Measures of noise strength
Several measures for noise strength have been defined in chflow. The below table summarizes the names and descriptions of the noise metrics.
| name | Description |
|---|---|
| dnorm | Diamond distance of the input channel from the identity channel |
| infid | 1 - (Fidelity of the input channel's Choi matrix to the Bell state) |
| frb | L2 - distance of the input channel's Choi matrix to the Bell state |
| trn | Trace norm distance between the input channel's Choi matrix and the Bell state |
| nonu | 1 - Unitarity of the input channel, as defined in |
| bd | Bures distance between the input channel and the identity channel |
| errp | A measure of error probability of the input channel, proposed in |
| entropy | Von Neumann entropy of the input channel's Choi matrix |
| uhl | Uhl-Josza fidelity of the input channel to the identity channel |
| np1 | L2 norm of the difference between the channel's Chi matrix and it's twirled approximation. |
| np2 | Least fidelity between the channel's Choi matrix and any bell state. |
| np4 | Maximum "amount" of Pauli channel that can be subtracted from the input Pauli channel, such that what remains is still a valid quantum channel. |
The metrics defined above can be evaluated on a set of quantum channels using the chcalib command, producing a plot as in the figure below (for the case of the Amplitude damping channel with various damping rates, cf. here).
The chcalib command can be invoked on a set of channels defined by a name and a parameter range specified in the format: <lower limit>,<upper limit>,<number of points>. If the channel has multiple parameters, thier respective ranges must be separated by ;. The noise metrics to be computed for every channel must also be specified. Multiple metric names can be provided separated by commas. If unspecified, the default metric is the infidelity (infid). For multiparamter channels, one can choose one (or two) of the noise parameters to analyze the change in the noise metrics with respect to the chosen parameter. If two parameters are chosen, the result is a 2D color plot. In summary, the usage of chcalib is:
chcalib <channel name> <noise range> [<metrics>] [<xcol>] [<ycol>].
Note that the last three parameters are optional. When chcalib is invoked, the noise metric values for all the channels are also stored in a numpy formmated file in chflow/temp/. If metric values are already present for the channels in question, then they are not recomputed and simply read from this file.