supermarq.qcvv.xeb

Tooling for cross entropy benchmark experiments.

Classes

`XEB`	Cross-entropy benchmarking (XEB) experiment.
`XEBResults`	Results from an XEB experiment.

Module Contents

class supermarq.qcvv.xeb.XEB(num_circuits: int, cycle_depths: collections.abc.Iterable[int], two_qubit_gate: cirq.Gate | cirq.Operation | None = cirq.CZ, single_qubit_gate_set: list[cirq.Gate] | None = None, *, random_seed: int | numpy.random.Generator | None = None, _samples: list[supermarq.qcvv.base_experiment.Sample] | None = None, **kwargs: str)

Bases: supermarq.qcvv.base_experiment.QCVVExperiment[XEBResults]

Cross-entropy benchmarking (XEB) experiment.

The XEB experiment can be used to estimate the combined fidelity of a repeating cycle of gates. In our case, where we restrict ourselves to two qubits, we use cycles made up of two randomly selected single qubit phased XZ gates and a constant two qubit gate. This is illustrated as follows:

For each randomly generated circuit, with a given number of cycle, we compare the simulated state probabilities, \(p(x)\) with those achieved by running the circuit on a given target, \(\hat{p}(x)\). The fidelity of a circuit containing \(d\) cycles, \(f_d\) can then be estimated as

\[\sum_{x \in \{0, 1\}^n} p(x) \hat{p}(x) - \frac{1}{2^n} = f_d \left(\sum_{x \in \{0, 1\}^n} p(x)^2 - \frac{1}{2^n}\right)\]

We can therefore fit a linear model to estimate the value of \(f_d\). We the estimate the fidelity of the cycle, \(f_{\mathrm{cycle}}\) as

\[f_d = A(f_{cycle})^d\]

Thus fitting another linear model to \(\log(f_d) \sim d\) provides us with an estimate of the cycle fidelity.

For more details see: https://www.nature.com/articles/s41586-019-1666-5

single_qubit_gate_set: list[cirq.Gate]: The single qubit gates to randomly sample from

two_qubit_gate: cirq.Gate | None: The two qubit gate to use for interleaving.

class supermarq.qcvv.xeb.XEBResults

Bases: supermarq.qcvv.base_experiment.QCVVResults

Results from an XEB experiment.

plot_results(filename: str | None = None) → matplotlib.pyplot.Figure

Plot the experiment data and the corresponding fits.

Parameters:: filename – Optional argument providing a filename to save the plots to. Defaults to None, indicating not to save the plot.
Returns:: A single matplotlib figure containing both the linear fit per cycle depth and the decay with cycle depth.
Raises:: RuntimeError – If there is no data stored.

plot_speckle(filename: str | None = None) → matplotlib.pyplot.Figure

Creates the speckle plot of the XEB data. See Fig. S18 of https://arxiv.org/abs/1910.11333 for an explanation of this plot.

Parameters:: filename – Optional argument providing a filename to save the plots to. Defaults to None, indicating not to save the plot.
Returns:: A matplotlib figure with the speckle plot.
Raises:: RuntimeError – If there is no data stored.

print_results() → None

property cycle_fidelity_estimate: float: Returns: Estimated cycle fidelity.

property cycle_fidelity_estimate_std: float: Returns: Standard deviation for the cycle fidelity estimate.