Fig. 1: A schematic overview of the robust shallow shadow protocol.
From: Demonstration of robust and efficient quantum property learning with shallow shadows
a We show an example of our randomized measurement scheme for a shallow circuit with d = 2, which is a brickwork circuit comprised of twirled two-qubit gates. As shown b these twirled gates are CNOT gates sandwiched by single-qubit random Cliffords. Our noise model is the sparse Pauli-Lindblad model74, which captures realistic noise effects such as qubit crosstalk. Upon twirling via single-qubit random Clifford gates, the effective noise channel simplifies from a full Pauli-Lindblad map (which has nine two-body terms on each edge and three one-body terms for each node) to the one illustrated in (c), which has only one parameter for each edge and one parameter for each node. The left half a shows the dataset collection process for both calibration and application states, and the right half shows our data postprocessing method. We use a Bayesian inference algorithm to estimate the noise parameters λ of the quantum device and use this to error mitigate our estimates of many different observables, ranging from fidelity to entanglement entropy.
