Performance Validation¶
This document contains specification and explanation of the hardware error definitions and benchmarks. The code to perform analysis for the hardware specification data in the Product Data Sheets can be found in the specified GitHub repository. Product data sheets are provided per generation of quantum computers, and specify representative error rates typical of standard machine operation, in addition to a max threshold the error rates are unlikely exceed.
Machine Specification¶
The product data sheets report representative error rates typical of standard machine operation, in addition to a max threshold the error rates are unlikely to exceed. The performance specifications detailed below are systematic and quantitative component-level metrics using the latest Randomized Benchmarking (RB) sweep [1]. Performance specifications are reported on a per machine basis.
Machine specifications are tabulated below for each hardware target available to customers. Each error rate is measured using component benchmarks detailed here. The total 1-qubit (2-qubit) fidelity, \(F_{T}\), includes both the fidelity, \(F_{RB}\), from RB and also the leakage error per 1-qubit (2-qubit) gate, \(L\). The total \(N\)-qubit fidelity is calculated as,
where D=1 (D=2). The 1-qubit (2-qubit) fidelity, \(F_T\) is reported as 1-Qubit Gate Error (2-Qubit Gate Error). Additionally, the leakage error rate per 1-qubit (2-qubit) gate, \(L\), is reported as 1-Qubit Gate Leakage Error (2-Qubit Gate Leakage Error). The reported Memory Error per Depth-1 Time captures the idling error of qubits during a random transport. Measurement Crosstalk Error measures the crosstalk due to Measurement and Reset on qubits in the trap that are not measured or reset. SPAM Error estimates the state-preparation and measurement error for the \(| 0 \rangle\) (\(| 1 \rangle\)) state.
Infidelity |
Uncertainty |
|
|---|---|---|
1-Qubit Gate Error |
1.8e-05 |
2.9e-06 |
1-Qubit Gate Leakage Error |
6.4e-06 |
1.2e-06 |
2-Qubit Gate Error |
9.7e-04 |
6.2e-05 |
2-Qubit Gate Leakage Error |
2.2e-04 |
2.7e-05 |
Memory Error per Depth-1 Circuit Time |
2.2e-04 |
9.2e-05 |
Measurement Crosstalk Error |
4.1e-05 |
1.7e-06 |
SPAM Error (0) |
1.2e-03 |
1.1e-04 |
SPAM Error (1) |
3.4e-03 |
1.8e-04 |
Infidelity |
Uncertainty |
|
|---|---|---|
1-Qubit Gate Error |
1.9e-05 |
4.2e-06 |
1-Qubit Gate Leakage Error |
4.8e-06 |
1.5e-06 |
2-Qubit Gate Error |
1.1e-03 |
8.1e-05 |
2-Qubit Gate Leakage Error |
1.4e-04 |
2.1e-05 |
Memory Error per Depth-1 Circuit Time |
2.0e-04 |
2.3e-05 |
Measurement Crosstalk Error |
6.6e-06 |
9.0e-07 |
SPAM Error (0) |
6.0e-04 |
8.2e-05 |
SPAM Error (1) |
1.4e-03 |
1.2e-04 |
Infidelity |
Uncertainty |
|
|---|---|---|
1-Qubit Gate Error |
2.8e-05 |
3.6e-06 |
1-Qubit Gate Leakage Error |
6.1e-06 |
1.3e-06 |
2-Qubit Gate Error |
8.3e-04 |
4.8e-05 |
2-Qubit Gate Leakage Error |
1.9e-04 |
1.7e-05 |
Memory Error per Depth-1 Circuit Time |
1.2e-04 |
2.0e-05 |
Measurement Crosstalk Error |
2.2e-05 |
5.3e-07 |
SPAM Error (0) |
6.7e-04 |
8.7e-05 |
SPAM Error (1) |
1.2e-03 |
1.1e-04 |
Infidelity |
Uncertainty |
|
|---|---|---|
1-Qubit Gate Error |
2.8e-03 |
4.0e-04 |
1-Qubit Gate Leakage Error |
1.7e-03 |
5.0e-04 |
2-Qubit Gate Error |
4.4e-03 |
1.2e-03 |
2-Qubit Gate Leakage Error |
3.1e-03 |
1.1e-03 |
Memory Error per Depth-1 Circuit Time |
1.3e-03 |
2.6e-04 |
Measurement Crosstalk Error |
1.3e-04 |
1.4e-04 |
SPAM Error (0) |
1.1e-16 |
3.2e-10 |
SPAM Error (1) |
7.0e-03 |
2.5e-03 |
Component Benchmarks¶
Component-level benchmarks capture the failure rate of specific quantum operations. These type of benchmarks are easier to interpret. Component validation is used in system-level models to better understand complete error budget for a specific machine.
1-qubit gate fidelity¶
The 1-qubit gate fidelity is measured using 1-qubit randomized benchmarking (RB) with random 1-qubit Clifford gates[2]. 1-qubit RB 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 [3]. 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[4]. 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.
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 are also used to estimate the spontaneous emission rate using the leakage gadget described above, but with a scaling for the number of 2-qubit gates per Clifford.
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. All gate zones are measured in parallel, and the experiment is performed on both of the qubits (left and right in below data) in each active gate zone.
