We experimentally create complete classes of twenty-nine four-qubit hypergraph states on a programmable silicon-photonic chip, and implement measurement-based protocols on hypergraph states, which provide an alternative resource for quantum information processing.
Complex entangled states are the key resources for measurement-based quantum computations, which is realised by performing a sequence of measurements on initially entangled qubits. Executable quantum algorithms in the graph-state quantum computing model are determined by the entanglement structure and the connectivity of entangled qubits. By generalisation from graph-type entanglement in which only the nearest qubits interact to a new type of hypergraph entanglement in which any subset of qubits can be arbitrarily entangled via hyperedges, hypergraph states represent more general resource states that allow arbitrary quantum computation with Pauli universality. Here we report experimental preparation, certification and processing of complete categories of four-qubit hypergraph states under the principle of local unitary equivalence, on a fully reprogrammable silicon-photonic quantum chip. Genuine multipartite entanglement for hypergraph states is certificated by the characterisation of entanglement witness, and the observation of violations of Mermin inequalities without any closure of distance or detection loopholes. A basic measurement-based protocol and an efficient resource state verification by color-encoding stabilizers are implemented with local Pauli measurement to benchmark the building blocks for hypergraph-state quantum computation. Our work prototypes hypergraph entanglement as a general resource for quantum information processing.
Multidimensional entangled photon states represent a useful resource for large-scale quantum communication networks. By leveraging multiple degrees of freedom (DoFs) of photons, the dimensionality of the Hilbert space can be expanded without increasing the number of particles, enhancing the efficiency of quantum information processing. Specifically, hyperentanglement, i.e. simultaneous entanglement across multiple DoFs, is robust against decoherence, thus providing strengthened performance in noisy quantum communication protocols with respect to n-photon quantum states [1].
Integrated photonics provides a scalable platform for quantum information processing. In this context, measurement-based quantum computing (MBQC) offers an attractive approach in which quantum computation is realised by adaptive measurements on highly entangled graph states, circumventing the need for deterministic photon-photon interactions. Here, we demonstrate MBQC on an integrated silicon photonic chip capable of generating photonic graph states with up to four qubits. We achieve fidelities of FStar=(83.5±1.8)% and FLin=(75.6±1.1)% for four-photon star and linear graph states, respectively. We use these resource states to implement MBQC-based single- and two-qubit gates and to demonstrate Grover's search algorithm and the Deutsch-Jozsa algorithm. These results establish the feasibility of reconfigurable four-photon MBQC on an integrated photonic platform and provide a foundation for future larger-scale implementations.