Our speakers will cover topics related to the theme of the event 
Testing and Applications for Quantum Computers

Andru Gheorghiu  Verification of universal quantum computation
Once faulttolerant and scalable quantum computing becomes a reality, quantum computers will be able to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can check whether quantum computers are indeed producing correct results, a task known as quantum verification.
In this talk, I will give a brief overview of protocols for quantum verification. I will then focus on a recent cryptographic approach to verification, that relies on the remote preparation of certain quantum states using classical communication.
The talk is based on the following works:

Vedran Dunjko  From Quantum machine learning to Quantum AI
The field of Quantum Machine Learning (QML) has been generating a substantial buzz in the last few years. QML applications are often singled out as particularly well suited for quantum computers, both in the context of nearterm applications, and in the context of fully scalable and robust quantum computers of the future.
In this talk we will focus on aspects of quantum reinforcement learning, and its connections to artificial intelligence.
In the second part, we will crossover to the domain of good oldfashioned AI (GOFAI), and will present a new paradigm which allows us to obtain speedups from (very) small quantum computers for constraint satisfaction problems, vital to much of symbolic reasoning.

Dominik Hangleiter  (How) can we verify quantum supremacy?
Demonstrating a superpolynomial quantum speedup using feasible schemes has become a key nearterm goal in the field of quantum simulation and computation. The most prominent schemes for "quantum supremacy" such as boson sampling or random circuit sampling are based on the task of sampling from the output distribution of a certain randomly chosen unitary. But to convince a skeptic of a successful demonstration of quantum supremacy, one must verify that the sampling device produces the correct outcomes. I will first identify a fundamental obstacle towards verifying such devices: sampleefficient certification based on the experimental output data alone is prohibited, ironically, by the same property that allows proving the robustness of quantum supremacy to small experimental errors. In the second part of the talk, I will view this nogo result as an invitation to be circumvented. I will discuss alternative certification schemes that exploit known structure of the device, in particular, the possibility to perform quantum measurements in different bases. I will then present a small example of a sampling protocol using such quantum certification.

Dan Mills  Benchmarking Near Term Quantum Computers
Academic institutions and private companies are collectively making significant progress in the construction of quantum computers. The exponential growth in the number of qubits, which we have seen in recent years, is incredibly promising. This has climaxed with announcements of the construction of a 72 qubit device by Google, and a 128 qubit device by Rigetti. However, the most famous algorithms, such as the polynomial time factoring of numbers into their prime divisors, required several orders of magnitude more qubits than this. This is most devastating as factoring would have given us a very simple way to verify the quality of a quantum computation: “here is a large number. Give me its factors”. Well constructed quantum computers would give the correct factor while badly built ones would give numbers not multiplying to give the original large number. I will discuss schemes for benchmarking near term devices; a vital check to ensure we are on the right path in our innovations. These benchmarks must not be passable by classical computers to ensure that the device is indeed utilising some quantum mechanics. This property is much harder to demonstrate in small, noisy devices, and an exploration of this problem will be covered by this talk.

Damian Markham  Introduction to Quantum Computing I
I will introduce the basic formalism of quantum computing and quantum mechanics (states, measurements, unitary evolution, entanglement). I will then describe some of the fundamental differences which arise when encoding computation into quantum systems, such as nocloning and contextuality and how they change the game.

Brian Coyle  Overview of Variational Algorithms in QML
Due to the development of small quantum computers, with few qubits, limited connectivity and nonnegligible noise rates, the question arises, what to do with them? In this talk, I will present an overview of some recently developed algorithms which are very suited to these types of devices. In particular, they are hybrid algorithms  with a core shallow depth quantum circuit, and a classical optimisation routine to perform a specific task. These algorithms are variational  they involve altering some parameters in an ansatz circuit through a training procedure which is similar in flavour to how classical neural networks are trained.
I will focus on the specific task of Generative modelling using near term quantum devices, but I will also discuss how similar algorithms can be devised for a range of tasks, including classification in classical Machine Learning, and more general purpose optimisation algorithms like the Quantum Approximate Optimisation Algorithm (QAOA).

Nathan Killoran  Optimization and quantum machine learning with PennyLane
Optimization and machine learning are two promising applications for quantum computers, particularly nearterm devices. Impressive progress has been made in these areas recently, making optimization and machine learning on quantum hardware (almost) as easy as on classical hardware. In this talk, I introduce PennyLane, a Pythonbased software framework for optimization and machine learning of quantum and hybrid quantumclassical computations. PennyLane’s core feature is a quantumaware version of the backpropagation algorithm  extending the automatic differentiation ability of libraries such as PyTorch and TensorFlow to be compatible with quantum computations. Hardware and framework agnostic, PennyLane is compatible with any gatebased quantum simulator or hardware, including leading quantum software platforms such as Xanadu's Strawberry Fields, IBM's Qiskit, and Rigetti's PyQuil. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

Ellen Derbyshire  Testing quantum gates with randomized benchmarking
Randomized benchmarking (RB) is a method to determine the holistic performance of a set of gates on a quantum hardware. The Clifford group is a 2design, an essential requirement for RB. RB relies on sampling random sequences of gates from the Clifford group (or any unitary 2design) and running these sequences plus an inversion gate which ought to return the quantum system to it's initial state. However, physical implementations of quantum gates will not be perfect, and RB provides a way to quantify the difference between the imperfect implementation and perfect gateset. It can be used to find the average error rate of the Clifford group on a quantum system, and in special cases other nonClifford gates. It can also be used to find the average error rate of a specific Clifford or quantum gate. It is a useful tool for characterising the overall performance of a quantum hardware in implementing a specific gateset and is efficiently scalable, and physically implementable, making it ideal for NISQ devices.

Petros Wallden  Introduction to Quantum Computing II: The Quantum Circuit Model and Basic Quantum Algorithms
In this talk I will start with basic notions of the theory of quantum computing (quantum Turing machines) and quantum complexity theory. Then I will introduce the quantum circuit model. Finally, basic quantum algorithms (DeutschJozsa, Grover, Quantum Fourier Transform) will be presented and explained.

Ashley Montanaro  The Theory of Quantum Computational Supremacy
After many years of theoretical and experimental developments, quantum computers are on the cusp of outperforming classical supercomputers, an event known as “quantum computational supremacy”. Demonstrating this with nearterm quantum computers is a significant challenge, because we require a task which is easy for the quantum computer to solve, but which is likely to be hard for the classical computer to solve. In this talk, I will introduce the theoretical background to this area, including some of the proposals for demonstrating quantum computational supremacy (random quantum circuits, commuting quantum circuits, and boson sampling).

Niel de Beaudrap  Introduction to Quantum Error Correction
Quantum systems are sensitive to noise, and quantum computing devices are currently sensitive to noise. I will introduce the subject of quantum error correction with stabiliser codes, drawing the connection to classical error correction with parity checks, and attempt to show how we can reason about these codes using the "stabiliser formalism"  a technique to efficiently simulate certain quantum circuits