 Sure. Can you see it? Yes. Okay. Okay, I've started recording. Recording in progress. So good afternoon, everyone. My name is Hortran and I'm a postdoc researcher at the Lawrence Berkeley National Lab. So first of all I'd like to thank the organizers for inviting me to give this presentation. And it's really a pleasure to be here. So today the title of my talk is the open corner student toolkit for Hamiltonian quantum computing. And this talk will be structured around the work I did during my PhD at USC with my supervisor, Daniel Lidar. So I will mainly focus on the software package which we published to simulate open corner system dynamics. So the software package itself is completely open source so you can find it in this GitHub report. So I'd like to divide my talk into five sections. First, I'd like to give a brief review of the theory of open corner system. And then I'd like to introduce our software, Hortran, and show how it can help us as scientists and researchers working in the field by presenting some application where Hortran was used as numerical tools. Finally, if time permits, I'd like to discuss some future development of Hortran. So let's get started. Of course, the theory of open corner system is a large theory which filled with a lot of active research so I cannot possibly cover all of them during this brief review. So my goal of this review is to convince you that first, we should care about the theory of open corner system in AQC or in quantum computing in general. Second, besides those empirical fitted model used by the gate-based community, we should also care about the first principle approaches for the open corner system. And finally, a software package like COX is indeed a good idea. So I'd like to start with the last by doing a brief study of all the available open corner system method. So of course, the theory of open corner system studies the property of a small corner system in contact with the large environment. And in this talk, I will mainly focus on the open system dynamics because this is arguably one of the most important things with respect to corner engineering. So here, this is the general setup and how do we proceed from here? So the standard approach is to write on a formal equation of the reduced system dynamics by some kind of separate the equation of motion into a system part and the best part. So unfortunately, solving those formal equations is usually as hard as solving the original problem. So at this point, we need to start making approximations if we want to proceed. So the first set of approximations we can make is we can apply some formal expansion to this equation. For example, if we apply the high convolutionist expansion or the T-cell expansion to the Nakajima-Rendez equation, we end up with the T-cell master equation. So we can do similar things here and we will end up with this generalized hierarchical equation of motion. So those formal expansions provide us a systematic way to approach the open system dynamics, however, without further approximation, those equations are still challenging to solve and they usually lack reverse fun on a range of applicability. So from this point, it's safe to say now the game becomes a trade-off between approximation we make and the computational cost of solving the model. For example, if we assume the best is Gaussian, then our life could be immediately simplified. We would say some of the most familiar names in this list, for example, if we make the Markovian approximation with a Gaussian mass of the second order T-cell master equation, we have our beloved Redfield equation. So we can keep going to the right of this chart making more and more approximation. There will be a lot of tools in the literature and here I list a few of them. So here I'd like to point out two methods. First, the antibiotic master equation, AME, and the non-interaction bleep approximation, NEBA. So those two are the most well-known open system models used to solving the dynamics in the B-wave quantum meter. So, of course, my goal of the previous slide is not to confuse you with all the four-liter or five-liter abbreviations. So hopefully, by showing you all those available open quantum system methods, you could agree with me that the challenge of putting the open quantum system theory into practice, is that many of those methods are tailored for specific models and adapting them to different scenarios is very hard and testing those models would become a tedious process of trial and error. Besides scaling up the computation of various open system models, the challenge in itself. So with this now, if we have a software package that uses a play with different open system models on different systems, physical system, that would greatly help us to address those challenges. So now I would assume that if one of you is convinced that talks do sound like a good idea, so then why should we care about the first principle approaches instead of using the free-date model that people are doing in the gate-based community? So there are two angles to answer this question. First, the QA devices are actually described like the first principle model. The intuition is because the QA is basically a continuous time process and there usually exists a small gap region during the new, which is somehow more important than the other places. So those features make it hard to find a fitting model that could capture the underlying fittings. So here I listed some of the previous works where people study the open system dynamics from the first principle model on the D-Wing machine. So, and I'd also like to point out those two papers where AME and NIBA were first used and hopefully by the end of the presentation I could also convince you that there is another good model for this, which is the Portland Transform Redfield Equation. Besides the D-Wing platform, researchers have also tested those first principle models on other platforms, for example the flux qubit and the great agreement between the experiment and CERA are reported. So, from the other angle is to say some hardness, some challenges of applying those fitting models. So usually to find a fitting NIMBA machine or general cross-map there needs to be a completed learning procedure with some local and fast assumption. So usually those learned models would depend on the system of matronium and if we change the system of matronium we would usually need to re-learn the model or we can only think about the average case. So this is highly undeniable in