Error Measurements¶
Here we explain the error definitions behind the H-Series specification benchmarks given in the Product Data Sheets found on these pages:
Benchmarking Data¶
The data for the measurements in the Product Data Sheets can be found here. This repository contains the raw data along with the analysis code.
1-qubit gate fidelity¶
The 1-qubit gate fidelity is measured using 1-qubit randomized benchmarking (RB) with random 1-qubit Clifford gates[1]. Benchmarking also uses final gate randomization to fix the asymptote of the RB decay curve, in order to reduce the number of fit parameters and allow fitting of shorter sequences [2]. We run 1-qubit RB with two qubits per active gate zone in parallel. The error rate is calculated by translating the RB decay curve to a per-Clifford average infidelity under the standard RB assumptions. Uncertainty is calculated from a semi-parametric bootstrap resampling of the collected data.
The spontaneous emission rate is also measured from 1-qubit RB experiments by applying a “leakage gadget” to the end of each circuit, which detects if a qubit leaks out of the computational subspace[3]. The number of leakage events depends on the number of gates applied and the spontaneous emission rate. By fitting the number of detected leakage events as a function of number of gates, we can extract an estimate of the spontaneous emission rate.
Survival rate from 1-qubit randomized benchmarking projects for H1-1¶
Survival rate from 1-qubit randomized benchmarking projects for H2-1¶
2-qubit gate fidelity¶
The 2-qubit gate fidelity is measured with 2-qubit RB using similar methods outlined above on 1-qubit RB. 2-qubit RB is run with 2-qubit random Clifford gates on pairs of qubits in each active gate zone in parallel. The infidelity of our native entangling gate is estimated by scaling per-Clifford infidelity by the average number of entangling gates per Clifford (= 1.5). Datasets also include the estimated spontaneous emission rate using the leakage gadget described above and scaled for the number of 2-qubit gates per Clifford.
Survival rate from 2-qubit randomized benchmarking projects for H1-1¶
Survival rate from 2-qubit randomized benchmarking projects for H2-1¶
State preparation and measurement (SPAM) error¶
The SPAM error is measured by preparing the qubits in the \(|0\rangle\) (or \(|1\rangle\) state) and measuring to determine the fraction of time the incorrect \(|1\rangle\) (or \(|0\rangle\)) state is returned. The reported SPAM error is the average between the \(|0\rangle\) and \(|1\rangle\) state-preparation experiments. The experiment is repeated for two qubits per active gate zone and done in parallel.
Mid-circuit measurement and reset cross-talk error¶
Although qubits are physically separated during measurement, there is a small chance that an unmeasured qubit in the \(|1\rangle\) state will absorb the detection light, destroying its quantum state, and potentially scattering to the non-computational states used for state detection. This is not an issue with measurement at the end of a circuit when all qubits are measured but can impact circuits with mid-circuit measurement and reset. The mid-circuit measurement and reset cross-talk errors are quantified by the population decay of an unmeasured qubit while applying many measurement or reset pulses to a neighboring qubit [4].
Memory error per qubit at depth-1 circuit time¶
To characterize memory error in depth-1 circuit time, we perform 1-qubit RB as described above, while interleaving specialized qasm commands that force transport to create random 2-qubit pairings and run the preset cooling. The net RB error measured is the average 1-qubit (and memory) error due to depth-1 circuits. We perform this test for all available qubits in the system.