Jérémie Roland

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We propose a new method for designing quantum search algorithms forfinding a "marked" element in the state space of a classical Markovchain. The algorithm is based on a quantum walk à la Szegedy [25] that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantumwalk in order to implement an(More)
We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it lower bounds the information complexity of any function. Our relaxed partition bound subsumes all norm based methods (e.g.(More)
Abstract Adiabatic quantum optimization has attracted a lot of attention because small scale simulations gave hope that it would allow to solve NP-complete problems efficiently. Later, negative results proved the existence of specifically designed hard instances where adiabatic optimization requires exponential time. In spite of this, there was still hope(More)
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $$M$$ M consists of a single vertex, the number of steps of the quantum walk is quadratically smaller than the classical hitting time $${{\mathrm{HT}}}(P,M)$$ HT ( P , M ) of any reversible random walk $$P$$ P(More)
We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target quantum states. There has been hope for quite some time that quantum state generation might be a route to tackle the(More)
Understanding NP-complete problems is a central topic in computer science (NP stands for nondeterministic polynomial time). This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer. The efficiency of this approach is limited by small spectral gaps(More)
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an input x, Bob gets an input y, and their goal is to each(More)
We solve an open problem of constructing a quantum walk that not only detects but also finds marked vertices in a graph. The number of steps of our quantum walk is quadratically smaller than the classical hitting time of any reversible random walk P on the graph. Our approach is new, simpler and more general than previous ones. We introduce a notion of(More)