This lecture starts the next paradigm for quantum algorithms: quantum walks, which mimic random walks in a way that allows speeding up the algorithmic applications, including sampling from complicated distributions and searching with spatial constraints.
How rapidly does order give way to randomness, and can quantum coherence accelerate this process? We address these questions through the paradigmatic problem of card shuffling, formulated as a random walk on the symmetric group $S_n$. We first recast the random-transposition walk studied by Diaconis and Shahshahani, as...
Feng He, Arthur Hutsalyuk, G. Mussardo et al.· 0 citations
Quantum walks are the quantum analogues of classical random walks or Markov chains. They are universal models of quantum computing, and they underpin a variety of quantum algorithms. We prove that a continuous-time quantum walk effected by a generalized Laplacian, which can arise in spin chains, can solve a computation...
The emergence of Quantum Computing has resulted in a slate of quantum algorithms that can solve a wide variety of algorithmic and computational problems faster than any classical computer. How we can apply these various quantum algorithms to practical problems in computing is still an ongoing area of research. In this...
Kahlil Dozier, Justin Beltran, Hugo Matousek et al.· ACM SIGMETRICS Performance E...· 0 citations
This thesis investigates two central challenges for quantum computing: identifying when quantum annealing can offer a computational advantage, and developing effective methods to control realistic quantum systems. It establishes complexity bounds for an adiabatic algorithm for combinatorial optimization, showing a univ...
Aarón Villanueva· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
