V Quantum Information School and Workshop - Paraty 2015  

Paraty, Rio de Janeiro, Brazil, 04-15 Aug 2015

5th International School on Quantum Information
04 - 08 Aug 2015



1 - Richard Jozsa, University of Cambridge, UK

Classical simulation of quantum computations

Quantum computation is widely regarded as being more powerful than classical computation. But despite great successes such as Shor’s quantum factoring algorithm, we still have relatively little understanding of how to characterise and effectively exploit the extra quantum computational power. The notion of classical simulation of a quantum computation provides a valuable theoretical tool for obtaining insights into both the possibilities and limitations of quantum computing.
In these lectures we will give an exposition of some principal results in this area with the following topics (subject to time and interest): an introduction to some relevant concepts from computational complexity and the notion of (strong and weak) classical simulation; discussion of the role of entanglement in quantum computational speed-up; classical simulation of Clifford circuits and the Gottesman-Knill theorem; some extensions of Clifford circuits illustrating the power of additional quantum resources; introduction to matchgate circuits and their simulation via the Jordan- Wigner formalism; the unexpected hardness of commuting quantum circuits; further probabilistic methods for classical simulation, and other recent results.

Lecture 1   Lecture 2
Lecture 3 

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2 - Philip Walther, Vienna University, Austria

Quantum information processing with photons

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3 - Leandro Aolita, Federal University of Rio de Janeiro, Brazil

Quantum certification of many-body quantum simulations

  • A major roadblock for large-scale quantum technologies is the lack of experimentally-friendly reliable certification tools. The ultimate challenge consists of making sure that classically intractable quantum machines work correctly. The field of many-body quantum certification, the topic of this two-lecture course, aims at providing solutions to this problem by exploiting quantum resources.
    • Lecture I: In the first lecture, I will first give a general motivation; review the notions of quantum and classical sampling problems; and discuss tools for quantum state characterisation — from brute-force quantum state tomography to efficient Matrix-product-state (MPS) tomography. I will then provide an informal definition of quantum-state certification tests and will finish with examples of direct fidelity-estimation techniques without state reconstruction.
    • Lecture II: In the second lecture, I will start with the formal definition of state certification tests and will discuss quantum interactive proofs as interactive certification tests for universal quantum computation. Then, I will move to certification tests for non-universal quantum simulations. There, I will discuss extremality-based fidelity lower bounds for the efficient certification of MPSs and multi-mode photonic quantum states. The latter will require some technicalities about local frustration-free parent Hamiltonians and non-Gaussian-state nullifiers, respectively. Finally, I will present a (long) list of open questions and discuss future perspectives for the field.

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4 - Fernando G.S.L. Brandão, Microsoft Research, USA and University College London, UK

Quantum thermodynamics

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5 - Ernesto F. Galvão, Universidade Federal Fluminense, Brazil

Ingredients for universal quantum computation

I will start by reviewing the main ingredients for a universal quantum computer in the circuit model: universal sets of gates, the importance of restricting input states and output measurements, etc. Then I will review the basics of alternative models of quantum computation, such as measurement-based quantum computation and models which use linear optics (e.g. the KLM scheme and Boson Sampling). By mixing and matching the various ingredients, we will identify different combinations which yield interesting regimes in terms of computational power: full universal quantum (or classical) computation, simulable quantum dynamics, or an intermediate or incomparable computational power (e.g. IQP, Boson Sampling, permutational quantum computing, DQC-1). This line of research helps identify what’s essential and what’s accessory for the quantum computational advantage, with practical implications for experimental implementations. I will give special attention to recent experimental progress in specialized linear optical computers to solve the Boson Sampling problem, which I will describe in some detail.

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6 - Matthew LaHaye, Syracuse University, USA

Mechanical Quantum Systems

The field of mechanical quantum systems has made great strides in recent years developing the technology to begin eliciting and studying quantum behavior of structures that are normally well-described by classical laws of physics. While the full potential of the field is yet unknown, it’s thought that these mechanical systems could have important applications serving as elements in quantum computing and quantum communication architectures and could also enable explorations of fundamental topics in quantum mechanics like the quantum-to-classical divide. In my lectures, I will give an overview of this diverse and burgeoning field from the perspective of an experimentalist who has worked in the field for nearly 15 years. Topics covered will include the basic physics of mechanical systems (including nanomechanical and micromechanical technologies), the quantum limits to measurement of mechanical systems, the integration of quantum technologies (e.g. superconducting circuits and qubits) with mechanical structures for manipulating and measuring quantum properties of motion, and discussions of the experimental challenges and open questions that researchers in our field face.

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Cancelled - Olivier Pfister, University of Virginia, USA

Recent advances in continuous-variable quantum information: on the (long?) road toward a massively scalable, fault-tolerant universal quantum computer

    • Lecture I
      Quantum information with oscillators. Not everything has to be a qubit. Introduction to qumodes: from squeezed states to the EPR Paradox. The magic of the beam splitter: the Bloch-Messiah theorem. Entangled states. Quantum teleportation. Quantum dense coding and superprecise measurements.

    • Lecture II
      Cluster states and measurement-based quantum computing. Massively scalable entanglement in the time and frequency domains. Experimental breakthroughs in 2 to 4 continents. How to turn the quantum optical frequency comb into an entangled quantum computing register.

    • Lecture III
      The Wigner function: why can’t we violate the Bell inequality with continuous variables? Entanglement distillation and fault tolerance. Back to qubits! The Gottesman- Kitaev-Preskill encoding. How much squeezing do you really need to quantum compute?