Entangling quantum gates using extended Hilbert space

Peter P. Rohde, Geoff J. Pryde, J. L. O Brien

Joseph Ho, Raj B. Patel, Timothy C. Ralph +1 more

We implement a four-qubit controlled-shift gate leveraging photon entanglement in extended Hilbert spaces and observe Psuccess = 0.25. This enables our demonstration of a DQC1 protocol and the quantum phase estimation algorithm featuring a multi-qubit unitary.

Schmidt-Kaler, Haffiier, Riebe +7 more

Yuting Huang, Lin Chen

Graph states are intuitive representations of quantum states that are useful in quantum computing and quantum information. In this paper, we investigate the role of entanglement and local unitary equivalence in quantum computing through graph states in high-dimensional Hilbert spaces. We introduce bipartitions on the vertices sets and demonstrate separability and local unitary equivalence based on different choices of partitions. By performing the two-qubit controlled phase shift gates on various pairs of multiqubit system, one can generate a genuinely entangled graph state based on simple connected graphs. We extend 2-dimensional Hilbert spaces to higher and mixed dimensions and examine pure quantum states that cannot be separated by any bipartition. In addition, we generalize the analysis on classification of local unitary equivalence beyond the controlled-Z gates to controlled phase gates. By examining graphs constructed from bipartition graphs, we have shown that graphs with identical bipartition subgraph structures are local unitary equivalent.

B. P. Lanyon, Marco Barbieri, Marcelo Pereira de Almeida +7 more

Ronak M Soni, Sandip P. Trivedi

A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories. We extend the electric centre definition of Casini, Huerta and Rosabal to the Non-Abelian case and find that it differs in an important term. We also find that the entanglement entropy does not agree with the maximum number of Bell pairs that can be extracted by the processes of entanglement distillation or dilution, and give protocols which achieve the maximum bound. Finally, we compute the topological entanglement entropy which follows from the extended Hilbert space definition and show that it correctly reproduces the total quantum dimension in a class of Toric code models based on Non-Abelian discrete groups.