Sound certification of memory-bounded quantum computers

Abstract: The rapid advancement of quantum hardware calls for the development of reliable methods to certify its correct functioning. However, existing certification tests often fall short: they either rely on flawless state preparation and measurement or lack soundness guarantees, meaning that they do not rule out incorrect implementations of the target operations by a quantum device. We introduce an approach, which we call quantum system quizzing, for the certification of quantum gates in a practical server-user scenario, where a classical user tests the results of quantum computations performed by a quantum server. Importantly, this approach does not require trusted state preparation and measurement and is thus inherently free from the associated systematic errors. For a wide range of relevant gate sets, including a universal one, we prove our certification protocol to be sound, i.e., it rejects any quantum model other than the targeted one, assuming a bound on the total memory of the quantum computer. A major technical challenge that we are first to resolve in the memory-bounded single-device setup is recovering the tensor product structure of a multi-qubit system. Our protocol is platform-agnostic, introducing a new paradigm for benchmarking diverse quantum architectures.