Adiabatic graph-state quantum computation

Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any measurement-based quantum computation on a graph state with \emph{gflow} can be converted into an adiabatically driven holonomic computation, which we call \emph{adiabatic graph-state quantum computation} (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of $\dot{H}$ as well as the degree of $H$, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated.Comment: 25 pages, 3 figure

Efficient Task Replication for Fast Response Times in Parallel Computation

One typical use case of large-scale distributed computing in data centers is to decompose a computation job into many independent tasks and run them in parallel on different machines, sometimes known as the "embarrassingly parallel" computation. For this type of computation, one challenge is that the time to execute a task for each machine is inherently variable, and the overall response time is constrained by the execution time of the slowest machine. To address this issue, system designers introduce task replication, which sends the same task to multiple machines, and obtains result from the machine that finishes first. While task replication reduces response time, it usually increases resource usage. In this work, we propose a theoretical framework to analyze the trade-off between response time and resource usage. We show that, while in general, there is a tension between response time and resource usage, there exist scenarios where replicating tasks judiciously reduces completion time and resource usage simultaneously. Given the execution time distribution for machines, we investigate the conditions for a scheduling policy to achieve optimal performance trade-off, and propose efficient algorithms to search for optimal or near-optimal scheduling policies. Our analysis gives insights on when and why replication helps, which can be used to guide scheduler design in large-scale distributed computing systems.Comment: Extended version of the 2-page paper accepted to ACM SIGMETRICS 201

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula simplifies the computation of the trade-off surface, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections; v3 has correction regarding the optimizatio