Protocols for quantum information processing on graph states

Massimiliano Proietti

Sophia E. Economou

Photonic graph states constitute important resources in quantum information processing. They are used in measurement-based and fusion-based quantum computing and in all-photonic repeaters for quantum networks. However, generating such highly entangled states is challenging due to the fact that photons do not interact with each other. We propose a protocol for generating arbitrary graph states using matter qubits as quantum emitters. Our approach guarantees the minimal number of emitters and provides in polynomial time the quantum circuit for the graph state generation (which includes the non-unitary process of photon emission). We find that the quantum circuit depth for general graphs also scale polynomially with system size.

Abbas Al-Shimary

Qingshan Xu, Xiaoqing Tan, Rui Huang +1 more

Verifiable blind quantum computation provides a cloud scenario for scalable quantum information processing. However, constructing one resource-efficient verification protocol is still an open problem. In this paper, the context of verification we consider is the measurement-based model, in which the client receives the graph state prepared by the server and performs single-qubit measurements on it to drive the computation. We first utilize three entanglement witnesses to estimate the fidelity of the prepared graph state. Applying entanglement witnesses to design the test phase, we propose verification protocols. Our protocol requires overhead in terms of copies of the graph state that scales as $O({n}^{2}logn)$, where $n$ is the number of qubits of the graph state. Furthermore, the soundness of our protocol is improved. The advantages of our protocol are derived from the fact that each entanglement witness can be implemented by the client with a fixed number of measurement settings.

Mehdi Mhalla, Mio Murao, Simon Perdrix +2 more

Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a structural characterization of the graph states that can be used for quantum information processing. The existence of a gflow (generalized flow) is known to be a requirement for open graphs (graph, input set and output set) to perform uniformly and strongly deterministic computations. We weaken the gflow conditions to define two new more general types of MBQC: uniform equiprobability and constant probability. These classes can be useful from a cryptographic and information point of view because even though we can not do a deterministic computation in general we can preserve the information and transfer it perfectly from the inputs to the outputs. We derive simple graph characterizations for these classes and prove that the deterministic and uniform equiprobability classes collapse when the cardinalities of inputs and outputs are the same. We also prove the reversibility of gflow in that case. The new graphical characterizations allow us to go from open graphs to graphs in general and to consider this question: given a graph with no inputs or outputs fixed, which vertices can be chosen as input and output for quantum information processing? We present a characterization of the sets of possible inputs and ouputs for the equiprobability class, which is also valid for deterministic computations with inputs and ouputs of the same cardinality.

Damian Markham