Aram Harrow - Quantum Monte Carlo vs Tunneling in Adiabatic Optimization

In this talk I'll present a quantum algorithm for solving semidefinite programs (SDPs). It has worst case running time O((nm)^1/2 r), with n and r the dimension and sparsity of the input matrices, respectively, and m the number of constraints. In contrast any classical method requires at least Omega(nm) time to solve the problem. I'll discuss how for some instances the algorithm might offer even exponential speed-ups, if the quantum Gibbs states of Hamiltonians given by linear combinations of the input matrices of the SDP can be prepared efficiently on a quantum computer. As an application I'll show how the Goemans-Williamson SDP for approximating max-cut can be solved quantum-mechanically in time linear in the number of vertices of the graph. This gives a speed-up over the best classical method, which requires linear time in the number of edges. Based on joint work with Krysta Svore Dmitri Maslov How to program a trapped ions quantum computer Abstract: In this talk, I will discuss ion-trap quantum computing, and specifically, how to program and efficiently compile physical-level experiments for an ion-trap quantum machine developed by the researchers at the University of Maryland. I will report a complete strategy, consisting of the full set of steps taken to sequentially decompose a quantum algorithm/circuit from a higher-level specification into progressively lower-level specifications until physical-level specification is reached. The different stages are structured so as to best assist with the optimization of the resulting physical-level implementation and while taking into account numerous optimization criteria, including minimizing the number of expensive two-qubit gates, minimizing the number of less expensive single-qubit gates, optimizing the runtime, minimizing the overall circuit error, as well as optimizing classical control sequences. There will furthermore be two types of compilation discussed: first allows executing a given quantum algorithm most efficiently via selecting physical qubits to work with, and second provides a fully parametrized physical-level circuit that can be executed on any set of qubits (moreover, sometimes, those parametrized circuits have free parameters that can be set arbitrarily). I will illustrate the efficiency of this compilation approach via comparing to the previously known results. I will also report the results of some physical-level experiments, providing a strong motivation for further study of and the development of tools for the trapped ions quantum information processing platform. In this talk, I will discuss ion-trap quantum computing, and specifically, how to program and efficiently compile physical-level experiments for an ion-trap quantum machine developed by the researchers at the University of Maryland. I will report a complete strategy, consisting of the full set of steps taken to sequentially decompose a quantum algorithm/circuit from a higher-level specification into progressively lower-level specifications until physical-level specification is reached. The different stages are structured so as to best assist with the optimization of the resulting physical-level implementation and while taking into account numerous optimization criteria, including minimizing the number of expensive two-qubit gates, minimizing the number of less expensive single-qubit gates, optimizing the runtime, minimizing the overall circuit error, as well as optimizing classical control sequences. There will furthermore be two types of compilation discussed: first allows executing a given quantum algorithm most efficiently via selecting physical qubits to work with, and second provides a fully parametrized physical-level circuit that can be executed on any set of qubits (moreover, sometimes, those parametrized circuits have free parameters that can be set arbitrarily). I will illustrate the efficiency of this compilation approach via comparing to the previously known results. I will also report the results of some physical-level experiments, providing a strong motivation for further study of and the development of tools for the trapped ions quantum information processing platform.