quantum devices.
Alistair W. R. Smith Johnnie Gray M. S. Kim