Sound and self-consistent certification of quantum computers

Quantum computers are highly sensitive to errors, so it is important to ensure they function correctly. Typically, we wish a quantum computer to correctly implement a target model given by state preparation, gate set and measurement (up to the inherent gauge freedom of such models). A quantum computer functions correctly if it is close to its target model in some relevant metric. Common protocols, such as the many randomized benchmarking protocols, do not satisfy this requirement. They only show that a quantum computer is consistent with the targeted model but not that it implements exactly that model. In technical terms, a certification protocol should be (i) complete, i.e. the targeted model passes the protocol and (ii) sound, i.e., no other model passes the protocol.

In this work, we provide a complete and sound certification protocol. It is the first protocol of this type that does not rely on computational assumptions. Our protocol is reminiscent of self-testing, but we have to rely on minimal assumptions given by the independence of the rounds of our protocol, context-independence of errors, and the underlying Hilbert space dimension.

Technically, our protocol identifies certain deterministic input-output correlations of the ideal target model, tested in each protocol round. We cover several interesting gate sets, including a universal one. A particular challenge is to recover the tensor-product structure of subsystems from the input-output relations without space-like separation. For the simplest case of a single-qubit model, we derive rigorous sampling complexity guarantees. We prove an inverse linear relation between the average gate infidelities and the protocol's sampling complexity, making our method applicable in most experimental setups.