Aléatoire pour le traitement de l'information quantique

Randomness for quantum information processing

• Auteur / Autrice : Rawad Mezher
• Direction : Damian J. H. Markham, Joseph Dgheim
• Type : Thèse de doctorat
• Discipline(s) : Informatique
• Date : Soutenance le 15/11/2019
• Etablissement(s) : Sorbonne université en cotutelle avec Université Libanaise
• Ecole(s) doctorale(s) : École doctorale Informatique, télécommunications et électronique de Paris (1992-...)
• Partenaire(s) de recherche : Laboratoire : LIP6 (1997-....)
• Jury : Président / Présidente : Elham Kashefi
• Jury : Examinateurs / Examinatrices : Joe Ghalbouni, Nancy Rahbany
• Jury : Rapporteurs / Rapporteuses : Ashley Montanaro, Peter R. Turner

Mots clés

Mots clés contrôlés

Théorie de l'information quantique

Marches aléatoires quantiques

Tolérance aux fautes (informatique)

Mots clés libres

Unitary t-design

Calcul quantique basé sur la mesure

Simulabilité classique

Tolérance aux fautes

Distillation d'état magique

Accélération quantique

Unitary t-design

Measurement based quantum computation

Fault tolerance

Quantum speedup

Résumé

Cette thèse est basée sur la génération et la compréhension de types particuliers des ensembles unitaires aleatoires. Ces ensembles est utile pour de nombreuses applications de physique et de l’Information Quantique, comme le benchmarking aléatoire, la physique des trous noirs, ainsi qu’à la démonstration de ce que l’on appelle un "quantum speedup" etc. D'une part, nous explorons comment générer une forme particulière d'évolution aléatoire appelée epsilon-approximateunitary t-designs . D'autre part, nous montrons comment cela peut également donner des exemples de quantum speedup, où les ordinateurs classiques ne peuvent pas simuler en temps polynomiale le caractère aléatoire. Nous montrons également que cela est toujours possible dans des environnements bruyants et réalistes.

This thesis is focused on the generation and understanding of particular kinds of quantum randomness. Randomness is useful for many tasks in physics and information processing, from randomized benchmarking , to black hole physics , as well demonstrating a so-called quantum speedup , and many other applications. On the one hand we explore how to generate a particular form of random evolution known as a t-design. On the other we show how this can also give instances for quantum speedup - where classical computers cannot simulate the randomness efficiently. We also show that this is still possible in noisy realistic settings. More specifically, this thesis is centered around three main topics. The first of these being the generation of epsilon-approximate unitary t-designs. In this direction, we first show that non-adaptive, fixed measurements on a graph state composed of poly(n,t,log(1/epsilon)) qubits, and with a regular structure (that of a brickwork state) effectively give rise to a random unitary ensemble which is a epsilon-approximate t-design. This work is presented in Chapter 3. Before this work, it was known that non-adaptive fixed XY measurements on a graph state give rise to unitary t-designs , however the graph states used there were of complicated structure and were therefore not natural candidates for measurement based quantum computing (MBQC), and the circuits to make them were complicated. The novelty in our work is showing that t-designs can be generated by fixed, non-adaptive measurements on graph states whose underlying graphs are regular 2D lattices. These graph states are universal resources for MBQC. Therefore, our result allows the natural integration of unitary t-designs, which provide a notion of quantum pseudorandomness which is very useful in quantum algorithms, into quantum algorithms running in MBQC. Moreover, in the circuit picture this construction for t-designs may be viewed as a constant depth quantum circuit, albeit with a polynomial number of ancillas. We then provide new constructions of epsilon-approximate unitary t-designs both in the circuit model and in MBQC which are based on a relaxation of technical requirements in previous constructions. These constructions are found in Chapters 4 and 5.