Quantum Algorithms: bridging the gap between theory and experiment

Abstract

[eng] As more sophisticated quantum devices are being developed, the scope of what can successfully be executed on them grows. In this period, an essential piece of this process is the hand-in-hand collaboration between the hardware and software specialists. This necessitates a particular philosophy when developing algorithms to be run on quantum devices, closely incorporating both the flaws of the machines, as well as its strengths, in the workings of the algorithms themselves. This thesis showcases this research philosophy by analysing several works that encapsulate it in one or more ways. More precisely, the first part covers the unary algorithm for option pricing, along with its hardware-aware modifications for its deployment on a special purpose quantum optical chip. This first chapter already shows how a complete pipeline from algorithm to hardware deployment works. Next, this philosophy is brought to the field of quantum cryptoanalysis, where a quantum attack on hash functions is detailed using toy examples to illustrate the methods. The work illustrates how intimate knowledge of the quantum implementation gives more accurate details of their security. This part also studies how quantum annealing, an analog hardware-friendly alternative can be harnessed to solve relevant cryptographic primitives. The following chapter shows via two different works how this approach can elevate algorithms meant for further away quantum devices. One is a novel way to reformulate constrained optimization problems to boosts the performance of quantum (and classical) solvers. The other, an in-depth look into efficient interpolation techniques using the Quantum Fourier Transform that leverage signal processing knowledge to ease the uploading of classical data on a quantum register. Lastly, we describe the Qibo environment, an open-source project for development of quantum algorithms, deployment in quantum hardware, and overall connected ecosystem to bring quantum computing experiments and algorithms together. This is the backdrop where all the algorithms shown reside, and acts as the first connection between the realm of algorithms and the more down-to-earth experimental efforts.

[cat] Durant els últims anys, el camp de la computació qüàntica ha vist una expansió massiva, tant en l'àmbit teòric com en el desenvolupament de nous dispositius quàntics. En aquest moment tan efervescent, la cooperació entre els dos extrems, algoritmia i experimental, és crucial per obtenir resultats i tirar el camp endavant. Aquesta tesi és una petita finestra a aquest esforç. A través de diversos treballs, tots sota aquest rerefons d'acostament entre l'abstracte i l'aplicat, es pot distingir com les dues modalitats es compenetren i es milloren l'una a l'altra. Els treballs discutits són els següents. Primer, com a model exemplar del tema central de la tesi, es discuteix l'algoritme unari per preuar opcions financeres. Aquí es pot contemplar el camí seguit des del desenvolupament de l'algoritme fins a totes les modificacions necessàries per poder executar-lo en un xip fotònic, fet expressament per aquest projecte. Després, s'analitza com el coneixement precís d'algoritmes i dispositius pot alterar camps com el de la criptografia, on la preparació mundial davant de adveniment de la computació quàntica requereix un precís coneixement d'aquesta. Aquest punt de vista es trasllada més enllà a dos projectes a llarg termini, optimització i tractament de senyals en ordinadors quàntics. Tancant aquesta finestra es troba la discussió sobre Qibo, un sistema operatiu pensat per mediar aquestes interaccions entre els algoritmes i els ordinadors quàntics a més baix nivell.