Sobolev space formulation of density-functional theory: Solving the v-representability problem.
14th September 13:00, room PS340, building P35.
Density-functional theory is one of the principal methods in physics, chemistry and materials science used for calculating properties of many-body systems based on their electronic structure. It rests on a reformulation of the explicit energy expression in terms of the full quantum state into an implicit energy functional defined for a reduced quantity, the one-particle density. While considerably reducing the computational complexity, if corresponding approximations are available, this reformulation introduces certain mathematical problems. Most notably, it is not explicitly known which set of densities actually stems from solutions to the quantum many-body problem, i.e., the lowest-eigenvalue solution to the time-independent Schrödinger equation. In this talk a recently found resolution to this so-called “v-representability problem” is presented in the reduced setting of a 1-dim ring system with densities from a Sobolev space.
This spring we had the pleasure of finally putting our quantum computers, if not on a pedestal, at least in a dedicated room. The room, PS340 in Pilestredet 35, also fits a few people, a nice screen and a small “quantum library”. Read more about it in this nice piece by Olav-Johan Øye:
Wednesday 16th of August, we had the pleasure of welcoming the newly appointed minister of research and higher education, Sandra Borch, at OsloMet. Our rector, Christen Krogh, guided her on a tour around our Oslo campus – at tour that involved an encounter with our quantum computer Hugin. Our dean, Laurance Habib, and Sølve Selstø assisted our rector in explaining why quantum computing – education within quantum computing, in particular – is important.
Our minister listened with interest and asked several relevant questions – strongly suggesting that our message got through.
In addition to the Munin you see, from right to left, Henriette Bøe, leader of the student parliament, Sandra Borch, Christen Krogh, our rector, and Sølve Selstø.
So far there is only one animal was involved into quantum physics, that is the famous Schrödinger’s cat. Now some researchers claim that there is one more.
In February 2019, I came across the piece “Quantum theory: the weird world of teleportation, tardigrades and entanglement” [1]: Gröblacher is also interested in experiments involving living creatures … He is currently working on putting a sheet of nitride into a superposition of states … “A superposition state of these membranes would allow us to demonstrate that objects that are visible to the naked eye still behave quantum, and we can really test decoherence – the transition between classical and quantum mechanics,” he says. He hopes to extend the experiment by placing tiny living organisms called tardigrades onto the membrane of silicon nitride, putting them into superposition too.
Targidrates are known for being tough [2]. These micro-animals (their official title) can enter a ‘hibernation state’ of near complete dehydration and metabolism rate decreased by factor 1/1000, and, being in this state, survive an exposure to outer space (almost perfect vacuum), high-intensity radiation of all kinds (including gamma rays), and pressure up to 1200 atmosphere. Therefore, they might hopefully withstand the cryogenic environment required to achieve ground state cooling of the membrane. If there an animal able to survive superposition this must be a tardigrade.
After reading the piece, my immediate thought was: But would the tardy feel the difference between just the groundstate and superposition of the groundstate and the first excited state of the membrane? And in what measurable terms? Or is this difference is simply negligible on the background of the mere exposure to the cryogenic environment?
Another thought back then: The typical size of silicon nitride membranes Gröblacher is dealing with is 0.5 mm. This is also the typical size of tardigrades. I do not know the masses of the membranes and tardigrades but expect them to be comparable. It is not possible to maintain the extra-high quality factor of such membranes after placing on them a tardigrade – unless the membranes are on-purpose designed and curved, with ‘nests’ for tardys (a-la seats of Space Jockeys [3]).
Three years have passed and in 2022 a work with a sensational title, “Entanglement in a qubit-qubit-tardigrade system”, was published in New journal of Physics [4].
Sketch of the experiment reported in the paper [4].
The authors claimed that hey set a tardigrade into entanglement with two qubits — and the former has survived it (“The animal is then observed to return to its active form after 420 hours at sub 10 mK temperatures and pressure of 6 × 10−6 mbar, setting a new record for the conditions that a complex form of life can survive“). But had the animal really been quantum entangled?
To prove it, one has to measure the quantum properties of the tardigrade, which the experiment does not do. Instead, a model was used (“The tomographic data shows entanglement in the qubit-qubit-tardigrade system, with the tardigrade modelled as an ensemble of harmonic oscillators or collection of electric dipoles“). Well, the quantum community is sceptical about such a ’proof’.
