stuff is going on!

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Guillaume graduated!

On Monday, Guillaume Acke graduated as a PhD in chemistry with his thesis Maximum Probability Domains: Theoretical Foundations and Computational Algorithms. The jury expressed its appreciation for the diversity in Guillaume's work, combining deep insight in theoretical ideas from quantum physics with strong computational skills. I couldn't agree more. Congrats!

On a side note, I could finally give my Hakmem 174 painting to Guillaume. While he was coding up the MPDs for the Hubbard model, I got very much inspired by Gosper's algorithm [see the Arts section].

[The Hakmem 147 painting is the one on the left]

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Saclay lectures

In september, I gave a full week of lectures on Richardson-Gaudin integrability to Thomas Duguet's group at CEA Saclay. I have decided to put my (hand written) notes publicly available on this website. You can find them via the navigation bar.

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welcome again!

Today, I am launching some new html. Not everything is included or updated yet, but please stay tuned in the coming weeks. There will be updates!

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publication

Two of our manuscripts got published this week

• The block-ZXZ paper (9 jun 2016) got published in Physical Review A. Recently, the journal had explicitly added quantum information to their coverage, so we are proud that we could immediately contribute.
• Our paper on the Birkhoff theorem for unitary matrices (29 jun 2016) got published in Linear Algebra and its Applications. The referee was as surprised as us that any odd permutation matrix can be written as a linear combination of only even matrices!

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book chapter

Springer just published the book Advances in Unconventional Computing: Volume 1: Theory, edited by Andrew Adamatzky. Alex and myself contributed a chapter on NEGATOR gates: The Group Zoo of Classical Reversible Computing and Quantum Computing

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graduated!

I have successfully passed the jury in my 4th year of painting at the Academie voor Beeldende Kunsten.

To the art section!!

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birkhoff theorem

Recently, Alex and myself extended the Birkhoff theorem for doubly stochastic matrices to unitary matrices, proving that a similar theorem can be formulated for unitary matrices.... at least for prime dimensions. We got contacted by Lin Chen and Li Yu, pointing out that a recent theorem by Klappenecker and Roetteler could be useful to prove the general case. And indeed, we worked our way through the proof, and even came up with an explicit parametrisation!

The details can be found in our recent arXiv.

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qcb/bps/celmekia

This is the year in which I was invited to speak on both the Quantum Chemistry in Belgium meeting and the meeting of the Belgian Physical Society. Whereas at QCB, I talked about our seniority project in quantum chemistry, the BPS talk was about its application in nuclear structure physics. The BPS meeting gives a nice overview of Belgian's finest in physics, and is nicely blogged about by colleague and collaborator Danny Vanpoucke

Another invitation to take the floor this year, came from the Celmeks art collective. I gave the very first talk on their very first event ever :-). I talked about the wonders of quantum mechanics, how they can defy all possible (classical) logic, how it has changed our lives and will continue to do so in unimaginable ways. It was basically a blackboard talk for a general audience (because we wanted to give it that sciency touch), but you can find my preparation notes here.

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read-green/block-zxz

There is news in the publication sector

Pieter's work on the Read-Green resonances has been published as a Rapid Communication in Physical Review B today. It is known that the p_x+ip_y superconductors have a zero-energy excitation mode at the (topological) Read-Green point, giving rise to a gapless spectrum. In the canonical case, the Read-Green point corresponds to the existence of a zero-rapidity mode in the Bethe Ansatz. This means that the system with N pairs is degenerate with a state of the N+1 system. By introducing a bath, allowing for particle exchange, it would be possible to see a resonance between the two states. Inna Lukyanenko and collaborators have shown that integrability can persist in such a system-bath coupling, so we set out to find the wave function and correlation functions. As was expected, the resonances are indeed visible in the pair-creation operator at the Read-Green points

Pieter will be presenting his results at the ISQS24 conference in beautiful Prague, so go up to him and say hi!

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block-zxz

And more news in the publication sector

Fuehr and Rzeszotnik recently put a twist on our matrix scaling algorithm, and proved (in theorem 8.1) that one can also scale a U(2^w) matrix into a block-ZXZ form in which each Z and X only contains U(2^w-1) matrices. Alex and myself worked out the explicit formulas for the block-Z and block-X matrices and showed how this can be used to decompose w-qubit circuits. Remarkably, in the case of a classical reversible circuit, the block-ZXZ decomposition of the associated permutation matrix P(2^w) reduces to the Birkhoff decomposition of reversible classical computing. In a previous version, we employed a Sinkhorn-like algorithm, but we figured out the explicit formulas from the proof of Fuehr and Rzeszotnik.

