Algorithmic qubits
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Algorithmic Qubits (AQ) are an application based benchmark of quantum computers. Introduced by IonQ in 2020, the goal was to define a "single number figure of merit to evaluate the performance of quantum computers for solving a representative set of quantum algorithms."[1] While other benchmarks such as IBM's Quantum volume are run on random quantum circuits that do not necessarily have practical applications, AQ is measured on specific algorithms which are known to have value by industry, such as those defined by the Quantum Economic Development Consortium.
Algorithms used to define AQ 1.0
IonQ published code for calculating AQ in a Git code repository. The formal definition of calculating AQ is composed of several steps:
- Let the set of circuits in the benchmark suite be denoted by C.
- Locate each circuit c ∈ C as a point on the 2D plot by its Width, wc (Number of qubits), and Depth, dc (Number of Controlled NOT (CX) gates)
- Define success probability for a Quantum circuit c, Fc
- The circuit passes if Fc - ϵc > t, where ϵc is the statistical error based on the number of shots, where sc is the number of runs, and t = 1/e = 0.37 is the threshold.
- Then, #AQ = N, where N=max.
The data is usually shown graphically as a volumetric plot.
| Algorithm | Circuit width | Number of circuits per width |
|---|---|---|
| Quantum Fourier transform | >2 | 3 |
| Quantum phase estimation algorithm | >3 | 3 |
| Quantum amplitude estimation | >3 | 3 |
| Monte Carlo sampling | >4 | 1 |
| VQE simulation | Even numbers between 4–12 | 3 |
| Hamiltonian simulation | Even numbers between 2–20 | 1 |
Table of scores
| Date | Company | Machine | AQ |
|---|---|---|---|
| March 2023 | IonQ | Aria | 20 [2] |
| March 2023 | Quantinuum | H1 | 12 [2] |
| March 2023 | IBM | Guadalupe | 6[2] |
| March 2023 | Rigetti | Aspen-M1 | 5[2] |
| September 2023 | IonQ | Forte | 29[3] |
| March 2024 | Quantinuum | H2-1 | 26[4] |
| March 2024 | IonQ | Forte | 9[4] |
| March 2024 | Quantinuum | H2-1 | 32[4] |
| March 2024 | IonQ | Forte | 29[4] |
| December 2024 | IonQ | Forte Enterprise | 36[5] |
| September 2025 | IonQ | Tempo | 64[6] |