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.
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.
There are several known limitations of the benchmark. Error mitigation techniques can enhance the performance of quantum computers being tested. Specifically, certain mitigations do not scale well to the size of the computer can result with misleading results. Additionally, the restricted number of different circuits used during protocol affects the robustness of results. [3]
The metric has been criticized as easy to manipulate. Quantinuum's Dr. Charlie Baldwin states "error mitigation, including plurality voting, may be a useful tool for some near-term quantum computing but it doesn’t work for every problem and it’s unlikely to be scalable to larger systems." [4]
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