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00:24:54.000 [BLANK_AUDIO] 381 00:24:54.000 --> 00:25:04.000 [BLANK_AUDIO] 382 00:25:04.000 --> 00:25:14.000 [BLANK_AUDIO] 383 00:25:14.000 --> 00:25:22.000 [BLANK_AUDIO] 384 00:25:22.000 --> 00:25:32.000 [BLANK_AUDIO] 385 00:25:32.000 --> 00:25:42.000 [BLANK_AUDIO] 386 00:25:42.000 --> 00:25:50.000 [BLANK_AUDIO] 387 00:25:50.000 --> 00:26:00.000 [BLANK_AUDIO] 388 00:26:00.000 --> 00:26:10.000 [BLANK_AUDIO] 389 00:26:10.000 --> 00:26:20.000 [BLANK_AUDIO] 390 00:26:20.000 --> 00:26:30.000 [BLANK_AUDIO] 391 00:26:30.000 --> 00:26:40.000 [BLANK_AUDIO] 392 00:26:40.000 --> 00:26:50.000 [BLANK_AUDIO] 393 00:26:50.000 --> 00:27:10.000 [BLANK_AUDIO] 394 00:27:10.000 --> 00:27:20.000 [BLANK_AUDIO] 395 00:27:20.000 --> 00:27:30.000 [BLANK_AUDIO] 396 00:27:30.000 --> 00:27:40.000 [BLANK_AUDIO] 397 00:27:40.000 --> 00:27:50.000 [BLANK_AUDIO] 398 00:27:50.000 --> 00:28:00.000 [BLANK_AUDIO] 399 00:28:00.000 --> 00:28:10.000 [BLANK_AUDIO] 400 00:28:10.000 --> 00:28:20.000 [BLANK_AUDIO] 401 00:28:20.000 --> 00:28:28.000 [BLANK_AUDIO] 402 00:28:28.000 --> 00:28:38.000 [BLANK_AUDIO] 403 00:28:38.000 --> 00:28:48.000 [BLANK_AUDIO] 404 00:28:48.000 --> 00:28:58.000 [BLANK_AUDIO] 405 00:28:58.000 --> 00:29:08.000 [BLANK_AUDIO] 406 00:29:08.000 --> 00:29:18.000 [BLANK_AUDIO] 407 00:29:18.000 --> 00:29:28.000 [BLANK_AUDIO] 408 00:29:28.000 --> 00:29:36.000 [BLANK_AUDIO] 409 00:29:36.000 --> 00:29:46.000 [BLANK_AUDIO] 410 00:29:46.000 --> 00:29:48.000 [BLANK_AUDIO] 411 00:29:48.000 --> 00:29:56.000 [BLANK_AUDIO] 412 00:29:56.000 --> 00:30:04.000 [BLANK_AUDIO] 413 00:30:04.000 --> 00:30:14.000 [BLANK_AUDIO] 414 00:30:14.000 --> 00:30:24.000 [BLANK_AUDIO] 415 00:30:24.000 --> 00:30:34.000 [BLANK_AUDIO] 416 00:30:34.000 --> 00:30:44.000 [BLANK_AUDIO] 417 00:30:44.000 --> 00:30:54.000 [BLANK_AUDIO] 418 00:30:54.000 --> 00:31:04.000 [BLANK_AUDIO] 419 00:31:04.000 --> 00:31:14.000 [BLANK_AUDIO] 420 00:31:14.000 --> 00:31:24.000 [BLANK_AUDIO] 421 00:31:24.000 --> 00:31:32.000 [BLANK_AUDIO] 422 00:31:32.000 --> 00:31:34.000 [BLANK_AUDIO] 423 00:31:34.000 --> 00:31:36.000 [BLANK_AUDIO] 424 00:31:36.000 --> 00:31:42.000 And so here the hybrid quantum classical algorithms have gained a lot of popularity 425 00:31:42.000 --> 00:31:48.000 because they kind of combine the power of classical computing with this quantum counterpart. 426 00:31:48.000 --> 00:31:50.000 So the idea goes as follows. 427 00:31:50.000 --> 00:31:56.000 Imagine that you want to find the ground state of this Hamiltonian H, which is built out of several terms. 428 00:31:56.000 --> 00:32:01.000 Then we are going to divide the work between a classical processor and a quantum processor. 429 00:32:01.000 --> 00:32:09.000 So the classical processor is shown here in yellow and this is the quantum processor QPU. 430 00:32:09.000 --> 00:32:15.000 And so the quantum processor does the job that is difficult for the classical one. 431 00:32:15.000 --> 00:32:19.000 Storing the quantum state, manipulating the quantum state. 432 00:32:19.000 --> 00:32:21.000 These are difficult because this requires the big matrices. 433 00:32:21.000 --> 00:32:27.000 But then you can make measurements and then those are numbers, right? 434 00:32:27.000 --> 00:32:37.000 And then you can use those numbers to solve an optimization problem on a classical processor. 435 00:32:37.000 --> 00:32:45.000 And in this way, you can iteratively determine the unitary operator that is needed for the state. 436 00:32:45.000 --> 00:32:51.000 Because usually you would start with a state that is, let's say, a product state, an easily prepareable state. 437 00:32:51.000 --> 00:32:55.000 And then you want to get to the eigenstate of a complicated interacting Hamiltonian. 438 00:32:55.000 --> 00:33:03.000 And this is a difficult problem because you have a large state that acts on a large Hilbert space. 439 00:33:03.000 --> 00:33:07.000 You want to find the unitary operation that takes you to another state. 440 00:33:07.000 --> 00:33:09.000 It's not easy to solve. 441 00:33:09.000 --> 00:33:13.000 And this is why you need to have an iterative way of solving it. 442 00:33:13.000 --> 00:33:23.000 And I should mention here that this kind of quantum classical approaches gained a lot of popularity because right now what we think in the field is that we are not going to give people quantum desktops. 