The power of quantum Fourier sampling

How powerful are Quantum Computers? Despite the prevailing belief that Quantum Computers are more powerful than their classical counterparts, this remains a conjecture backed by little formal evidence. Shor's famous factoring algorithm [Shor97] gives an example of a problem that can be solved efficiently on a quantum computer with no known efficient classical algorithm. Factoring, however, is unlikely to be NP-Hard, meaning that few unexpected formal consequences would arise, should such a classical algorithm be discovered. Could it then be the case that any quantum algorithm can be simulated efficiently classically? Likewise, could it be the case that Quantum Computers can quickly solve problems much harder than factoring? If so, where does this power come from, and what classical computational resources do we need to solve the hardest problems for which there exist efficient quantum algorithms?

We make progress toward understanding these questions through studying the relationship between classical nondeterminism and quantum computing. In particular, is there a problem that can be solved efficiently on a Quantum Computer that cannot be efficiently solved using nondeterminism? In this thesis we address this problem from the perspective of sampling problems. Namely, we give evidence that approximately sampling the Quantum Fourier Transform of an efficiently computable function, while easy quantumly, is hard for any classical machine in the Polynomial Time Hierarchy. In particular, we prove the existence of a class of distributions that can be sampled efficiently by a Quantum Computer, that likely cannot be approximately sampled in randomized polynomial time with an oracle for the Polynomial Time Hierarchy.

Our work complements and generalizes the evidence given in Aaronson and Arkhipov's work [AA2013] where a different distribution with the same computational properties was given. Our result is more general than theirs, but requires a more powerful quantum sampler.

Aperiodic structures in optics and integrated optics and the transverse Bragg reflector laser

The first part of this work describes the uses of aperiodic structures in optics and integrated optics. In particular, devices are designed, fabricated, tested and analyzed which make use of a chirped grating corrugation on the surface of a dielectric waveguide. These structures can be used as input-output couplers, multiplexers and demultiplexers, and broad band filters.

Next, a theoretical analysis is made of the effects of a random statistical variation in the thicknesses of layers in a dielectric mirror on its reflectivity properties. Unlike the intentional aperiodicity introduced in the chirped gratings, the aperiodicity in the Bragg reflector mirrors is unintentional and is present to some extent in all devices made. The analysis involved in studying these problems relies heavily on the coupled mode formalism. The results are compared with computer experiments, as well as tests of actual mirrors.

The second part of this work describes a novel method for confining light in the transverse direction in an injection laser. These so-called transverse Bragg reflector lasers confine light normal to the junction plane in the active region, through reflection from an adjacent layered medium. Thus, in principle, it is possible to guide light in a dielectric layer whose index is lower than that of the surrounding material. The design, theory and testing of these diode lasers are discussed.

基于统计光学的无透镜鬼成像数值模拟与实验验证

作为量子信息领域分支的鬼成像,由于物体的像将出现在不包含物体的光路上的特点,使得这一领域的研究引人入胜。一度认为,只有基于纠缠态双光子的纠缠光源,才能实现鬼成像;但近年来的研究表明,经典热光场也能实现这一过程。从经典统计光学入手,建立了热光场的数值模型,模拟符合热光特性的光场变化、光场传播、以及物体透射函数对热光场的调制,进而从光强度起伏的关联函数中,分别重现振幅型物体和纯相位型物体的傅里叶变换图像;通过与真实实验结果的对比,表明基于统计光学原理的该数值模型所预测的实验结果,与真实的实验结果完全一致。

相位恢复算法在量子关联衍射成像中的应用研究

随着研究工作的逐步深入,目前已经利用经典热光源实现了关联衍射成像,使得该技术有望在X射线以及中子衍射成像等方面得到广泛应用。在实验利用非相干光得到物体无透镜傅里叶变换频谱的基础上,采用误差消除与输入输出恢复算法,并结合过采样理论,实现了实验所用物体透射率函数的恢复。分别得到了纯振幅物体的振幅分布函数与纯相位物体的相位分布函数。此外,还讨论了实验所得傅里叶变换频谱的噪声等因素对图像恢复结果的影响。

A two-step phase-retrieval method in Fourier-transform ghost imaging

A two-step phase-retrieval method, based on Fourier-transform ghost imaging, was demonstrated. For the complex objects, the phase-retrieval process was divided into two steps: first got the complex object's amplitude from the Fourier-transform patterns of the squared object function, then combining with the Fourier-transform patterns of the object function to get the phase. The theoretical basis of this technique is outlined, and the experimental results are presented. (C) 2008 Elsevier B.V. All rights reserved.

