Abstract
Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks. In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential for reliable quantum computing. Several verification protocols for graph states have been proposed, but none of these are particularly resource efficient: multiple copies are required to extract a single state that is guaranteed to be close to the ideal one. The best protocol currently known requires O(n15) copies of the state, where n is the size of the graph state. In this paper, we construct a significantly more resource-efficient verification protocol for graph states that only requires O(n5 log n) copies. The key idea is to employ Serfling’s bound, which is a probability inequality in classical statistics. Utilizing Serfling’s bound also enables us to generalize our protocol for qudit and continuous-variable graph states. Constructing a resource-efficient verification protocol for them is non-trivial. For example, the previous verification protocols for qubit graph states that use the quantum de Finetti theorem cannot be generalized to qudit and continuous-variable graph states without tremendously increasing the resource overhead. This is because the overhead caused by the quantum de Finetti theorem depends on the local dimension. On the other hand, in our protocol, the resource overhead is independent of the local dimension, and therefore generalizing to qudit or continuous-variable graph states does not increase the overhead. The flexibility of Serfling’s bound also makes our protocol robust: our protocol accepts slightly noisy but still useful graph states.
Highlights
The verification of quantum states plays an important role in ensuring the integrity of a number of quantum technologies including quantum computing, quantum cryptography, and quantum simulations
With respect to CV weighted hypergraph states, we review their definitions and construct a stabilizer test
After that, based on the stabilizer tests, we propose our verification protocol, which is the main result of this paper
Summary
The verification of quantum states plays an important role in ensuring the integrity of a number of quantum technologies including quantum computing, quantum cryptography, and quantum simulations. Several verification protocols, including ones based on selftesting, have been proposed for graph states.[11,12,13,14,15,16,17,18] all the previous protocols encounter at least one of the three problems described below They are not resource efficient, i.e., Ntotal is large. 11,12 use the idea of the quantum de Finetti theorem[19] to make ρB close to independent and identically distributed (i.i.d.) copies of a single fixed state, but this comes at the cost of large overhead Such protocols require Ntotal = O(n21) to complete the verification. Tate extremely large quantum processors due to the relatively large key sizes necessary for cryptographic security
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