practice. On the other hand, by design the first principle model would allow us to describe the noise with the smallest number of free parameters and the noise model would be independent from the system. So finally why should we care about the material of the quantum system in quantum annealing? So this is relatively easy to answer. So the first thing on one hand we know that open system is a source of decoherence. So if there is too much decoherence our system becomes classical and we may lose any potential for quantum speedup. This reason so the researchers in the field have been rigorously benchmark the experiment data against open quantum system model and classical model in search for unique quantum signatures. So on the other hand people also argue that maybe the thermal effect could help us in quantum annealing by helping the system to reach the most ground state faster with thermalization. So there are two examples in this line of research. One is assembly assisted turning and another is this mean annealing gap protocol. So hopefully at this point everyone will agree with me that Hawke says actually a good idea and open quantum theory of open quantum system is important. So now I'd like to change the gear a little bit by introducing Hawke's point of view of software. So as mentioned before this is an open source package which is hosted in this public available github repo and this can also be directly installed using the Julia package manager as a component too. So this is our humble first step of the grand goal I just described. So our goal is of course to provide as many tools as many as possible components as a tool to a user and the package should be user friendly without compromising performance. So to achieve this we adopted this three layer design of Hawke's so there is this user interface layer where people specify different objects in an open quantum system description like the bash, the system bash interaction and the hamper. So this package will describe store those things at intermediate representation only when the software is caught the package will convert those intermediate representation to some more hardware friendly and then fill it to the low-level routine for example an ODE driver in this case and of course when I began to work on Hawke's our main competitor on the market is the Qtip so here at least a comparison chart of the supported software type between Hawke's and Qtip. So you can see here the advantage of Hawke's that it supports some of the newly developed master equation time which believe to be will be useful in quantum computing. So finally at the end of the second section I'd like to present some benchmarking results of Hawke's. First of benchmarking I'm considering simulating the annealing process with this alternating sector chain program. So this program was first introduced in this paper as a toy model to search for any quantum signature so at this point the store guy would assume everyone is familiar with annealing. So basically the setup is that we have a proven Hamiltonian specified as an alternating sector chain and this Hamiltonian can be transformed into a free-form Hamiltonian so it's analytically soluble so but for the benchmarking purpose we solve the annealing process using the adiabatic master equation using both Qt and Hawke's and report the runtime in the figure on the right. So in this figure the X axis is the dimension of the system we simulate and the Y axis is the runtime so and we can already see here that's for this time dependent open assistant problem Hawke's already achieved order of magnitude comparing with Qt. So of course it's necessary to do more benchmarking on other methods of Hawke's and then we are still working on less and set up a dedicated benchmark report. So now here is our third section where I would like to showcase how Hawke's can help us as scientists and researchers in this field by presenting some project where Hawke's were used as numerical tools. So for the first set of examples I would like to put them in the category as the strong group, strong research we company with in quantum engineering. So the methodology of those researches is to compare the data from real-world devices with two different system models. One is our beloved adiabatic force equation the other is something called the polar transform rate field equation or the PDRE. So basically this equation PDRE is the real field equation we derived in the polar round frame. So the polar round frame is generated by this unitary. So the nice feature of PDRE is that it works in the range of AME. So if we consider this line as the system best coupling streams, AME actually works in the weak coupling limit where we create the system best interacting Hamiltonian at the perturbation and the symbolization happens in the eigenbasis of the Hamiltonian. So the PDRE everything actually happens in a rotated basis. So in the strongest limit of PDRE we have basically the Neva limit where we treat for the single cubic example we treat this transverse field streams as perturbation and the symbolization would happen in the low curve basis on the computational basis. So by comparing the real-world data with those two different models we observe that there is a signature of strong coupling limits in real-world quantum device. So the first experiment is the tunnel spectroscopy experiment. That experiment was proposed by scientists at D-Wave as a way to prove entanglement during the new. So the main idea of the experiment is instead of the common system qubits for a new we attach a probe qubit to it, to them. So the probe qubit somehow split the energy of the system into two different sectors and we can align the gone state of sector one to any state of sector zero by change the local field frames of the probe qubit. So then if we turn on the transverse field we would expect that the tunneling would happen between the two sectors and then we can plot the tunneling rate between the two sectors with respect to how we align the gone state with other energy states. So the experiment was reported in this figure as a start shift curve. So a following up study on this problem the author used the AME to study this process. So one mystery at that time was AME feels to capture this line-wise tunneling of the tunneling rate peaks. And people tried very hard and it seems that the AME did not capture this feature. So with HOX actually I can test this with different type of open system models and see how we compare with the experiment