Also, there is a strong scepticism about that entanglement can be obtained by simply placing a tardy on top of a qubit. After that the qubit is no longer a resonator with well-tuned characteristics so one should not talk about ‘groundstate’ and ‘excited state’. From the point of view of quantum physics, a tardy is a system with macroscopically many degrees of freedom so it decoheres the qubit by working as an external environment. But doesn’t the environment become entangled with the object it is acting on? But is it measurable?
The problem is that the animal is not a quantum object in a sense that its state cannot be described as a superposition of a few basis states. So where is the entanglement? In such situation, the entanglement cannot be located and thus cannot be measured. We could also say that we are entangled with an electron in a oxygen atom of 02 floating somewhere inside out right lung – but it is not measurable and therefore does not exist (at least for quantum physics).
Anyway, the ‘entanglement’ claimed in the paper was not assessed in experiment and therefore the clam is much stronger than the experimental data can support. Schrödinger’s tardigrade is not yet here and Schrödinger’s cat has to wait for a companion.
We are excited to announce that the OsloMet Quantum Hub has secured funding for a new PhD student who will be dedicated to advancing the field of quantum mechanics visualization. This position is a collaboration between the Department of Computer Science (with A. Laestadius) and the Department of Art, Design and Drama (K. Bergaust) and will be in alignment with the Hub’s efforts to explore innovative ways of communicating complex quantum concepts through visualization tools.
The selected PhD student will have the unique opportunity to contribute to research bridging the gap between quantum theory and visual representation. This initiative underscores the Quantum Hub’s commitment to not only enhancing quantum literacy but also pushing the boundaries of understanding in the world of quantum mechanics. We look forward to the contributions this collaboration will bring to the field.
Announcement of the position will follow during the autumn.
August 7th we had the pleasure of welcoming researchers from Equinor to our hub. A group of strong researchers, including mathematicians, physicists and software engineers, have spent significant time and effort looking into the quantum opportunities for their company.
The Hub’s own Aleksandar Davidov shared promising results on quantum boosted predictions and optimization for Ruter while Tobi Giesgen, who is leading Equinor’s quantum technology project, and colleges presented interesting ideas on the prospect of applying emerging quantum technology within their company. After sharing and discussing experiences and expectations, our visitors got the chance to play around with our own quantum computers, Hugin and Munin.
We look forward to their next visit!
Tobi Giesgen, Quantum technology project leader at Equinor, is running a quantum circuit at Munin. Unfortunately, Munin was not in top shape that day as our CNOT gate was flawed due to an error in calibration the week before.
In relation to the position paper that was published following the QCNorway workshop, Christine Gulbrandsen interviewed the main author, Are Magnus Bruaset, along with Sølve Selstø, about the content – and the message that we are aiming to convey. You can read the full interview in Forskning.no here (in Norwegian):
Monday May 19th we had the pleasure of having Justin Wells visiting our hub. He gave a very interesting presentation on his work within experimental condensed matter physics. It spent quite widely – ranging from implementing qubits in silicon to magnetic properties – and how they are related to ducklings. Despite this rather wide scope, those of us who attended go to hear a presentation which was both accessible and even entertaining.
If you want to learn more about Justin’s research activities, you can read more here:
Our own, until recently, Master’s student Maryam Lotfigolian, has been hired to work on Ruter’s quantum AI-project this summer. We are proud of you, Maryam!
Read more about her interest in quantum computing in this article.
Here you can see a presentation given by Umair Imam on this promising quantum application:
The talk was given on the QCNorway workshop in November 2022.
Friday June 9th 2023 we had the pleasure of listening to Tanner Culpitt, postdoc at the Hylleraas Centre, giving a presentation entitled Electronic Structure and Molecular Dynamics in a Strong Magnetic Field. In addition to outlining how such systems can be studied non-perturbatively, he also shared ideas on how quantum computers may be useful in this context.
The electronic structure and dynamics of molecules in magnetic fields have historically been treated perturbatively. A perturbative treatment is successful at weaker field strengths, such as those found on Earth. At higher field strengths such as those found in white dwarf stars or neutron stars, a perturbative treatment is inadequate, and new tools are needed to accurately model electronic structure and dynamics. This talk will focus on the theoretical development and application of these tools. Additionally, recent developments in the application of quantum algorithms for the calculation of molecular properties in a magnetic field will be discussed.
