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- Frédéric Magniez, Ashwin Nayak, Jérémie Roland, Miklos Santha
- SIAM J. Comput.
- 2007

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)

- Hari Krovi, Frédéric Magniez, Maris Ozols, Jérémie Roland
- Algorithmica
- 2015

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)

- Iordanis Kerenidis, Sophie Laplante, Virginie Lerays, Jérémie Roland, David Xiao
- 2012 IEEE 53rd Annual Symposium on Foundations of…
- 2012

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)

- Boris Altshuler, Hari Krovi, Jérémie Roland
- Proceedings of the National Academy of Sciences…
- 2010

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)

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover's algorithm. In this paper, we… (More)

- Julien Degorre, Marc Kaplan, Sophie Laplante, Jérémie Roland
- MFCS
- 2009

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)

- Maris Ozols, Martin Rötteler, Jérémie Roland
- ITCS
- 2012

Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann [1951] and has many applications in classical computing. We define a quantum analogue of rejection sampling: given a black box producing a coherent superposition of… (More)

- Andris Ambainis, Loïck Magnin, Martin Rötteler, Jérémie Roland
- 2011 IEEE 26th Annual Conference on Computational…
- 2010

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)

- Troy Lee, Jérémie Roland
- computational complexity
- 2012

We show that quantum query complexity satisfies a strong direct product theorem. This means that computing k copies of a function with fewer than k times the quantum queries needed to compute one copy of the function implies that the overall success probability will be exponentially small in k. For a boolean function f, we also show an XOR lemma—computing… (More)

- Hari Krovi, Frédéric Magniez, Maris Ozols, Jérémie Roland
- ICALP
- 2010

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)