Introduction to quantum information
Timothée Hoffreumon, INRIA, LMF, Université Paris-Saclay
TBA

Quantum foundations
Roger Colbeck, Department of Mathematics, University of York
TBA

Quantum foundations
Roger Colbeck, Department of Mathematics, University of York

Higher Order Quantum Theory
Matthew Wilson, CentraleSupélec, Université Paris-Saclay

Higher order quantum operations can be motivated in at-least three ways. First, one might simply ask a mathematical question, “which operations can be applied to part of a quantum channel to return a new one”. Second, one might ask, “what are the most general causal correlations compatible with local quantum theory”. Third, one might ask, “what is the right generalisation of non-markovian processes to the quantum regime”. In either case, one lands on variants of the same mathematical objects called higher order quantum operations. In this lecture we will review the motivations and basic theory of higher order processes, along with current open questions in the field. 

Quantum Cryptography
Peter Brown, Télécom Paris, Institut Polytechnique de Paris.
TBA

Quantum Cryptography
TBA
TBA

An introduction to Stochastic Master Equation (SME) for open quantum systems
Pierre Rouchon, LPENS, Mines Paris-PSL, Inria, ENS-PSL, Université PSL, CNRS, Sorbonne Université

-1- SME of the photon box: wave-function/density-operator formulation, dispersive/resonant propagator, Markov model, quantum Monte-Carlo trajectories, (super)-martingales, Quantum Non-Demolition (QND) measurement of photons, Bayesian inference to include measurement imperfections and decoherence,   simulation and convergence analysis.

-2- Structure of dynamical models describing open quantum systems including measurement back-action and decoherence: discrete-time models based on quantum channels and left stochastic matrices;  continuous-time models driven by Wiener processes (weak measurement) or Poisson processes (quantum jump and counting measurement), and their time-discretization.

Quantum Information Theory
Nilanjana Datta, Faculty of Mathematics, University of Cambridge, Pembroke College
TBA

Quantum Information Theory
Salman Beigi, School of Mathematics, Institute for Research in Fundamental Sciences
TBA

Quantum Feedback Networks: Theory and Applications in Quantum Control Systems
John Gough, Aberystwyth University

We review the theory of quantum feedback networks and show how it gives a framework for a system theoretic description applicable to quantum engineering. The network rules are presented along with an overview of feedback based control. There are two main approaches: feedback by the observed output signal; and feedback by the actual quantum output itself. We will illustrate this with several current examples from quantum technology, in particular, quantum optics and super-conducting qubits. We introduce the  Hudson-Parthasarathy quantum stochastic calculus and the input-output theory for open quantum systems (known as the « SLH » formalism), and review the theory of quantum feedback networks. We will give an overview of feedback techniques, including current directions in quantum measurement-based and quantum coherent feedback control.

Optimal estimation of quantum Markov chains using coherent absorbers and displaced-null measurements
Madalin Guta, School of Mathematics, University of Nottingham

In this presentation I will discuss the problem of estimating dynamical parameters of a quantum Markov chain. The key tool will be the use of a coherent quantum absorber which transforms the problem into a simpler one pertaining to a system with a pure stationary state at a reference parameter value. Motivated by the proposal in [1] I will consider counting output measurements and show how the statistics of the counts can be used to compute a simple, asymptotically optimal estimator of the unknown parameter. For this, I will introduce translationally invariant modes (TIMs) of the output and show that these modes are Gaussian in the limit of large times and capture the entire quantum  Fisher information of the output. Moreover, the counting measurement provides an effective joint measurement of the TIMs number operators. The unknown parameter is estimated using a two stage estimation procedure. A rough estimator is first computed using a simple measurement, and is used to set the absorber parameter. Due to non-identifiability issues of the counting measurement the reference parameter needs to be shifted away from the initial rough estimator, as shown in the displaced-null measurements theory [2]. Finally, an optimal estimator is computed in terms of the total number of excitations of the TIMs, avoiding the need for expensive estimation procedures. Details can be found in [3].
 
 [1] D. Yang, S. F. Huelga, and M. B. Plenio PRX Quantum 13, 031012 (2023) 
 [2] F. Girotti, A. Godley and M. Guta, arXiv:J. Phys. A 57 245304 (2024)
 [3] F. Girotti, A. Godley and M. Guta, arXiv: 2408.00626

Quantum Algorithm
Cambyse Rouzé, Inria, Télécom Paris, Institut Polytechnique de Paris
TBA

Quantum Algorithm
TBA
TBA

Quantum Programming languages with classical control
Benoit Valiron, LMF, Université Paris-Saclay

This lecture is devoted to the programming model of circuit description languages. We first overview a few typical structures found in quantum algorithms and derive the necessary constructors for implementing them. We then analyse several standard approaches found both in the literature and in concrete programming languages. We finally focus on the typical type systems used for quantum circuit description languages.

Quantum Compilation
Alejandro Diaz-Caro, INRIA, LORIA
TBA

Graphical languages for quantum computation
Marc de Visme, INRIA, LMF, Université Paris-Saclay

In this lecture, we present graphical languages for quantum computation. While we focus on the most used ones, that is quantum circuits and the ZX calculus, we also give an overview of the diversity existing in graphical languages, the reasons why one might use graphical languages over textual languages, and the theoretical framework underlying.

Emulating Quantum Computation
Simon Martiel, IBM Quantum, IBM France Lab,

In this lecture, we present graphical languages for quantum computation. While we focus on the most used ones, that is quantum circuits and the ZX calculus, we also give an overview of the diversity existing in graphical languages, the reasons why one might use graphical languages over textual languages, and the theoretical framework underlying.

Quantum algorithms for high performance computing
Marc Baboulin, LMF, ENS Paris-Saclay, CNRS, Université Paris-Saclay

In this lecture, we will investigate the different known quantum simulation algorithms, ranging from direct linear algebra simulation and tensor network contraction, to simulation of Clifford circuits through Tableau formalism. We will attempt to list classes of circuits for which efficient simulation techniques are known, and prove hardness of some other classes of circuits. The goal is to provide a collection of tools that can be used to explore quantum algorithms as efficiently as possible, and enough knowledge to discriminate between « hard » and « easy » quantum circuits.In this lecture we explain how core tasks in scientific computing can be addressed by quantum algorithms, possibly combined with classical ones. In particular we describe recent advances in algorithms for decomposing and handling matrices (generic, or coming from PDE’s) in quantum computers. We also present promising methods for the solution of linear systems of equations with improvement in terms of accuracy and cost for the solution.