Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements leads to the generation of ensembles of random unitaries, where each random unitary is identified with a string of possible measurement results. We show that repeating an MB scheme an efficient number of times, on a simple graph state, with measurements at fixed angles and no feed-forward corrections, produces a random unitary ensemble that is an ε-approximate t-design on n-qubits. Unlike previous constructions, the graph is regular and is also a universal resource for measurement based quantum computing, closely related to the brickwork state.

At its core a t-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics.We construct new families of quantum circuits on n-qubits giving rise to ε-approximate unitary tdesigns efficiently in O(n 3 t 12 ) depth. These quantum circuits are based on a relaxation of technical requirements in previous constructions. In particular, the construction of circuits which give efficient approximate t-designs by Brandao, Harrow and Horodecki [11] required choosing gates from ensembles which contained inverses for all elements, and that the entries of the unitaries are algebraic. We reduce these requirements, to sets that contain elements without inverses in the set, and non-algebraic entries, which we dub partially invertible universal sets.We then adapt this circuit construction to the framework of measurement based quantum computation (MBQC) and give new explicit examples of n-qubit graph states with fixed assignments of measurements (graph gadgets) giving rise to unitary t-designs based on partially invertible universal sets, in a natural way.We further show that these graph gadgets demonstrate a quantum speedup, up to standard complexity theoretic conjectures. We provide numerical and analytical evidence that almost any assignment of fixed measurement angles on an n-qubit cluster state give efficient t-designs and demonstrate a quantum speedup.

Compiled 10 février 2018We have experimentally implemented the distribution of photon pairs produced by spontaneous parametric down conversion through telecom dense wavelength division multiplexing filters. Using the measured counts and coincidences between symmetric channels, we evaluate the maximum fringe visibility that can be obtained with polarization entangled photons and compare different filter technologies. c 2018 Optical Society of America OCIS codes: 060.5565, 060.2340, 060.4265.In order to be truly useful for technological applications, future quantum communication networks will require a large number of high quality entangled photon pair sources. An attractive way to reduce the associated cost is to use the wide spectrum produced by spontaneous parametric down conversion (SPDC) in combination with standard off-the-shelf dense wavelength division multiplexing (DWDM) filters to distribute nondegenerate photon pairs to a large number of users. It is then an important task to test photon pair sources in a WDM environment with various types of filters, in order to unveil filter characteristics that are necessary to obtain sources featuring high visibility while maintaining a useful brightness. Among previous works based on the idea of DWDM distribution of photon pairs [1-4], Lim et al [1] performed a proof-of-principle experiment using a dichroic mirror to separate the two photons of the pair and tunable filters on each channel to simulate the demultiplexing operation. Furthermore, a wavelength selective switch, based on arrayed waveguide grating technology, was tested in [2]. Frequency dependent losses were taken into account to explain the experimental coincidence probabilities, however the system required a different tuning of the pump for distribution over the various channel pairs, hence it could not be simultaneously multi-user in that configuration. In this work, we compare various DWDM filters with respect to the quality of a photon pair source with the ultimate goal of determining the filter performances required for quantum communication applications. The WDM photon pair distribution device is based on the energy conservation condition of spontaneous parametric down conversion : if ω p is the pump frequency, then the frequencies of the signal and idler photons ω s and ω i are symmetric with respect to ω p /2. The idea then is to tune the degeneracy frequency ω p /2 to the central frequency of the filter, so that the signal and idler photons can be transmitted by symmetric channel pairs. The users that will receive the two photons of an entangled pair can be determined by using a standard telecom switching device. If we wanted each user to receive a given channel permanently, then distributing entanglement, for instance, to Alice (ω A ) and Bob (ω B ), would mean tuning the pump frequency to ω A + ω B .Commercial optical demultiplexing filters are based on three main technologies [5] : (a) dielectric thin-film filters (DTF), consisting of Fabry-Perot cavities and quarter wavelength layers ; thes...