Quantum pattern matching fast on average

The $d$-dimensional pattern matching problem is to find an occurrence of a pattern of length $m \times \dots \times m$ within a text of length $n \times \dots \times n$, with $n \ge m$. This task models various problems in text and image processing, among other application areas. This work describes a quantum algorithm which solves the pattern matching problem for random patterns and texts in time $\widetilde{O}((n/m)^{d/2} 2^{O(d^{3/2}\sqrt{\log m})})$. For large $m$ this is super-polynomially faster than the best possible classical algorithm, which requires time $\widetilde{\Omega}( (n/m)^d + n^{d/2} )$. The algorithm is based on the use of a quantum subroutine for finding hidden shifts in $d$ dimensions, which is a variant of algorithms proposed by Kuperberg.Comment: 22 pages, 2 figures; v3: further minor changes, essentially published versio

Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization

Many artificial intelligence (AI) problems naturally map to NP-hard optimization problems. This has the interesting consequence that enabling human-level capability in machines often requires systems that can handle formally intractable problems. This issue can sometimes (but possibly not always) be resolved by building special-purpose heuristic algorithms, tailored to the problem in question. Because of the continued difficulties in automating certain tasks that are natural for humans, there remains a strong motivation for AI researchers to investigate and apply new algorithms and techniques to hard AI problems. Recently a novel class of relevant algorithms that require quantum mechanical hardware have been proposed. These algorithms, referred to as quantum adiabatic algorithms, represent a new approach to designing both complete and heuristic solvers for NP-hard optimization problems. In this work we describe how to formulate image recognition, which is a canonical NP-hard AI problem, as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The QUBO format corresponds to the input format required for D-Wave superconducting adiabatic quantum computing (AQC) processors.Comment: 7 pages, 3 figure

Strategy for reliable strain measurement in InAs/GaAs materials from high-resolution Z-contrast STEM images

Geometric phase analysis (GPA), a fast and simple Fourier space method for strain analysis, can give useful information on accumulated strain and defect propagation in multiple layers of semiconductors, including quantum dot materials. In this work, GPA has been applied to high resolution Z-contrast scanning transmission electron microscopy (STEM) images. Strain maps determined from different g vectors of these images are compared to each other, in order to analyze and assess the GPA technique in terms of accuracy. The SmartAlign tool has been used to improve the STEM image quality getting more reliable results. Strain maps from template matching as a real space approach are compared with strain maps from GPA, and it is discussed that a real space analysis is a better approach than GPA for aberration corrected STEM images

Squeezed Light and Entangled Images from Four-Wave-Mixing in Hot Rubidium Vapor

Entangled multi-spatial-mode fields have interesting applications in quantum information, such as parallel quantum information protocols, quantum computing, and quantum imaging. We study the use of a nondegenerate four-wave mixing process in rubidium vapor at 795 nm to demonstrate generation of quantum-entangled images. Owing to the lack of an optical resonator cavity, the four-wave mixing scheme generates inherently multi-spatial-mode output fields. We have verified the presence of entanglement between the multi-mode beams by analyzing the amplitude difference and the phase sum noise using a dual homodyne detection scheme, measuring more than 4 dB of squeezing in both cases. This paper will discuss the quantum properties of amplifiers based on four-wave-mixing, along with the multi mode properties of such devices.Comment: 11 pages, 8 figures. SPIE Optics and Photonics 2008 proceeding (San Diego, CA

EPR-based ghost imaging using a single-photon-sensitive camera

Correlated photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments, two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated photon ghost imaging experiments have scanned a single-pixel detector through the field of view to obtain spatial information. However, scanning leads to poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work, we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far field of the photon pair source, taking advantage of the Einstein–Podolsky–Rosen-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing