Self-testing of Quantum Circuits

Abstract

We prove that a quantum circuit together with measurement apparatuses and EPR sources can be fully verified without any reference to some other trusted set of quantum devices. Our main assumption is that the physical system we are working with consists of several identifiable sub-systems, on which we can apply some given gates locally.To achieve our goal we define the notions of simulation and equivalence. The concept of simulation refers to producing the correct probabilities when measuring physical systems. To enable the efficient testing of the composition of quantum operations, we introduce the notion of equivalence. Unlike simulation, which refers to measured quantities (i.e., probabilities of outcomes), equivalence relates mathematical objects like states, subspaces or gates.Using these two concepts, we prove that if a system satisfies some simulation conditions, then it is equivalent to the one it is purposed to implement. In addition, with our formalism, we can show that these statements are robust, and the degree of robustness can be made explicit (unlike the robustness results of [DMMS00]). In particular, we also prove the robustness of the EPR Test [MY98]. Finally, we design a test for any quantum circuit whose complexity is linear in the number of gates and qubits, and polynomial in the required precision.

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“…In follow-up work, Magniez et al [121] study self-testing of quantum circuits together with measurement apparatuses and sources of EPR-pairs, introducing notions of simulation and equivalence.…”

“…McKague et al [127] give a more general framework for bipartite robust self-testing that subsumes the CHSH inequality, the Mayers-Yao self-test (simplifying [121]), as well as others. Yang and Navascués [170] give robust self-tests for any entangled two-qubit states, not just maximally entangled ones; the noise-resistance was further improved in [25].…”

Device-independent state estimation based on Bell’s inequalities

“…It is also related to the concept of "dimension witness": sufficient violation of some Bell inequalities can guarantee that the quantum state has a minimum dimension [4,5,6]. One possible application of the present work could be to devise improved self testing of quantum computers [7,8].…”

Quantum cryptography beyond quantum key distribution

“…In fact, on the topic of self-testing quantum devices [163,174,175,178], Reichardt, Unger and Vazirani have shown a strong robustness result [197] in the sense that being close to winning the CHSH-game with optimal probability implies that the players must essentially be in possession of a state which is close to an EPR pair. This is an extremely powerful result which has various applications.…”