Error mitigation can substantially improve measured observables. But ‘mitigation on’ is not a single, universal switch. Different methods target different errors and use different additional information. We investigated several approaches in this project; they must not be combined into one overarching label on the latest hardware table.
Readout: calibrating the measurement
A qubit prepared as zero can sometimes be read as one, and vice versa. We estimate a confusion matrix using known prepared states. Readout mitigation then corrects the measured distribution or relevant moments according to that calibration model.
This helps with measurement errors. It cannot simply recover information lost earlier during thousands of gates. An overly simple readout model may also miss correlated errors.
ZNE and PEC: increasing noise or compensating statistically
Zero-noise extrapolation, or ZNE, compares executions at different noise levels and extrapolates to zero noise. With CZ folding, for example, we replace one CZ with three CZ gates. Because CZ squared is the identity, the ideal operation remains unchanged. The additional physical gates increase exposure to noise, provided an optimiser does not remove them again.
Probabilistic error cancellation, or PEC, combines noisy operations using signed quasiprobability weights. Its quality depends on the noise model, and the required sample count can grow substantially. Both methods therefore require more than selecting a name in a settings menu. See Temme, Bravyi and Gambetta.
TFLO: learning from a tractable neighbouring problem
Training with Fermionic Linear Optics uses circuits that can be simulated efficiently on a classical computer. In our application, we use U=0 training circuits and learn the relationship between their exact and noisy Pauli moments. We then apply that correction to the U=8 target. The approach is inspired by Montanaro and Stanisic.
The latest paired test used six training times per arm: 0.04; 0.08; 0.12; 0.24; 0.32; 0.48. Two other U=0 times, 0.2 and 0.4, served as holdouts. The U=8 target at 0.4 did not supply a correct reference value to the fit. The affine correction was learned separately for each Pauli and circuit arm, with a small regularisation towards the identity.
This is a testable design, but the holdouts failed our chosen accuracy requirements. A control without target hardware input also came closer to the chi64 reference for some quantities. An attractive TFLO result therefore cannot be attributed solely to the measured U=8 dynamics. The training itself contributes substantial information.
The label on the latest run
The newest original/compact comparison used readout correction and TFLO. ZNE, PEC, postselection and DD were not enabled. A separate earlier DD experiment is archived under a different job ID.
Our mitigated estimates are much more interesting than the almost flat raw spin profiles, but remain unvalidated estimates. Negative reconstructed local probabilities and failed holdouts are therefore reported openly. This makes targeted improvement possible.
Sources: HARDWARE_COMPACT_TFLO_PROTOCOL.md, TFLO_DD_6X6_PROTOCOL.md and the corresponding raw data, fits, holdouts and ablations in the project repository.