After a week of studying quantum computing, I arrived at a question that no class had properly answered: how do you test a quantum algorithm? I decided to venture a few hypotheses of my own.
One of the prerequisites for testing quantum algorithms is a grasp of statistics and probability in order to select the right margin of tolerance. However, it is also necessary to understand the source of the variation being tolerated—whether it stems from the algorithm’s inherent nature or from hardware noise—because this fundamentally changes the definition of a “success” or “failure” test result.
I identified four potential differences between quantum testing and the testing methods we use today. This doesn’t mean I’m necessarily right, nor does it rule out the existence of other possibilities.
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You cannot “debug” by simply examining the state. By this, I mean you cannot inspect a variable mid-execution. Why? Because there is no such thing as a consequence-free “qubit print” in the middle of an algorithm. Measuring a qubit collapses the superposition; the very act of observation destroys the information you intended to observe.
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Many quantum algorithms are probabilistic by nature. Running the same circuit twice might yield different results—not as a bug, but as expected behavior. Consequently, in many cases, an “expected result” test makes no sense on its own; you have to test the distribution rather than a single value.
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You cannot simulate everything. This depends on the number of qubits and the specific operations the hardware performs. Once you reach a few dozen qubits (roughly 30 to 40, depending on the circuit and simulator), the exponential explosion of states renders classical simulation unfeasible—which is, in fact, the very reason quantum computing exists. Predictability fades as the problem scales up.
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Hardware noise gets conflated with logic bugs. On a real QPU, coherence issues and gate errors introduce deviations that have nothing to do with whether the algorithm itself is correct or incorrect. Distinguishing between “my algorithm is wrong” and “the hardware has noise” is, in itself, a testing challenge.
Given these differences, as I see it, we can perform six types of tests—though this doesn’t mean other possibilities don’t exist.
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Simulator testing. This is akin to unit testing, as the logic functions as a pure function: there is a known input and an exact expected output. The simulator provides a controlled environment.
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Statistical testing. The circuit is run multiple times to validate whether the distribution of results matches expectations, within a certain margin of tolerance.
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Property verification (invariants). This is similar to business rule testing. Regardless of the execution flow, the requirement must be met. In quantum testing, these involve the laws of physics: probabilities must always sum to 100%, and unitary operations must preserve properties such as reversibility and unitarity. In the classical world, this approach is known as property-based testing.
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Reference cases. Here, a small-scale instance with a known correct answer is used to verify whether the algorithm arrives at that result.
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Differential testing. The same circuit is run on different simulators, and the results are compared. If two simulators disagree, one of them has a problem.
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Separating logic from hardware. In this scenario, you test on the simulator first and only then run the circuit on actual hardware as a separate test—focusing on measuring noise-induced degradation rather than re-validating the logic.
I am still at the beginning of my journey to understand quantum computing from a QA perspective.
Does anyone have experience testing quantum algorithms, or any ideas on how we should approach testing them from a QA standpoint?