Tomographically reconstructed master equations for any open quantum dynamics

Memory effects in open quantum dynamics are often incorporated in the equation of motion through a superoperator known as the memory kernel, which encodes how past states affect future dynamics. However, the usual prescription for determining the memory kernel requires information about the underlying system-environment dynamics. Here, by deriving the transfer tensor method from first principles, we show how a memory kernel master equation, for any quantum process, can be entirely expressed in terms of a family of completely positive dynamical maps. These can be reconstructed through quantum process tomography on the system alone, either experimentally or numerically, and the resulting equation of motion is equivalent to a generalised Nakajima-Zwanzig equation. For experimental settings, we give a full prescription for the reconstruction procedure, rendering the memory kernel operational. When simulation of an open system is the goal, we show how our procedure yields a considerable advantage for numerically calculating dynamics, even when the system is arbitrarily periodically (or transiently) driven or initially correlated with its environment. Namely, we show that the long time dynamics can be efficiently obtained from a set of reconstructed maps over a much shorter time.Comment: 10+4 pages, 5 figure

Positivity in the presence of initial system-environment correlation

The constraints imposed by the initial system-environment correlation can lead to nonpositive Dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models.Comment: close to the published version. 5 pages, 1 figur

Non-Markovian memory in IBMQX4

We measure and quantify non-Markovian effects in IBM's Quantum Experience. Specifically, we analyze the temporal correlations in a sequence of gates by characterizing the performance of a gate conditioned on the gate that preceded it. With this method, we estimate (i) the size of fluctuations in the performance of a gate, i.e., errors due to non-Markovianity; (ii) the length of the memory; and (iii) the total size of the memory. Our results strongly indicate the presence of non-trivial non-Markovian effects in almost all gates in the universal set. However, based on our findings, we discuss the potential for cleaner computation by adequately accounting the non-Markovian nature of the machine.Comment: 8 page

An introduction to operational quantum dynamics

In the summer of 2016, physicists gathered in Torun, Poland for the 48th annual Symposium on Mathematical Physics. This Symposium was special; it celebrated the 40th anniversary of the discovery of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, which is widely used in quantum physics and quantum chemistry. This article forms part of a Special Volume of the journal Open Systems & Information Dynamics arising from that conference; and it aims to celebrate a related discovery -- also by Sudarshan -- that of Quantum Maps (which had their 55th anniversary in the same year). Nowadays, much like the master equation, quantum maps are ubiquitous in physics and chemistry. Their importance in quantum information and related fields cannot be overstated. In this manuscript, we motivate quantum maps from a tomographic perspective, and derive their well-known representations. We then dive into the murky world beyond these maps, where recent research has yielded their generalisation to non-Markovian quantum processes.Comment: Submitted to Special OSID volume "40 years of GKLS

Tight, robust, and feasible quantum speed limits for open dynamics

Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics. Our methods rely on measuring angles and distances between (mixed) states represented as generalized Bloch vectors. We study the properties of our bound and present its form for closed and open evolution, with the latter in both Lindblad form and in terms of a memory kernel. Our speed limit is provably robust under composition and mixing, features that largely improve the effectiveness of quantum speed limits for open evolution of mixed states. We also demonstrate that our bound is easier to compute and measure than other quantum speed limits for open evolution, and that it is tighter than the previous bounds for almost all open processes. Finally, we discuss the usefulness of quantum speed limits and their impact in current research.Comment: Main: 11 pages, 3 figures. Appendix: 2 pages, 1 figur

Information Systems Undergraduate Degree Project: Gaining a Better Understanding of the Final Year Project Module

The place of an individual project in the final year of Information Systems (IS) undergraduate degrees at UK universities is well established. In this paper we compare the final year project modules at four UK universities: the University of Brighton, the University of South Wales, University of West London and the University of Westminster. We find that the aims of the projects are similar, emphasising the application of the knowledge and skills from the taught element of their course in a complex development project, often including interactions with a real client. Although we show in this analysis that projects serve a similar purpose in the IS degree courses, the associated learning outcomes and the assessment practice varies across the institutions. We identify some gaps in the skills and abilities that are not being assessed. In further work we are planning to consult final year students undertaking their projects and their supervisors, in order to gain an understanding of how project assessment criteria are actually put to use

Reconstructing large-scale structure with neutral hydrogen surveys

Upcoming 21-cm intensity surveys will use the hyperfine transition in emission to map out neutral hydrogen in large volumes of the universe. Unfortunately, large spatial scales are completely contaminated with spectrally smooth astrophysical foregrounds which are orders of magnitude brighter than the signal. This contamination also leaks into smaller radial and angular modes to form a foreground wedge, further limiting the usefulness of 21-cm observations for different science cases, especially cross-correlations with tracers that have wide kernels in the radial direction. In this paper, we investigate reconstructing these modes within a forward modeling framework. Starting with an initial density field, a suitable bias parameterization and non-linear dynamics to model the observed 21-cm field, our reconstruction proceeds by {combining} the likelihood of a forward simulation to match the observations (under given modeling error and a data noise model) {with the Gaussian prior on initial conditions and maximizing the obtained posterior}. For redshifts z=2 and 4, we are able to reconstruct 21cm field with cross correlation, rc > 0.8 on all scales for both our optimistic and pessimistic assumptions about foreground contamination and for different levels of thermal noise. The performance deteriorates slightly at z=6. The large-scale line-of-sight modes are reconstructed almost perfectly. We demonstrate how our method also provides a technique for density field reconstruction for baryon acoustic oscillations, outperforming standard methods on all scales. We also describe how our reconstructed field can provide superb clustering redshift estimation at high redshifts, where it is otherwise extremely difficult to obtain dense spectroscopic samples, as well as open up a wealth of cross-correlation opportunities with projected fields (e.g. lensing) which are restricted to modes transverse to the line of sight

Stroke and HIV - casual or coincidental co-occurrence?

No Abstract. South African Medical Journal Vol. 96 (12) 2006: pp.1247-124

Linear Assignment Maps for Correlated System-Environment States

An assignment map is a mathematical operator that describes initial system-environment states for open quantum systems. We reexamine the notion of assignments, introduced by Pechukas, and show the conditions assignments can account for correlations between the system and the environment, concluding that assignment maps can be made linear at the expense of positivity or consistency is more reasonable. We study the role of other conditions, such as consistency and positivity of the map, and show the effects of relaxing these. Finally, we establish a connection between the violation of positivity of linear assignments and the no-broadcasting theorem.Comment: 6 pages, 1 tabl