443 00:33:23.000 --> 00:33:31.000 We are going to have these quantum computers in high performance computing centers or in data centers. 444 00:33:31.000 --> 00:33:35.000 And there they are going to be embedded in a classical computing stack. 445 00:33:35.000 --> 00:33:39.000 And what we are going to do is to access these quantum computers as needed. 446 00:33:39.000 --> 00:33:49.000 And this kind of fast communication between classical and quantum computing facilities is something that's extremely popular. 447 00:33:49.000 --> 00:33:58.000 And so here there are two longitudinal questions that you have to find a way to parameterize this this unitary operator that prepares the state. 448 00:33:58.000 --> 00:34:04.000 And you have to determine these parameters by solving this complex optimization problem. 449 00:34:04.000 --> 00:34:10.000 And what I'm going to show you is that none of these are show stoppers and we have found nice ways to solve these problems. 450 00:34:10.000 --> 00:34:17.000 And we are quite optimistic about applying them to large scale quantum problems. 451 00:34:17.000 --> 00:34:20.000 So for now let us just focus on quantum state preparation. 452 00:34:20.000 --> 00:34:30.000 So here the problem is very simple simply stated at least which is that you have some initial state that you would easily prepare like a product state. 453 00:34:30.000 --> 00:34:35.000 Then you would apply some unitary operation to get to the target state. 454 00:34:35.000 --> 00:34:44.000 And typically we think that we are going to apply the unitary operation different unitary operations that labeled by one two and so on. 455 00:34:44.000 --> 00:34:47.000 These are the called the layers of unitary operation. 456 00:34:47.000 --> 00:34:55.000 And the issue that we often encounter is that there is not really a universal way to choose these operators. 457 00:34:55.000 --> 00:35:08.000 And there is a lot of heuristics that goes into this there. There are these well known approaches called adapt VQE which is adaptive variant of variational quantum item solver or the quantum alternating operator unsatz QA away. 458 00:35:08.000 --> 00:35:16.000 These are all these acronyms that show up and let me say you the trouble of going through all of that and I'm we're going to just answer this question. 459 00:35:16.000 --> 00:35:22.000 Is there a universal unsatz that kind of avoids all these heuristics? 460 00:35:22.000 --> 00:35:25.000 And the simplest idea worked. 461 00:35:25.000 --> 00:35:30.000 So the idea was to apply for all single and two qubit rotations. 462 00:35:30.000 --> 00:35:37.000 And we are going to allow for geometric locality that means that qubits that are close by will be will be coupled together. 463 00:35:37.000 --> 00:35:39.000 If it's needed by hardware. 464 00:35:39.000 --> 00:35:49.000 So for instance in superconducting quantum architectures, you have qubits that are side sitting side by side and then the nearest ones can talk to each other. 465 00:35:49.000 --> 00:35:54.000 And if you want to couple this qubit with a distant qubit, you have to go through all the other qubits. 466 00:35:54.000 --> 00:35:57.000 This is difficult to do it adds overhead. 467 00:35:57.000 --> 00:36:02.000 But in trapped ion architectures, all the qubits can couple to all of them. 468 00:36:02.000 --> 00:36:12.000 And so then we can just depending on what hardware we implement on, we can just impose the geometry locality or not. 469 00:36:12.000 --> 00:36:17.000 Now the alignment matrix is very simple. It relies on 17th and 18th century works. 470 00:36:17.000 --> 00:36:23.000 So where we just decompose this unitary operation into a brick wall or this nearest neighbor interactions like this. 471 00:36:23.000 --> 00:36:25.000 These are SU4 matrices. 472 00:36:25.000 --> 00:36:35.000 And then we use Euler and cartons decompositions to to come up with these elliptical unitaries and show you what these elliptical boxes are. 473 00:36:35.000 --> 00:36:47.000 So the first is cartons KAK decomposition. It just decomposes an SU4 matrix into four SU2 rotations and an SU4 in rectangular. 474 00:36:47.000 --> 00:36:51.000 You know that an SU2 rotation can be decomposed into three Euler angles. 475 00:36:51.000 --> 00:36:53.000 This is something that's just quantum mechanics. 