Title of talk: Approximating Invertible Maps by Recovery Channels: Optimality and an Analysis of Qudit Channels

Speaker: Prof Nadja Bernardes

(Federal University of Pernambuco, Brazil)

Abstract:

We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing, and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. Furthermore, we extend our analysis to qudit channels by devising a state-independent framework that quantifies the ability of the Petz map to recover a state for any dimension. Under certain conditions, dimensionality plays a role in state recovery.

Bio:

Nadja Bernardes is a Professor of Physics at the Federal University of Pernambuco (Recife, Brazil), with research focusing on quantum information theory, particularly open quantum systems and non-Markovian dynamics. Nadja holds a PhD in Physics from the Max Planck Institute for the Science of Light (Erlangen, Germany 2012), where she researched long-distance quantum communication. She is on the board of the Brazilian Physical Society and a researcher at the National Institute of Quantum Information Science and Technology.

The announcement can be found here.

Title of talk: Analog quantum simulation of partial differential equations

Speaker: Prof Nana Liu

(Institute of Natural Sciences, University of Michigan- Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University  and Visiting Scholar at University of Oxford)

Abstract:

Quantum simulators were originally proposed to be helpful for simulating one partial differential equation (PDE) in particular – Schrodinger’s equation. If quantum simulators can be useful for simulating Schrodinger’s equation, it is hoped that they may also be helpful for simulating other PDEs. As with large-scale quantum systems, classical methods for other high-dimensional and large-scale PDEs often suffer from the curse-of-dimensionality (costs scale exponentially in the dimension D of the PDE), which a quantum treatment might in certain cases be able to mitigate. To enable simulation of PDEs on quantum devices that obey Schrodinger’s equations, it is crucial to first develop good methods for mapping other PDEs onto Schrodinger’s equations.

In this talk, I will introduce the notion of Schrodingerisation: a procedure for transforming non-Schrodinger PDEs into a Schrodinger-form. This simple methodology can be used directly on analog or continuous quantum degrees of freedom – called qumodes, and not only on qubits. This continuous representation can be more natural for PDEs since, unlike most computational methods, one does not need to discretise the PDE first. In this way, we can directly map D-dimensional linear PDEs onto a (D + 1)-qumode quantum system where analog Hamiltonian simulation on (D + 1) qumodes can be used.

I show how this method can be applied to linear PDEs, certain nonlinear PDEs, nonlinear ODEs and also linear PDEs with random coefficients, which is important in uncertainty quantification.

Bio: Nana Liu is an associate professor and PI of the Quantum Information and Technologies (QIT) group in the Institute of Natural Sciences at Shanghai Jiao Tong University and the University of Michigan-Shanghai Jiao Tong University Joint Institute. She received her PhD from the University of Oxford as a Clarendon Scholar and was a Postdoctoral Research Fellow at the Center for Quantum Technologies in the National University of Singapore and the Singapore University of Technology and Design. She is the 2019 recipient of the MIT Technology Review’s 10 Innovators under 35 in the Asia-Pacific region. Her current research interests include quantum algorithms for scientific computing and quantum protocols relevant for a future quantum internet.

The announcement will be found here.

Rivan Rughubar (UCT)

Approximating classical kernels on NISQ computers

Abstract:

The talk will aim to demonstrate how a kernel function can be approximated on a NISQ computer and to demonstrate the limitations of this method.

Kernel methods are used throughout classical and quantum machine learning. Over the last few years there has also been much exploration into the link between variational quantum circuits and their kernels and feature maps. Building quantum circuits which exactly implement a given kernel function is not a trivial task. We will look at a method for approximating kernel functions which can be implemented on NISQ computers. This method also attempts to avoid the black box problem in hopes that it can be iterated on and used to approximate a larger family of functions in the future.

Please, download the announcement here.

Title of talk: Modelling non-Markovian noise in driven superconducting qubits.

Speaker: Abhishek Agarwal

Abstract:

Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.

Bio:

Abhishek Agarwal is a Higher Scientist at the National Physical Laboratory (NPL) in the United Kingdom. He graduated with a degree in Physics and Philosophy from University of Oxford (MPhysPhil) in 2020 and has since been working at NPL. His research interests include modelling noise in quantum computers and developing quantum algorithms for materials simulations.

