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.

The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary t-design is designed to tackle this challenge in an efficient way, yet constructions to date rely on heavy constraints. In particular, they are composed of ensembles of unitaries which, for technical reasons, must contain inverses and whose entries are algebraic. In this work, we reduce the requirements for generating an ε-approximate unitary t-design. To do so, we first construct a specific n-qubit random quantum circuit composed of a sequence of, randomly chosen, 2-qubit gates, chosen from a set of unitaries which is approximately universal on U (4), yet need not contain unitaries and their inverses, nor are in general composed of unitaries whose entries are algebraic; dubbed relaxed seed. We then show that this relaxed seed, when used as a basis for our construction, gives rise to an ε-approximate unitary t-design efficiently, where the depth of our random circuit scales as poly(n, t, log(1/ε)), thereby overcoming the two requirements which limited previous constructions. We suspect the result found here is not optimal, and can be improved. Particularly because the number of gates in the relaxed seeds introduced here grows with n and t. We conjecture that constant sized seeds such as those in [2,13] are sufficient.

Hollow-core concrete blocks constitute the main method of construction for vertical walls in Lebanon where almost all walls are masonry and use the same block shape. The detailed investigation of the main parameters involved in the heat transfer in these blocks is thus of great importance for analyzing and understanding them and providing recommendations for their improvement.This paper offers an experimental and numerical analysis of heat performance the Lebanese concrete hollow block. After validating the numerical model by comparing it to experimental results, a deep and detailed analysis is done for understanding the complexity of heat transfer phenomena inside the block. Then a parametric study is performed to understand the effect of various parameters on the overall thermal resistance of the block, these parameters include the concrete solid mixture, the cavities infill material, and the geometry configuration of the block.

Hollow concrete blocks can be thermally improved either by modifying their cavities shapes or by adding insulation materials into these cavities. It is also possible to improve the thermal conductivity of concrete solid matrix by incorporating some materials to its composition like recycled solid wastes for example. This paper offers a solid and comprehensive study for thermally improved hollow blocks through a case study from the Lebanese context and provides a scientific basis for improving the thermal performance of these blocks. The effect of adding EPS (expanded polystyrene) beads to the concrete solid mixture was investigated in this work through numerical and experimental approaches. The experimental and numerical results were in good agreement and the potential thermal improvement by adding EPS beads to concrete mixture was examined on both numerical and experimental levels.The numerical results for the 3D model allow the visualization of the heat flux and temperature distribution in the block as well as the air velocity and convective heat exchanges inside the cavities of the block.The results showed that the block thermal resistance can almost double by adding 18g of polystyrene bead the its concrete mixture.