Projected Least-Squares Quantum Process Tomography

We propose and investigate a new method of quantum process tomography (QPT) which we call projected least squares (PLS). In short, PLS consists first computing the least-squares estimator Choi matrix an unknown channel, subsequently projecting it onto convex set matrices. consider four experimental setups including direct QPT with Pauli eigenvectors as input measurements, ancilla-assisted mutually unbiased bases (MUB) measurements. each case, provide closed form solution for matrix. novel, two-step these estimators matrices representing physical channels, fast numerical implementation in hyperplane intersection projection algorithm. rigorous, non-asymptotic concentration bounds, sampling complexities confidence regions Frobenius trace-norm error estimators. For error, bounds are linear rank matrix, low ranks, they improve rates by factor d2, where xmlns:mml="http://www.w3.org/1998/Math/MathML">d is system dimension. illustrate experiments involving channels on systems up to 7 qubits, find that has highly competitive accuracy computational tractability.