476 00:36:53.000 --> 00:36:59.000 And this one is a bit more recent that you can write it out in terms of synod gates and single qubit rotations. 477 00:36:59.000 --> 00:37:02.000 You do not need to keep track of all these boxes. 478 00:37:02.000 --> 00:37:08.000 I just know that at the end, when the dust settles, we have some nice parameterization of these ellipses. 479 00:37:08.000 --> 00:37:11.000 Okay, so there are 10 parameters here. 480 00:37:11.000 --> 00:37:17.000 Okay, the 10 single qubit rotations, they all the parameters are in principle distinct. 481 00:37:17.000 --> 00:37:21.000 And we can use this to parameterize this elliptical box. 482 00:37:21.000 --> 00:37:32.000 And for a distant minor remark is that actually you need nine parameters and so you can get rid of here, but we just keep it for ease of implementation. 483 00:37:32.000 --> 00:37:40.000 Now this is still a very complex parameter space. You have lots of lots of room and so it's very hard to solve this optimization problem. 484 00:37:40.000 --> 00:37:46.000 And so we can impose symmetries when you can when you have them to make the problem easier. 485 00:37:46.000 --> 00:37:58.000 Imagine that you have a translation invariant Hamiltonian, you want to find its ground state, start from a translation invariant state and then choose the the answers, conserving that translation symmetry. 486 00:37:58.000 --> 00:38:10.000 You can also choose to conserve particle number, spin, spin parity, whatever you want and we played with several of these ideas. 487 00:38:10.000 --> 00:38:15.000 And then we can go on to the more difficult problem of how to solve this optimization. 488 00:38:15.000 --> 00:38:21.000 And so this is something I'm going to in the interest of time going to skip the details on this, but you can ask me afterwards. 489 00:38:21.000 --> 00:38:32.000 But we found a very nice way to do this optimizations relying on what is called a quantum natural gradient, which really was very. 490 00:38:32.000 --> 00:38:44.000 Yeah, I'm going to get to that question. So I'll tell you the question and then answer it. So so the quantum energy gradient helps in getting very nice circuits that are that are short dead. 491 00:38:44.000 --> 00:38:53.000 Now Greg has correctly pointed out that the number of parameters in s you for is n square minus one. So it's four square minus one is 15 and that is absolutely correct. 492 00:38:53.000 --> 00:39:07.000 And now that's why the work compress appears that if you see the can you see my mouse? No, Greg, Greg, can you see my mouse? 493 00:39:07.000 --> 00:39:18.000 Yes, yes. So see them when you when you concatenate these unitary this unitary combines with the next unitary that is sitting on top, right? 494 00:39:18.000 --> 00:39:36.000 So the blue box of this one and this one combined. And so then you don't have to solve separately for two s you two rotations, but solve for the one that combines the two in this way you can reduce the number of parameters from 15 to 9. 495 00:39:36.000 --> 00:39:55.000 Okay, very good. Hoping someone would be okay. So so now the benchmark. So and we are going to now show the noise less classical simulations. These are going to be just ground state. So we are going to look at three different models. 496 00:39:55.000 --> 00:40:09.000 And we're going to what is important is that we're going to use the same answers. We have this vision that we have a ring of cubits, let's say. And the cubits don't know what model I want to analyze the circuit. 497 00:40:09.000 --> 00:40:28.000 So the answer also doesn't need to know I will just put in the same answers and then solve just optimization problem that depends only on the Hamiltonian and that's how it should be somehow it's how it's how when you when you think of solving a problem on a classical computer even rebuild your computer every time you solve a problem right you have a universal machine. 498 00:40:28.000 --> 00:40:38.000 That's the kind of universal answers we are trying to go for. And so here are the three models that we have these are one eventual lattice quantum spin chains. 499 00:40:38.000 --> 00:40:44.000 There is the icing model, the three state parts model and the and there is another model called a massive swing or more. 500 00:40:44.000 --> 00:40:50.000 And here the different markers correspond to different system sizes different numbers of cubits. 