Quantum computing offers the promise of "exponential" increases in the speed of certain types of computations compared to classical computing machines.  However, such devices have limitations as to the type of operations that are admissible, and some operations carry with them levels of interference so great as to make the result unusable.  Thus, well-established (e.g., numerical linear algebraic) algorithms must be ported over and adapted to this setting, representing interesting, highly non-trivial new numerical analysis challenges.

In this talk, we discuss our first steps in exploring the adaption of Krylov subspace approaches to the quantum computing setting. The problem we consider is the estimation of the ground state eigenvalue of a Hamiltonian matrix (i.e., the left-most eigenvalue of a Hermitian matrix). This setting presents a number of challenges, including that we can only work with specifically prepared unitary matrices.  We overcome these challenges by constructing a specific "super Krylov" subspace using a unitary matrix and using a hybrid quantum-classical approach to take advantage of the strengths of both computational settings.  Theoretical analysis and practical numerical results demonstrate the utility of this approach.

Collaborators: Joint work with Adam Byrne (Trinity College Dublin/IBM Research) and Will Kirby, Sergiy Zhuk (IBM Research)

Objectives:
How can I make an impact in professional contexts such as small-talk situations at conferences? What can help me in situations where I face an international crowd and how can I connect to an interdisciplinary audience? The workshop Make an Impact! offers the opportunity to enhance overall effective communication (verbal and non-verbal), as well as interpersonal settings, in order to improve networking and self-promotion opportunities.

Description:
Throughout the workshop, participants will be guided through interactive exercises to improve their communication, as well as focus on the quality of their language content and physical expression. The aim is to develop strategies to make a lasting and positive impact on groups, colleagues, and significant contact persons (networking). 
Trainer input will provide the opportunity to gain new insights in effective communication and learn how to present themselves more effectively and to make the best impression and strongest impact.

Contents:
• Self-marketing: effectively promoting oneself (verbal business cards)
• Spontaneous small talk: informal chatting with a purpose
• Developing awareness skills
• Concise and effective introductions: make an impact!
• Body language focus

Methods:
• Theoretical sessions to highlight key aspects and strategies
• Role-play scenarios
• Hands-on exercises for practicing
• Both group and individual feedback