## AWS Quantum Technologies Blog

# Amazon Braket launches IonQ Aria with built-in error mitigation

Today, we are excited to announce that IonQ’s trapped-ion quantum computer, *IonQ **Aria*, is available on Amazon Braket, the quantum computing service of AWS. With Aria, customers can take advantage of 25 qubits, higher fidelities, and for the first time on Braket, *error mitigation*, making it possible to run more complex quantum algorithms with improved accuracy.

Aria joins Braket alongside the 11-qubit IonQ Harmony device, which has been available to customers since general availability of the service. Both the Aria and Harmony quantum processing units (QPUs) are now available for 15 hours daily, Monday-Friday.

Trapped-ion quantum computers encode quantum information in the electronic spin state of charged atoms (in IonQ’s case, ytterbium) that are confined in a linear electromagnetic trap. Entangling gates are realized via controlled, collective vibrations running through the chain of atoms. This type of interaction brings “all-to-all” connectivity to both Aria and Harmony, making it possible to perform gates between any qubit pair in the device. This can reduce the number of gates needed to run complex circuits, thereby decreasing the probability of errors in the circuit, which is a major limiting factor for today’s quantum hardware.

The availability of both Aria and Harmony on Braket gives customers the ability to choose the trapped-ion device that best suits their specific needs. For instance, customers may wish to test out their quantum circuit on Harmony before scaling to the larger and higher fidelity Aria.

Aria is the first QPU on Braket to feature *error mitigation (EM):* techniques designed to improve the accuracy of current-generation noisy quantum hardware. EM, an active area of research, will be crucial to make the most out of near-term quantum hardware. With this launch, customers can now experiment with EM techniques and, by toggling them on or off, study the impact of these techniques on algorithm performance.

In this post, you will learn how to get started using Aria on Braket. You’ll learn about two built-in EM techniques, how to switch between them, and the performance difference you can expect to see with and without these techniques for several example problems.

## Error mitigation with debiasing

Quantum computers work by manipulating delicate quantum states. Even small imperfections in gate calibrations or unwanted environmental interactions can lead to errors in computation. These errors can accumulate in circuits with many gates, rendering the overall results inaccurate.

Debiasing is an EM technique developed by IonQ [1] which aims to mitigate the effects of *coherent errors*. Coherent errors are small, systematic imperfections in the basic control operations implemented by the device. For instance, a single qubit gate could be miscalibrated to rotate qubits marginally less than the desired angle. Coherent errors can be particularly detrimental because they may accumulate faster than incoherent noise [2].

Debiasing aims to minimize the effect of coherent errors by randomizing their effect across multiple circuit implementations [1]. Debiasing is designed to take an input circuit and create multiple logically equivalent *variant implementations*. This is accomplished via random qubit permutations and/or gate decompositions. The resulting measurement counts from each variant are then summed into a single distribution. Any other result types, such as expectation values, are computed using the total measurement counts. Because the variants are selected at random, the effects of coherent, systematic imperfections should cancel each other out, which can improve the accuracy of your results. Since debiasing allocates shots across multiple implementations, you’ll need a minimum of 2500 shots to run debiasing.

With Aria, Braket customers can now experiment with debiasing on and off by only changing one line of code. For this code sample, we’ll show how to run debiasing for a Quantum Circuit Born Machine (QCBM) trained to reproduce a normal distribution with five qubits and five entangling layers. This circuit contains 75 one-qubit rotation gates and 25 two-qubit gates. We have precomputed the optimal angles for the rotation gates so that the circuit’s output distribution reproduces the target normal distribution. Note that we conveniently reference Braket’s Algorithm Library for a ready-to-use QCBM implementation.

```
from braket.aws import AwsDevice
from braket.circuits import Circuit
from braket.error_mitigation import Debias
device = AwsDevice("arn:aws:braket:us-east-1::device/qpu/ionq/Aria-1")
from braket.experimental.algorithms.quantum_circuit_born_machine import QCBM
# Load in optimal parameters previously found
parameters = np.load("optimal_qcbm_angles.npz")
# Define QCBM instance
qcbm = QCBM(aria, n_qubits=5, n_layers=5, target_probabilities=gaussian(5, 2**4-1, 2**3))
circ = qcbm.bound_circuit(parameters)
task = device.run(circ, shots=5000, device_parameters={"errorMitigation": Debias()})
```