data. So what I tested includes two variables of adiabatic cluster equations and one of the program transformed red field equation with different pre-RE achieved the best agreement between the experiment data and the theory. And also it's correctly captured the line-wise tunneling feature of the experiment data. So this is the first experiment and then let's talk about the second experiment which was reported in this newly published paper which is the written of the weak coupling limit in corner annealing. So of course there are more results in this paper than what I listed here. So what I do here is to present the part where HOX is relevant as a showcase and while presenting the main idea of those papers. So here in this paper we actually simulate a reverse annealing algorithm with p equals two p-speed model. So the p-speed model is defined by this Hamiltonian. The nice thing about this Hamiltonian is it has two degenerate gone states. So let's think of a reverse annealing problem. So if we start from one state of the classical Hamiltonian and reverse back to some point of the annealing procedure and return to the classical Hamiltonian. If we think about this process if our system is really in the weak coupling limit and the civilisation is happening between the energy eigenstate we would expect that at the end of the experiment the population of those two degenerate eigenstates should be the same. This is also the prediction given by AAME where the X axis is the reversion point meaning how deep we go for this reverse annealing problem and the Y axis is the total success probability and instead of the population of the two degenerate gone states. So if we can say that AAME would predict that those two degenerate gone states would have the same population. However, this is not true in the experiment so with D-Wave data we observe a split between the two degenerate gone states with a change of the reverse choice of the reverse point. This feature can actually be correctly captured by the PTRU simulation where the similarization action happens in the local or computational basis instead of the energy eigenbasis. This suggests that in the current configuration of D-Wave it might work in the region of the strong coupling limit but it is worse to invest in the region for maybe a smaller annealing time or the region of more coherent annealing. So then there is the final project. Actually this project was also presented in this conference on Tuesday so I will just briefly go over this project again which is led by Xi and Groping for University of Waterloo with collaborations for USC and GC and MIT LinkedIn app. So the idea of this project is we have this new device flux QV device made for coordinate annealing and the good thing about this flux QV is that it offers more control. So we use the flux QV to perform the Landau-Wiener experiment. So then the nice thing is that the minimal gap of this Landau-Wiener experiment can be tuned by control the X flux on this flux loop. So and also of course we can think about this Landau-Wiener program as a toy model for coordinate annealing. So think about we start at the one stage of the Hamiltonian and we slip across the loop and avoid level crossing and we measure the population of element. We report it in the leftmost panel. So this the X axis being the dimension time of this Landau-Wiener sweep and the Y axis being the population of the one stage at the end of the experiment. So the nice feature of this experiment is that if we look at how the curve changes when we tune the X flux and as a result tuning the gap. So when the gap is large the experiment curve looks a lot more similar to the AME simulation result and when we turn down the gap makes the gap smaller the experiment curve becomes more similar to the PTRU result. This suggests that we actually by turning rescaling the Hamiltonian we can actually observe the transition from the strong to weak coupling limits on hardware. So and another interesting feature is that if we look at its turning rate the turning rate actually the strong coupling limit is more closer to the coherent turning rate and the weak coupling limit. So this is the argument people use to argue that several similar assisted quantum turning would actually help us. So then after the first three projects I would like to change the gear a little bit and present some use case of course outside the field of quantum engineering. So and hopefully this would still be interesting enough for my audience here today. So for this first project we instead of a actually try to simulate the quantum system dynamics on an IBM quantum device. So the idea is that in a typical IBM quantum computer we pick some qubit as the main qubit and we refer the rest of the qubit and the spectator qubit and what we do is to keep applying dynamical coupling sequence to the spectator qubit and measure or observe the dynamics of the main qubit. So the goal of this experiment is to demonstrate that dynamic decoupling can help us suppress the data across the device. So and without we reported in this paper besides that there are a lot more interesting results here and the readers could refer to our paper for more detailed discussion but here what I'd like to show is the experiment results and the simulation results from course. So what we did was to provide the fidelity of the main qubit with different choices of the initial state of the spectator qubit with and without dynamic decoupling and we can see our simulation without any experiment achieve very good qualitatively agreement. So we can also go one step further by asking how far we can push the limit of the first principle open quantum system models the first principle open quantum system models by making a more detailed construction of the open quantum system model. So in a follow-up study we instead of we make the following adjustment instead of those toy two level models we use the transformer circuit Hamiltonian in our description and we use the drag process instead of the instantaneous gate and we choose the system bath interacting Hamiltonian as a following. So for system bath interacting Hamiltonian we couple a bath to the charge operator of the transformer circuit we call it the X bath and we couple the bath to the current operator of the transformer circuit and also we add a stochastic noise telegraph noise to the charge operator of the transformer circuit to model the one over the noise in this process and we have a three step procedure to calibrate