Register in advance for this meeting:

https://nithecs-ac-za.zoom.us/meeting/register/tJMqdeiurjspHteN8DvEFtOpsgyzIMf4b3lr#

The announcement can be found here.

https://qiskit.org/events/summer-school-2023/

Title of talk: Path integral in position deformed Heisenberg algebra.

Speaker: Dr Latévi M. Lawson.

Abstract:

The deformed Heisenberg algebra is one of the promising candidate approaches to probe quantum gravity at the Planck scale. It consists of deforming the ordinary Heisenberg algebra in momentum or in position operators. Recently, we proposed in [1], a position deformed Heisenberg algebra in 2D with simultaneously existence of minimal and maximal length uncertainties. Its applications run from quantum well [2], quantum optics [3], quantum statistics [4] to quantum non-Hermitian operators [5].

More recently in [6], we have studied the effects of this deformation on the trajectories of a system moving from one point to another. As result, we have shown that this system can travel very faster in this deformed space with very low energies. As interpretation, this result can be understood as if deformation effects shorten the paths of the system, allowing it to move in this space in a short time using minimal kinetic energy.

[1] L. Lawson, Minimal and maximal lengths from position-dependent noncommutativity, J. Phys. A: Math. Theor. 53, 115303 (2020)
[2] L. Lawson, Position-dependent mass in strong quantum gravitational background fields, J. Phys. A: Math. Theor. 55, 105303 (2022)
[3] L. Lawson and P. Osei, Gazeau-Klauder coherent states in position-deformed Heisenberg algebra, J. Phys. Commun. 6, 085016 (2022)
[4] L. Lawson, Statistical description of ideal gas at Planck scale with strong quantum gravity measurement, Heliyon 8, e10564 (2022)
[5] L. Lawson, Minimal and maximal lengths of quantum gravity from non-Hermitian position-dependent noncommutativity, Scientific Reports 12, 20650 (2022)
[6] L. Lawson and P. Osei, K. Sodoga, F. Soglohu, Path integral in position deformed Heisenberg algebra with maximal length uncertainty, Annal of Phys doi:10.1016/j.aop.2023.169389 (2023)

Bio:

Dr Lawson is Togolese in nationality, residing in Ghana. He attended the University of Lomé, Togo (2006-2010) where he studied Physics and Chemistry. After three years of teaching Physics in secondary schools, he moved to IMSP (Institut de Mathématiques et de Sciences Physiques) in Benin, from 2013 to 2018, where he obtained an MSc and PhD in Mathematical Physics. He then returned to the University of Lomé and lectured as a teaching assistant in the Physics department for two years. In October 2020, he began Postdoctoral research and served as a tutor at AIMS in Ghana. His research interests are in noncommutative quantum mechanics, quantum groups, representation theory of differential operators and machine learning.

Title of talk: A generalized dominance ordering for 1/2-BPS states.

Speaker: Dr Garry Kemp.

Abstract:

I discuss a generalized dominance ordering for irreducible representations of the symmetric group $S_{n}$ with the aim of distinguishing the corresponding states in the 1/2-BPS sector of $U(N)$ Super Yang-Mills theory when a certain finite number of Casimir operators are known. Having knowledge of a restricted set of Casimir operators was proposed as a mechanism for information loss in this sector and its dual gravity theory in AdS$_{5}\times S^{5}$. It is well-known that the states in this sector are labeled by Young diagrams with n boxes. I propose a generalization of the well-known dominance ordering of Young diagrams. Using this generalization, I posit a conjecture to determine an upper bound for the number of Casimir operators needed to distinguish between the 1/2-BPS states and thus also between their duals in the gravity theory. I offer numerical and analytic evidence for the conjecture. Lastly, I discuss implications of this conjecture when the energy $n$ of the states is asymptotically large.

Bio:

Dr Garry Kemp is a theoretical physicist and lecturer at the University of Johannesburg. He obtained his PhD at the University of the Witwatersrand working in high energy physics and AdS/CFT. He is also currently interested in quantum information in quantum field theory.