# Calibration Metrics¶

Quantum processors periodically undergo calibrations to maintain the quality of the programs that can be run on them. During this calibration metrics about the performance of the quantum computer are collected. This calibration data is stored by Quantum Engine and users can then query for the current or previous state of the calibration. Calibrations are also available for past jobs.

A calibration object is a dictionary from metric name (see below) to the value of the metric. Note that the value of the metric is also usually a dictionary (for instance, from qubit or qubit pair to a float value).

## Retrieving calibration metrics¶

You can view calibration metrics in the Cloud Console by clicking on the relevant processor in the processors list. A dropdown menu will let you choose the current characterization or historical metrics from a previous run. Calibration metrics can also be retrieved programmatically using an engine instance or with a job.

import cirq.google as cg

# Create an Engine object to use.
# Replace YOUR_PROJECT_ID with the id from your cloud project.
engine = cg.Engine(project_id=YOUR_PROJECT_ID)
processor = engine.get_processor(processor_id=PROCESSOR_ID)

# Get the latest calibration metrics.
latest_calibration = processor.get_current_calibration()

# If you know the timestamp of a previous calibration, you can retrieve the
# calibration using the timestamp in epoch seconds.
previous_calibration = processor.get_calibration(CALIBRATION_SECONDS)

# If you would like to find a calibration from a time-frame, use this.
calibration_list = processor.list_calibration(START_SECONDS, END_SECONDS)

# If you know the job-id, you can retrieve the calibration that the job used.
job = engine.get_job("projects/" + PROJECT_ID
+ "/programs/"+PROGRAM_ID
+ "/jobs/" + JOB_ID)
job_calibration = cg.EngineJob(cg.JobConfig(), job, engine).get_calibration()

# The calibration can be iterated through using something like the following.
for metric_name in latest_calibration:
print(metric_name)
print('------')
for qubit_or_pair in latest_calibration[metric_name]:
# Note that although the value is often singular,
# the metric_value is of the type list and can have multiple values.
metric_value = latest_calibration[metric_name][qubit_or_pair]
print(f'{qubit_or_pair} = {metric_value}')


Calibration metrics will also soon be available from the Google Cloud Platform Console.

## Average, Pauli and Incoherent Error¶

Several metrics below define average error, Pauli error and incoherent error. This section explains the difference between each of these metrics.

The average error is equal to one minus fidelity averaged over all possible input states.

Pauli error defines decoherence of a single qubit in one of the Pauli channels X, Y, or Z. If the errors are distributed in the uniform distribution over all three axes, the probability of applying an erroneous Pauli gate X, Y, or Z will be the Pauli error divided by three. The Pauli error and average error are related by a multiplicative factor dependent on the number of qubits.

See Table 1 on page 11 of the Supplementary Information document for a description and comparison between average error, Pauli error, and depolarization error.

The incoherent error is the “unitarity” of the gate or cycle. This is defined as the decay rate per gate (or cycle) of the Purity when fit to an exponential curve. This rate has been scaled to match the average error per Clifford gate (or per 2-qubit cycle). For more about purity benchmarking, see Section 6.3 of this thesis.

The purity error can be interpreted as a measure of the incoherent error, such as those caused by stochastic processes such as relaxation. The average error can be interpreted as containing both this incoherent error as well as the coherent error resulting from improper control or calibration of the device.

Note that, due to statistical fluctuations, it is possible that the purity error can exceed the average error by small amounts.

## Individual Metrics¶

Each metric can be referenced by its key in the calibration object, e.g. latest_calibration['single_qubit_idle_t1_micros'].

Note that the metric names below are subject to change without notice.

• Metric key: single_qubit_p00_error

• Metric key: parallel_p00_error

The p_00 is defined as the probability that the state is measured as |0⟩ after being prepared in the |0⟩ state. The p_00 error is defined as one minus this result.

There are several sources of error in this model. This error is primarily composed of error in measurement (readout) of the qubit while in the ground state. However, this probability also contains the error than the qubit was not reset into the |0⟩ ground state properly. This is often called the SPAM (state preparation and measurement) error.

The single qubit error is when the readout is measured in isolation (only one qubit is measured at a time), while the parallel error is taken for all qubits at the same time.

