Hard limits on the postselectability of optical graph states

Coherent control of large entangled graph states enables a wide variety of quantum information processing tasks, including error-corrected quantum computation. The linear optical approach offers excellent control and coherence, but today most photon sources and entangling gates---required for the construction of large graph states---are probabilistic and rely on postselection. In this work, we provide proofs and heuristics to aid experimental design using postselection. We derive a fundamental limitation on the generation of photonic qubit states using postselected entangling gates: experiments which contain a cycle of postselected gates cannot be postselected. Further, we analyse experiments that use photons from postselected photon pair sources, and lower bound the number of classes of graph state entanglement that are accessible in the non-degenerate case---graph state entanglement classes that contain a tree are are always accessible. Numerical investigation up to 9-qubits shows that the proportion of graph states that are accessible using postselection diminishes rapidly. We provide tables showing which classes are accessible for a variety of up to nine qubit resource states and sources. We also use our methods to evaluate near-term multi-photon experiments, and provide our algorithms for doing so.Comment: Our manuscript comprises 4843 words, 6 figures, 1 table, 47 references, and a supplementary material of 1741 words, 2 figures, 1 table, and a Mathematica code listin

Mapping graph state orbits under local complementation

Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay---our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement

Programmable four-photon graph states on a silicon chip

Future quantum computers require a scalable architecture on a scalable technology---one that supports millions of high-performance components. Measurement-based protocols, based on graph states, represent the state of the art in architectures for optical quantum computing. Silicon photonics offers enormous scale and proven quantum optical functionality. Here we report the first demonstration of photonic graph states on a mass-manufactured chip using four on-chip generated photons. We generate both star- and line-type graph states, implementing a basic measurement-based protocol, and measure heralded interference of the chip's four photons. We develop a model of the device and bound the dominant sources of error using Bayesian inference. The two-photon barrier, which has constrained chip-scale quantum optics, is now broken; future increases in on-chip photon number now depend solely on reducing loss, and increasing rates. This experiment, combining silicon technology with a graph-based architecture, illuminates one path to a large-scale quantum future