Where we define `gaussian`

as follows:

```
def gaussian(n_qubits, mu, sigma=1):
x = np.arange(2**n_qubits)
gaussian = 1.0 / np.sqrt(2 * np.pi * sigma**2) * np.exp(-((x - mu) ** 2) / (2 * sigma**2))
return gaussian / sum(gaussian)
```

In Figure 1, we show the output distribution from Aria with and without debiasing.

We see that, in Figure 1, debiasing reduces certain peaks in the distribution and improves the fidelity between the normal distribution and the circuit probabilities by 1.3%. Additionally, the mean-squared-error (MSE) has nearly a 3x improvement by using debiasing.

One advantage of debiasing is that it is designed not to make assumptions about the output distribution of our circuit. In other words, debiasing mitigates the impact from certain coherent errors without amplifying other error sources. However, if you have knowledge about the characteristics of the ideal output distribution of your circuit, you can improve the results further.

## Error mitigation with sharpening

For quantum circuits where the expected output distribution is sparse, IonQ’s s*harpening *technique can further improve the results of a debiased task. Instead of adding up all measurement counts, sharpening compares the counts of each variant and discards inconsistent shots, favoring the most likely measurement outcome across variants. Note that, since there is a minimum probability threshold for a shot to be considered consistent, sharpening can distort the probability distribution for non-sparse output distributions, reducing the fidelity of your results. As sharpening is a purely classical post-processing technique, Braket offers a sharpened probability distribution for all debiased tasks, which you can retrieve from the task’s `additional_metadata`

at no additional cost.

To show an example where sharpening improves results, we’ll run a quantum phase estimation (QPE) circuit on 23 qubits. Again, we’ll assume the circuit has already been defined as `qpe_circuit`

for simplicity, but you can import it from your favorite library (e.g. PennyLane or Qiskit) or use our example implementation. In Figure 2, we show 10 most likely bitstrings from running QPE on Aria with debiasing and with sharpening on/off.

```
task = device.run(qpe_circuit, shots=2500, device_parameters={"errorMitigation": Debias()})
sharp_probs = task.result().additional_metadata.ionqMetadata.sharpenedProbabilities
```

Notice how sharpening the debiased results gives 100% fidelity compared to 17.4% for only debiasing. This is where there is only one high-probability bitstring, in contrast to the QCBM example with many probable bitstrings.

## Conclusion

Amazon Braket is committed to accelerating innovation in quantum computing by giving customers access to diverse quantum hardware across a range of quantum computing modalities, including trapped-ion, superconducting, photonic, and analog systems.

With the addition of Aria, researchers and developers now have even wider access to quantum computing technologies, with the familiar on-demand pricing and no upfront commitments. With Aria and Harmony, each available 15 hours per day on weekdays, customers around the world can choose a device based on their use case and switch between them with one line of code. For detailed pricing info on Aria and all other Braket devices, see our pricing page.

To try out Aria, check out our example notebook, which demonstrates how to use its built-in EM techniques to get improved performance on your quantum circuits. If you are running a hybrid variational workload, you can also use Amazon Braket Hybrid Jobs to gain priority access to the QPU. Aria and Harmony are both accessible in the US East (N. Virginia) Region.

We invite academic researchers interested in exploring applications of Aria to apply for research credits through the AWS Cloud Credits for Research program.

### References

[1] “Enhancing quantum computer performance via symmetrization”, https://arxiv.org/abs/2301.07233

*Note that this paper refers to debiasing as “symmetrization with component-wise averaging”, and sharpening as “symmetrization with plurality voting”.*

[2] “Coherence in logical quantum channels”, https://arxiv.org/abs/1912.04319