Quantum speedup for active learning agents

Can quantum mechanics help us in building intelligent robots and agents? One of the defining characteristics of intelligent behavior is the capacity to learn from experience. However, a major bottleneck for agents to learn in any real-life situation is the size and complexity of the corresponding task environment. Owing to, e.g., a large space of possible strategies, learning is typically slow. Even for a moderate task environment, it may simply take too long to rationally respond to a given situation. If the environment is impatient, allowing only a certain time for a response, an agent may then be unable to cope with the situation and to learn at all. Here we show that quantum physics can help and provide a significant speed-up for active learning as a genuine problem of artificial intelligence. We introduce a large class of quantum learning agents for which we show a quadratic boost in their active learning efficiency over their classical analogues. This result will be particularly relevant for applications involving complex task environments.Comment: Minor updates, 14 pages, 3 figure

Decoherence in quantum walks - a review

The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small amounts of decoherence in a quantum walk on the line can produce more uniform spreading (a top-hat distribution), without losing the quantum speed up. This paper reviews the work on decoherence, and more generally on non-unitary evolution, in quantum walks and suggests what future questions might prove interesting to pursue in this area.Comment: 52 pages, invited review, v2 & v3 updates to include significant work since first posted and corrections from comments received; some non-trivial typos fixed. Comments now limited to changes that can be applied at proof stag

SQUWALS: A Szegedy QUantum WALks Simulator

Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a classical simulator. However, the current simulation algorithms require a great deal of memory due to the particular formulation of this quantum walk. In this paper we propose a memory-saving algorithm that scales as $\mathcal{O}(N^2)$ with the size $N$ of the graph. We provide additional procedures for simulating Szegedy's quantum walk over mixed states and also the Semiclassical Szegedy walk. With these techniques we have built a classical simulator in Python called SQUWALS. We show that our simulator scales as $\mathcal{O}(N^2)$ in both time and memory resources. This package provides some high-level applications for algorithms based on Szegedy's quantum walk, as for example the quantum PageRank.Comment: RevTex 4.2, 16 pages, 9 color figure