Search results for "quantum walk"
showing 10 items of 70 documents
Dynamical learning of a photonics quantum-state engineering process
2021
Abstract. Experimental engineering of high-dimensional quantum states is a crucial task for several quantum information protocols. However, a high degree of precision in the characterization of the noisy experimental apparatus is required to apply existing quantum-state engineering protocols. This is often lacking in practical scenarios, affecting the quality of the engineered states. We implement, experimentally, an automated adaptive optimization protocol to engineer photonic orbital angular momentum (OAM) states. The protocol, given a target output state, performs an online estimation of the quality of the currently produced states, relying on output measurement statistics, and determine…
Quantum Walk and Wigner function on a lattice
2014
201 páginas. Tesis Doctoral del Departamento de Física Teórica de la Universidad de Valencia y del Instituto de Física Corpuscular (IFIC).
Quantum state engineering using one-dimensional discrete-time quantum walks
2017
Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin, and providing …
Machine Learning-Based Classification of Vector Vortex Beams.
2020
Structured light is attracting significant attention for its diverse applications in both classical and quantum optics. The so-called vector vortex beams display peculiar properties in both contexts due to the non-trivial correlations between optical polarization and orbital angular momentum. Here we demonstrate a new, flexible experimental approach to the classification of vortex vector beams. We first describe a platform for generating arbitrary complex vector vortex beams inspired to photonic quantum walks. We then exploit recent machine learning methods -- namely convolutional neural networks and principal component analysis -- to recognize and classify specific polarization patterns. O…
Quantum Walks on Two-Dimensional Grids with Multiple Marked Locations
2016
The running time of a quantum walk search algorithm depends on both the structure of the search space graph and the configuration of marked locations. While the first dependence has been studied in a number of papers, the second dependence remains mostly unstudied. We study search by quantum walks on the two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. The original paper analyses one and two marked locations only. We move beyond two marked locations and study the behaviour of the algorithm for an arbitrary configuration of marked locations. In this paper, we prove two results showing the importance of how the marked locations are arranged. First, we present tw…
Exceptional Configurations of Quantum Walks with Grover’s Coin
2016
We study search by quantum walk on a two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. We show what the most natural coin transformation -- Grover's diffusion transformation -- has a wide class of exceptional configurations of marked locations, for which the probability of finding any of the marked locations does not grow over time. This extends the class of known exceptional configurations; until now the only known such configuration was the "diagonal construction" by [AR08].
Search by Quantum Walks on Two-Dimensional Grid without Amplitude Amplification
2013
We study search by quantum walk on a finite two dimensional grid. The algorithm of Ambainis, Kempe, Rivosh [AKR05] uses \(O(\sqrt{N \log{N}})\) steps and finds a marked location with probability O(1 / logN) for grid of size \(\sqrt{N} \times \sqrt{N}\). This probability is small, thus [AKR05] needs amplitude amplification to get Θ(1) probability. The amplitude amplification adds an additional \(O(\sqrt{\log{N}})\) factor to the number of steps, making it \(O(\sqrt{N} \log{N})\).
Almost Tight Bound for the Union of Fat Tetrahedra in Three Dimensions
2007
For any AND-OR formula of size N, there exists a bounded-error N1/2+o(1)-time quantum algorithm, based on a discrete-time quantum walk, that evaluates this formula on a black-box input. Balanced, or "approximately balanced," formulas can be evaluated in O(radicN) queries, which is optimal. It follows that the (2-o(1))th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy.
Span programs for functions with constant-sized 1-certificates
2012
Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the element distinctness, the triangle and other problems. The usual way to solve them is by quantum walk on the Johnson graph. We propose a solution for the same problems using span programs. The span program is a computational model equivalent to the quantum query algorithm in its strength, and yet very different in its outfit. We prove the power of our approach by designing a quantum algorithm for the triangle problem with query complexity O(n35/27) that is better than O(n13/10) of the best p…
Quantum Identification of Boolean Oracles
2004
The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is \(O(\sqrt{N {\rm log} M {\rm log} N}{\rm log log} M)\) for anyS such that M = |S| > N, which is better than the obvious bound N if M \(< 2^{N/log^3 N}\). (ii) It is \…