Technical details can be found on the arxiv

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maximum probability domains

... & spring again

We did some nice work on Maximum Probability Domains (MPDs) in quantum chemistry. An MPD(N) is defined as the (local) domain for which the probability to find N particles is maximal. It is to be expected that the MPD(N=2) will give a visual picture of where the Lewis pairs are. Guillaume has performed the very first MPD calculation for a fully correlated (CI) wavefunction. We developed the formalism for Hubbard-like molecules because all quote-orbitals-unquote are orthogonal, and the number operators become beautiful projection operators.

And did we see the Lewis pairs? First of all, we found out that MPDs must be spin-resolved, and we saw indeed some pointers, but no smoking gun (yet :-)). We published our findings in an honorary issue for Andreas Savin, the father of the MPDs, in Molecular Physics.

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book chapter

Alex and yours truly wrote a chapter for the book Problems and New Solutions in the Boolean Domain edited by Bernd Steinbach. It contains an early discussion on how the ZXZ matrix scaling decomposition can lead to the decomposition of an arbitrary quantum circuit.

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splash

fall 2015, part iv

The year almost slipped by without notice... lots of reading, calculating, analyzing, thinking, recalculating, drawing, rethinking, writing, rewriting, painting, etc.

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QCB12

fall 2015, part iii

Tomorrow, I will be at the Quantum Chemistry in Belgium (QCB12) meeting, presenting recent activities from the UGent-McMaster collaboration on seniority methods (Geminals, truncated DOCI, v2DM-DOCI). Title of my talk? When two is better than one: the seniority scheme as a new tool to build wave functions, perfectly fit in the spirit of Valentine. Please come over and say hi!

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jaynes-cummings-dicke

fall 2015, part ii

The year almost slipped by without notice... lots of reading, calculating, analyzing, thinking, recalculating, drawing, rethinking, writing, rewriting, painting, etc. On the Richardson-Gaudin side, Pieter's paper on the generalized Dicke models and their correlation functions in Faribault's eigenvalue based formalism (see 16 jun 2015) is now published in J. Phys. A: Math. Theor., and even received a special mentioning by means of an interview by the editorial office!

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v2dm-doci

fall 2015, part ii

Ward Poelmans published his first first-author paper on the variational optimization of the 2-body density matrix (v2DM). The v2DM method basically suffers from two demons. The first one is the N-representability problem, which states that any density matrix method must be derivable from an N-particle wavefunction. The second is the pernicious computatational scaling, due to the very nature of the semidefinte programming method. We felt ambitious and tried to mitigate both at once by reformulating the v2DM in paired space only, i.e. within the seniority scheme, or DOCI. As for all DOCI variants, the computational scaling is indeed much better, but we could not fix the size-consistency failure of v2DM. Although, in certain cases ....

A typical H8 (8 hydrogens on a chain) test calculation, with typical DOCI accuracy: missing dynamical correlations at equilibrium, but full static correlations at dissociation.

This paper constituted the backbone for Ward's (succesfully defended!) PhD thesis.

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doci

fall 2015, part i

The year almost slipped by without notice... lots of reading, calculating, analyzing, thinking, recalculating, drawing, rethinking, writing, rewriting, painting, etc. On the quantum chemistry side, two nice publications came out

Mario Van Raemdonck also published DOCI results, but now within a full Configuration Interaction (fCI) framework. We have recently started to understand that DOCI is almost tailor made for strong static correlations, because the Valence Bond resonances are basically contained somewhere in the seniority-zero space. But what about the missing correlations? Mario performed CISD-DOCI calculations, pointing out that all missing dynamic correlations are within the CISD space, with respect to the orbital optimized reference scheme. Also, we observed that better (variational) energies not always lead to better wavefunctions. Sometimes, the variational orbital optimizer is biased towards a few Slater determinants that will gain you energy, however chipping in on the accuracy of the wavefunction. The seniority-minimizing orbital optimizer is more reliable with that respect.

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