 So this work is based on so these people so I come to one one one two one five two eight three and So this work was provided in Conducted in collaboration with so you are sticky and you drill matadaki and shirokawa butter Okay, so Okay So we so we introduce Our purpose and results so Yes, so So that so when we We when we perform the QA so that's sources of computational error in QA it consists of two component and And no adiabatic transition and the effects of the coherence work So environmental noise So our purpose is to reduce the computational error in QA and So our result in this work it So three component and at first So proposal of method for national action of the homogeneous we did operated on the driver coming Tonya and The next one so demonstration of the above method for grand state search of hydrogen molecule And so last one so know I would know adiabatic transitions for The above method and estimate of the effect of the coherence Okay Okay, so we introduce The quantum annealing So we prepare that annealing Hamiltonian the other for all so this one so Equation number one So where HP denotes the problem Hamiltonian and HD denotes the drive Hamiltonian so So first so step one so we prepare the grand state of HD and Next step so time above was multi from zero to watch T using so this Hamiltonian so annealing Hamiltonian and So watch T is called annealing time And last step so we obtain the grand state of HP Okay, so this is quantum annealing and So next so we introduce a twist operator So in our method, so we use This operator so we define the twist operator as a forum. So this one so equation number to this one and So where so sigma JK so this one You know the problem at receipt and you find on the jet side and Next so watch air denotes the side number and so this one So she the J, you know the twist parameter parameters and We define the annealing Hamiltonian with twist parameter as a forum. So this one and so HD mean Drive Hamiltonian and HP denote problem Hamiltonian and Raji T denotes the annealing Hamiltonian So we make the annealing Hamiltonian adding a homogeneous twist operators to the drive Hamiltonian So we want to open multiple meter so theta J set So here we use the gradient descent method to find the optimal theta set Okay So we introduce the update so gradient descent or update method Okay So at first The first step is so make a reference a show so numerical numerical difference a show is So this formula and So where so E so a and this one You know the grand state energy obtained by Q a and so next So if she won't put this one and this one, you know The small value to which we choose and What's the one this one? So watch T opt so denotes the optimal annealing time T and so next So when we so using the numerical differentiation So we updated twist operators theta so using numerical differentiation to other forums so this one and so Alpha denotes the running way and this is as we choose so this value and So we repeat for step one and step two so we can obtain optimal twist parameter theta Okay, so we reveal the our method and And So our mess in the concept of our method is this figure so we obtain Energy using twisted Q a so this one this one and Update twisted parameter so using crossbar computer and so This is all Twisted parameter and this is new twisted parameter. And so next one. So we obtain the Energy using twisted Q a with new Twisted parameter and so we repeat we Repeat for this cycle Okay, so we find the optimal twist parameter using the gradient descent For their wings up energy as a cost function Okay, it's okay. So next So we perform the maker calculation using a following the GK as a master equation What are the master equation and so this equation is this one and And So sigma J K 1 N K denotes a parametric is on the jazz side and so we truly as so Sigma J Z so this one and World T denotes the death in matrix this one is this in matrix and Gamma denotes that the coherence rate and so we truly as so gamma equal this value and so in This make our calculation so we choose Running rate as this value Okay and so we Demonstrate So when the problem Hamiltonian is the hydrogen marker the Hamiltonian of hydrogen marker is given by so this one and Well, so we use the ST or standard basis and Jordan we not transformation the coefficient and so as well and each one 14 of the Hamiltonian depending on the interatomic distance And Yeah, so we obtained the deep value using open fermion software It is not that the grand state of hydrogen marker is Approximately the product state in a hundred four approximation and so we choose that it atomic distance as 0.74 Okay, we show numerical results at first So energy spectrum So left here this one is energy spectrum of conventional QA and So this one so white white figure is energy spectrum of Twisted QA and we can see that energy gap is open. So here and here and So next Energy step against energy against step number. So So blue line, you know, but it's not twisted case and so don't line the non-conventional scheme case and So This label means energy error So this figure showed so energy convergence and So next Make a result. So energy again are new in time And so blue line Means a variation of twisted case. So our scheme and so orange line means conventional scheme and So this this rubber means annealing time So the annealing time corresponding to the peak of energy for twisted QA is shorter than that for conventional QA and We find that the effect of no adiabatic function is less than the effect of the coherence Okay and so the last Make a result purity the beauty defined as this this value and so this value means that how close to the Best debt it is Okay, and so blue line. So this one this here is variational case and So this orange line is a conventional case So the purity of twisted QA is higher than the top conventional QA So therefore twisted QA supports the effects of the coherence compared to conventional QA Okay, so this is summary in talk Okay So summary so we propose a method for improving the accuracy of quantum annealing using twisted beretta and so this method The concept of this method is this figure and so We try to demonstrate for hydrogen molecule and And our method suppress the effect of the coherence and our method Suppresses no adiabatic traditions So thank you for Thank you Time for a few questions on the online participants Can you go to the slide where you're showing error versus annealing time Error versus annealing time annealing time Error versus annealing time yes Before this yeah energy error So why does it seem to be a drop leg for the variational twist method? Why is it dropping and then increasing again? I mean that error seems to be very less for very less annealing time So so in this demonstration So So the effect of the coherence So therefore So we can see that peak of energy error so It is okay not Okay, so the effect of the coherence is the reason for this increase at long times, right? Do I understand well other questions? Daniel, could you go to the slide where you define the lint blood? master equation model Yes, and now could you explain why the twists can Overcome or cancel this decoherence Oh Okay, so yes so we we choose it as So dick this decoherence type and so our twisted operator is so this one and So This operator this So yeah, so So this Hamiltonian it So Is represent Sigma X plus So she was it. Yes. So alpha sigma X plus alpha sigma Z that So playing so we can find Optimal so therefore So for example the HD if Dr. Hamiltonian is so wrongly to it Magni magnetic field So we can suppress That this type So decoherence See if it's okay No, no, I find it hard to believe that this works The reason is that are changing the Hamiltonian only and There's nothing that that seems to cancel out the The term that causes decoherence the sum over n Which is not Hamiltonian, right? There's a technique called dynamical decoupling which Reminds me a little bit of what you're doing here, but that would involve Fast pulsing so turning on and off on and off very fast the the driver Like like you seem to be doing but but but you're not doing that you're not turning the driver on and off you're You're just changing it once Finds then correctly It's very hard to see why you can cancel decoherence here. Anyway, maybe we can discuss that later Okay, so other questions if not, let's thank Dr. Kimoto again We have a coffee break on the