Avg. SPAM error |
Avg. SPAM error uncertainty |
0 SPAM error |
1 SPAM error |
|
G1-left |
2.95e-03 |
3.83e-04 |
2.10e-03 |
3.80e-03 |
G1-right |
2.15e-03 |
3.27e-04 |
1.60e-03 |
2.70e-03 |
G2-left |
1.80e-03 |
3.00e-04 |
8.00e-04 |
2.80e-03 |
G2-right |
2.40e-03 |
3.46e-04 |
7.00e-04 |
4.10e-03 |
G3-left |
2.85e-03 |
3.77e-04 |
1.30e-03 |
4.40e-03 |
G3-right |
2.55e-03 |
3.57e-04 |
1.80e-03 |
3.30e-03 |
G4-left |
2.30e-03 |
3.39e-04 |
1.50e-03 |
3.10e-03 |
G4-right |
1.85e-03 |
3.04e-04 |
1.10e-03 |
2.60e-03 |
G5-left |
2.35e-03 |
3.42e-04 |
9.00e-04 |
3.80e-03 |
G5-right |
2.05e-03 |
3.20e-04 |
4.00e-04 |
3.70e-03 |
Mean |
2.33e-03 |
1.08e-04 |
1.22e-03 |
3.43e-03 |
Avg. SPAM error |
Avg. SPAM error uncertainty |
0 SPAM error |
1 SPAM error |
|
G1-left |
1.00e-03 |
2.23e-04 |
4.00e-04 |
1.60e-03 |
G1-right |
9.50e-04 |
2.18e-04 |
5.00e-04 |
1.40e-03 |
G2-left |
9.00e-04 |
2.12e-04 |
6.00e-04 |
1.20e-03 |
G2-right |
1.10e-03 |
2.34e-04 |
8.00e-04 |
1.40e-03 |
G3-left |
1.05e-03 |
2.29e-04 |
6.00e-04 |
1.50e-03 |
G3-right |
1.15e-03 |
2.40e-04 |
4.00e-04 |
1.90e-03 |
G4-left |
8.00e-04 |
2.00e-04 |
7.00e-04 |
9.00e-04 |
G4-right |
1.00e-03 |
2.23e-04 |
8.00e-04 |
1.20e-03 |
Mean |
9.94e-04 |
7.88e-05 |
6.00e-04 |
1.39e-03 |
Avg. SPAM error |
Avg. SPAM error uncertainty |
0 SPAM error |
1 SPAM error |
|
G1-left |
1.10e-03 |
2.34e-04 |
5.00e-04 |
1.70e-03 |
G1-right |
7.00e-04 |
1.87e-04 |
3.00e-04 |
1.10e-03 |
G2-left |
4.00e-04 |
1.41e-04 |
4.00e-04 |
4.00e-04 |
G2-right |
9.00e-04 |
2.12e-04 |
5.00e-04 |
1.30e-03 |
G3-left |
9.50e-04 |
2.18e-04 |
1.30e-03 |
6.00e-04 |
G3-right |
1.45e-03 |
2.69e-04 |
1.70e-03 |
1.20e-03 |
G4-left |
1.05e-03 |
2.29e-04 |
3.00e-04 |
1.80e-03 |
G4-right |
8.00e-04 |
2.00e-04 |
4.00e-04 |
1.20e-03 |
Mean |
9.19e-04 |
7.57e-05 |
6.75e-04 |
1.16e-03 |
Avg. SPAM error |
Avg. SPAM error uncertainty |
0 SPAM error |
1 SPAM error |
|
G1-left |
4.100e-03 |
4.518e-04 |
4.700e-03 |
3.500e-03 |
G1-right |
4.400e-03 |
4.679e-04 |
5.500e-03 |
3.300e-03 |
G2-left |
4.300e-03 |
4.625e-04 |
2.400e-03 |
6.200e-03 |
G2-right |
3.950e-03 |
4.433e-04 |
2.000e-03 |
5.900e-03 |
G3-left |
3.050e-03 |
3.897e-04 |
1.100e-03 |
5.000e-03 |
G3-right |
3.600e-03 |
4.234e-04 |
2.300e-03 |
4.900e-03 |
G4-left |
4.300e-03 |
4.623e-04 |
1.800e-03 |
6.800e-03 |
G4-right |
4.450e-03 |
4.704e-04 |
2.400e-03 |
6.500e-03 |
G5-left |
3.550e-03 |
4.204e-04 |
2.000e-03 |
5.100e-03 |
G5-right |
4.200e-03 |
4.572e-04 |
3.100e-03 |
5.300e-03 |
Mean |
3.990e-03 |
1.409e-04 |
2.730e-03 |
5.250e-03 |
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 1-qubit and memory error, averaged across all qubits, due to depth-1 circuits. We perform this test for all available qubits in the system. The figures below average across the survival rate across all qubits on the system.
Survival rate from 1-qubit and memory randomized benchmarking projects for H1-1¶
Survival rate from 1-qubit and memory randomized benchmarking projects for H2-1¶
Survival rate from 1-qubit and memory randomized benchmarking projects for H2-2¶
Survival rate from 1-qubit and memory randomized benchmarking projects for reimei¶
Mid-circuit measurement cross-talk error¶
Although qubits are physically separated during measurement and reset, 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 [5].