基于多台阶反射光栅的飞秒脉冲压缩装置

反射式光栅对是一种具有负色散性质的器件,可用于飞秒激光脉冲的压缩和展宽,具有无材料色散的优点。给出了一种基于多台阶反射光栅的脉冲压缩装置。该装置为倍密度光栅结构,由两个周期分别为40μm和20μm的四台阶反射式光栅组成。实验得到的衍射效率可以达到70%以上,输入脉冲经过两个光栅的衍射后会按原路返回,从而达到色散补偿的效果。利用此压缩装置,脉冲宽度为66.8 fs的输入脉冲压缩至接近傅里叶变换极限脉冲,即46.6 fs,由此证明只要多台阶光栅效率足够高,此装置就有可能成为不同于棱镜对进行飞秒脉冲腔内和腔外压缩的另一种途径。

自由空间激光远距离传输的地面模拟研究

根据透镜的傅里叶变换性质，提出了采用光学傅里叶变换加级联光学成像放大并结合有限口径接收的方法来实现自由空间激光光束远距离传输的实验室模拟。由此原理设计了自由空间激光远距离传输模拟装置，该装置主要由大口径、长焦距的傅里叶变换平行光管和三级成像放大镜所组成，最大等效传输距离达2.4×10^5km，可用于星间激光通信终端综合通信性能的评估，在设定的误码率下测量终端可能的通信距离，或者在设定的作用通信距离下检测通信的误码率。

Optical interconnection for neural networks by use of a self-imaging function

A grating-lens combination unit is developed to form a scaling self-transform function that can self-image on scale. Then an array of many such grating-lens units is used for the optical interconnection of a two-dimensional neural network, and experiments are carried out. We find that our idea is feasible, the optical interconnection system is simple, and optical adjustment is easy. (C) 1998 Optical Society of America.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Optical multichannel-scale range-tunable Fourier-transforming system: experiment

The authors have demonstrated the principle of a novel optical multichannel-scale range-tunable Fourier-transforming system. The experimental results show good agreement with the theoretical analysis.

Aberration measurement of projection optics in lithographic tools based on two-beam interference theory

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy. (c) 2006 Optical Society of America.

Aberration measurement of projection optics in lithographic tools by use of an alternating phase-shifting mask

As a critical dimension shrinks, the degradation in image quality caused by wavefront aberrations of projection optics in lithographic tools becomes a serious problem. It is necessary to establish a technique for a fast and accurate in situ aberration measurement. We introduce what we believe to be a novel technique for characterizing the aberrations of projection optics by using an alternating phase-shifting mask. The even aberrations, such as spherical aberration and astigmatism, and the odd aberrations, such as coma, are extracted from focus shifts and image displacements of the phase-shifted pattern, respectively. The focus shifts and the image displacements are measured by a transmission image sensor. The simulation results show that, compared with the accuracy of the previous straightforward measurement technique, the accuracy of the coma measurement increases by more than 30% and the accuracy of the spherical-aberration measurement increases by approximately 20%. (c) 2006 Optical Society of America.

Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools

As the feature size decreases, degradation of image quality caused by wavefront aberrations of projection optics in lithographic tools has become a serious problem in the low-k1 process. We propose a novel measurement technique for in situ characterizing aberrations of projection optics in lithographic tools. Considering the impact of the partial coherence illumination, we introduce a novel algorithm that accurately describes the pattern displacement and focus shift induced by aberrations. Employing the algorithm, the measurement condition is extended from three-beam interference to two-, three-, and hybrid-beam interferences. The experiments are performed to measure the aberrations of projection optics in an ArF scanner. (C) 2006 Optical Society of America.

Phase-space analysis of wavefront coding imaging systems

We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function (PSF) of an incoherant defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invarient to the defocous-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function.