• Metric key: single_qubit_p11_error

• Metric key: parallel_p11_error

The p_11 is defined as the probability that the state is measured as |1⟩ after being prepared in the |1⟩ state. The p_11 error is defined as one minus this result.

This is dominated by the error in measurement (readout) of the qubit, but it implicitly contains several different types of error. Also possible is that the excited state |1⟩ was not prepared correctly or that the state decayed before measurement. This error is generally expected to be higher than the P_00 error.

The single qubit error is when the readout is measured in isolation (only one qubit is measured at a time), while the parallel error is taken for all qubits at the same time.

When measured by the system, the |0⟩ and |1⟩ states manifest as outgoing analog signals. These signals must be interpreted as signifying one state or the other. Since these analog signals are continuous distributions, there will be some statistical overlap in the two distributions that would be theoretically impossible to distinguish. This is classified as the separation error, and is calculated by fitting Gaussian distributions to the signals prepared in the |0⟩ state and |1⟩ state and calculating the overlap between the two distributions. Note that this is a component of both the p_00 and p_11 errors and is included within those metrics.

### Isolated 1 qubit randomized benchmark error:¶

• Metric key: single_qubit_rb_average_error_per_gate

• Metric key: single_qubit_rb_pauli_error_per_gate

• Metric key: single_qubit_rb_incoherent_error_per_gate

Single qubit gate error is estimated using randomized benchmarking by taking sequences of varying length of the 24 gates within the Clifford group (those that preserve the Pauli group under conjugation) then applying the inverse of the unitary equivalent to the executed gate sequence. The result of the total sequence should always be the identity (|0⟩ state). The final error is measured and compared against this state to produce the total error. This error is calculated for one qubit at a time while all other qubits on the device are idle (isolated). See the above section for descriptions of total versus purity error.

### T1¶

• Metric key: single_qubit_idle_t1_micros

The T1 of a qubit represents the time constant of the exponential decay of a qubit in the excited |1⟩ state into the ground |0⟩ state. This is calculated by preparing the excited state with a microwave pulse (a.k.a. an X gate), measured after a variety of decay times.

An exponential curve is then fit to the resulting data to determine the T1 time, which is reported in microseconds.

### 2-qubit Isolated XEB error¶

• Metric key: two_qubit_sqrt_iswap_gate_xeb_average_error_per_cycle

• Metric key: two_qubit_sqrt_iswap_gate_xeb_pauli_error_per_cycle

• Metric key: two_qubit_sqrt_iswap_gate_xeb_incoherent_error_per_cycle

• Metric key: two_qubit_sycamore_gate_xeb_average_error_per_cycle

• Metric key: two_qubit_sycamore_gate_xeb_pauli_error_per_cycle

• Metric key: two_qubit_sycamore_gate_xeb_incoherent_error_per_cycle

Two qubit error is primarily characterized by applying cross-entropy benchmarking (XEB). This procedure repeatedly performs a “cycle” of a random one-qubit gate on each qubit followed by the two qubit entangling gate. The resulting distribution is analyzed and compared to the expected distribution using cross entropy. The value reported is the error rate per cycle (both the 1 qubit gates as well as the 2 qubit gate).

See the above section for descriptions of average, Pauli, and incoherent error.

These errors are isolated, meaning that, during the metric measurement, only the pair of qubits being considered is active. All other qubits are idle.

### 2-qubit Parallel XEB error¶

• Metric key: two_qubit_parallel_sqrt_iswap_gate_xeb_average_error_per_cycle

• Metric key: two_qubit_parallel_sqrt_iswap_gate_xeb_pauli_error_per_cycle

• Metric key: two_qubit_parallel_sqrt_iswap_gate_xeb_incoherent_error_per_cycle

• Metric key: two_qubit_parallel_sycamore_gate_xeb_average_error_per_cycle

• Metric key: two_qubit_parallel_sycamore_gate_xeb_pauli_error_per_cycle

• Metric key: two_qubit_parallel_sycamore_gate_xeb_incoherent_error_per_cycle

These metrics are calculated the same way as the 2-qubit isolated XEB error metrics. However, this metric quantifies the error of multiple parallel 2-qubit cycles at a time. Four different discrete patterns of 2-qubits are used, with each pair of qubits in only one pattern.

Since there are many different possible layouts of parallel two-qubit gates and each layout may have different cross-talk effects, users may want to perform this experiment on their own if they have a specific layout commonly used in their experiment.