this noise model so first we calibrate the noise bath model of this X bath by using P1 data and then we calibrate the bath along the axis by using the data after we applied the DD where DD supposed to figure out all the snow noise in this process and finally we use the entire data set to capture those one over the F noise model and with the calibration procedure then what we did is to predict the dynamics of this transformer circuit with different initial states and on both free evolution and DD evolution so the result of this work was reported on those two figures where we report the relative error of our prediction and total evolution time so here the evolution time is reported as the number of gates so as we can see by using this first principle model we can achieve a relatively good we can achieve good relative error to in predicting the dynamics of the transformer circuit so finally things we I think I'm ahead of my schedule so I'd like to talk about some future development of course so here the question I would like to ask is can we simulate the open quantum system dynamics using a compressed format representation so what is so it seems that I have a question so I will try to answer the question in the Q&A section so sorry for this and so give me a second soon stop working so the compressed format is what used in the community of mathematician as a way to find a compact format of tensor network for things like data compression and machine learning so and one well known compressed format is the tensor train or maybe also known as matrix product state or matrix product operator by physicist so what's interesting is that mathematicians have been doing this for a long time where they know how we can do a matrix vector product using those compressed format so if we look at how we would solve an abatic master equation as an algorithm we would realize that every step in this algorithm what we really did were doing matrix vector product or matrix matrix product so the interesting question to ask of course is how do we replace everything here in this algorithm with compressed format and thus scale up our simulation capability of component system algorithm so this here we have some preliminary result what we did was we replaced those two steps with the compressed tensor train format so we would describe our density matrix and Hamiltonian in tensor train format and also we would change our eigen decomposition routine with different matrix with tensor train format and we use the density matrix renormalization group and the locally optimal flow precondition conjugate gradient method for this eigenvalue decomposition and by doing this we can actually scale up on the Davis master equation solver so here I reported some of the preliminary result we have where we compare our TT based solver with exact solutions so as we can see the result matched quickly even though we are making a lot more approximation here by using the tensor train format so lastly in my conclusion so in this talk I reviewed the serial open quantum system with a focus on quantum annealing and I presented our open source Julia package the Hawks and I illustrated the usage of Hawks by demonstrating application of Hawks in both QA and gate based quantum computing so that concludes my talk and thanks for listening and if you have any questions I would like I'm happy to answer so I think there is some question on the chat so let me read it okay so the question is could you explain why Lieba approximation is enough to account for the coherence effect in the intermediate coupling region it is usually a good approximation only for limited range of coupling strength so this is true and actually what you said is true so I think you are referring to this slide so what I'm saying is that Lieba actually can only work in the storm coupling region where Listerna T is created as a perturbation parameter the intermediate coupling region what can work if the poron transform red field equation you can think of it as an extension of Lieba so there are a lot of free parameters you can tune in PDRE so in one case if we choose our backs to be omics and we if we choose this system rotation you enter it to be an identity so in those limits we have power in Lieba so it works in the storm coupling but in general PDRE has a larger range of ability in Lieba and hopefully this answers your question would you clarify on slide 27 28 you described the tensor train so what was the topology of the system oh so here I'm doing an annealing experiment with the alternative sector chain problem so the topology is described here so it says a annealing problem with this 1D chain so in principle we would expect that the tensor train works however we did try a lot of other programs we tried the totally gadget program proposed by Google and a bunch of others and it seems that the tensor train format works really well so and I think the general philosophy here is to at least for me to treat this tensor train format as a mathematical decomposition data compression techniques instead of starting for any critical intuition maybe I mean we can try other possible tensor decomposition algorithms instead of tensor train and maybe we can expand a similar assessment to other critical configurations quickly share the github page so people can see what they need to do to download hox part of the goal of this talk was to provide people to access this program which we think is a nice compliment to qtip and as I showed in some cases actually seems to be faster than qtip so could you give people a quick pointer there yes okay let me share my screen actually I have a quick question about that is it faster than qtip because you use Julia sorry is it faster than qtip because you are using Julia yes that's part of the reason and another reason I'm using one of the best low-level ODE servers which is also written in Julia and they're about professional mathematical maintenance of ODE so that ODE server is also potentially much faster than what people use in Python so here I mean this is the github page of the hox so and you can see here is a readme file and it's described how you can install a hox so it's actually very easy so you just install Julia and you open Julia and run those two lines of code and you automatically install everything for you so the address of this is of course the open content tools so the name is different than hox because we want to conform with the Julia package then get guidelines alright let's thank the speaker again