Quantum Information Science

Quantum computing is implicated as a next-generation solution to supplement traditional von Neumann architectures in an era of post-Moores law computing. As classical computational infrastructure becomes more limited, quantum platforms offer expandability in terms of scale, energy-consumption, and native three-dimensional problem modeling. Quantum information science is a multidisciplinary field drawing from physics, mathematics, computer science, and photonics. Quantum systems are expressed with the properties of superposition and entanglement, evolved indirectly with operators (ladder operators, master equations, neural operators, and quantum walks), and transmitted (via quantum teleportation) with entanglement generation, operator size manipulation, and error correction protocols. This paper discusses emerging applications in quantum cryptography, quantum machine learning, quantum finance, quantum neuroscience, quantum networks, and quantum error correction

Detecting quantum speedup of random walks with machine learning

We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and convolutional neural networks) for identifying linear, cyclic, and random graphs that yield quantum speedups in terms of the hitting time for reaching a target node after starting in another node of the graph. Our results indicate that carefully building the data set for training can improve the performance of the neural networks, but all architectures we test struggle to classify large random graphs and generalize from training on one graph size to testing on another. If classification accuracy can be improved further, valuable insights about quantum advantage may be gleaned from these neural networks, not only for random walks, but more generally for quantum computing and quantum transport.Comment: 15 pages, 8 figure

Quantum walk on a graph of spins: magnetism and entanglement

We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a one dimensional lattice, to investigate its magnetic and entanglement properties. In the continuum limit, we recover a Landau-Lifshitz equation that describes the precession of spins. A rich dynamics is observed, with regimes of particle propagation and localization, together with spin oscillations and relaxation. Entanglement of the asymptotic states follows a volume law for most parameters (the coin rotation angle and the particle-spin coupling).Comment: 50 pages, 114 references, 30 figure

How to Compute Using Quantum Walks

Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walks in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied. In this paper, I explain the relationship between quantum walks as models and quantum walks as computational tools, and give some examples of their application in both contexts.Comment: In Proceedings QSQW 2020, arXiv:2004.0106