501 00:40:50.000 --> 00:41:07.000 And the different colors correspond to the different number of unitary layers that I applied. And the lines the black lines that you see here the horizontal lines are the are the benchmark energies that you would get from density matrix normalization technique. 502 00:41:07.000 --> 00:41:13.000 This is a very powerful technique that for these models essentially gives us the energy to machine precision. 503 00:41:13.000 --> 00:41:20.000 And these are the Hamiltonians they look different and but they can be easily mapped to cubits. 504 00:41:20.000 --> 00:41:26.000 So this is this is easily it's already in terms of cubits. These are Pauli X Pauli Z and Pauli X's again. 505 00:41:26.000 --> 00:41:35.000 This is the Hamiltonian I'm not really discussing the physics of them of the Hamiltonian right now just look at them as Hamiltonians generic Hamilton. 506 00:41:35.000 --> 00:41:48.000 So this is this is the parts model where you have three states and I can just encode them into cubits. There is no no non trivial step here and then I can write down the Hamiltonian in the cubit language. 507 00:41:48.000 --> 00:41:59.000 And the other one is the model of one dimensional quantum dynamics where you have fermions coupled to an electromagnetic environment and here we're looking at one dimensional model with open boundaries. 508 00:41:59.000 --> 00:42:12.000 So you can eliminate the electromagnetic mode in terms of the in terms of the fermions then you can map the map the fermions to spins using Jordan Wigner transformation. 509 00:42:12.000 --> 00:42:16.000 And if you do all that calculation then you end up with a spin Hamiltonian. 510 00:42:16.000 --> 00:42:20.000 This is an all two all coupling Hamiltonian every spin couples to every other. 511 00:42:20.000 --> 00:42:26.000 This is a model which couples about five spins or so and this is the one that is just nearest neighbor. 512 00:42:26.000 --> 00:42:40.000 What is important is you see that here, even for n equals two or three that's very small number of layers and pretty much up to L equals 20 we get very good precision for all these modes. 513 00:42:40.000 --> 00:42:47.000 It doesn't care if the model has long range coupling like all to all if it has only a few side coupling on nearest neighbor. 514 00:42:47.000 --> 00:42:58.000 And if you're not seeing the precision achieved here is what I will show you, but first let me say that the order of magnitude, shallower circuits were produced here in this work. 515 00:42:58.000 --> 00:43:01.000 And this is the kind of precision we have. 516 00:43:01.000 --> 00:43:08.000 So for instance, you can look at the precision is up like three or four digits of precision. 517 00:43:08.000 --> 00:43:17.000 A very natural question is, why should it not work? There is no noise. So am I showing something tribute? No, the answer is no. 518 00:43:17.000 --> 00:43:26.000 And the reason is there is an ocean of expressibility in in these kind of quantum algorithms that I came up with a parameterization of a unitary operator. 519 00:43:26.000 --> 00:43:36.000 Right. And then I solved an optimization problem. The express ability tells us if the parameterization that I came up with is good enough to get to that state. 520 00:43:36.000 --> 00:43:42.000 And the fact that it works so well shows us that the optimization method that we have come up with actually working quite well. 521 00:43:42.000 --> 00:43:48.000 And so this is the main point of showing these noise less results. 522 00:43:48.000 --> 00:43:56.000 Yes, I just the statement of this result is that so you have all these models with different length of qubits. 523 00:43:56.000 --> 00:44:07.000 And in order for you to get to variationally get to the ground state, you only need to have an answer. So the depth that is. 524 00:44:07.000 --> 00:44:14.000 Yeah. So it's and so makes it the depth of the answers. It does it depend. Yes. So that's the next line. 525 00:44:14.000 --> 00:44:20.000 So here what we found and that's why encouraging is that the circuit depth scales with a correlation length. 526 00:44:20.000 --> 00:44:26.000 And it's intuitively very very meaningful because you think of the qubits are entangled across a length scale. 527 00:44:26.000 --> 00:44:31.000 And so you need to entangle only those qubits and a depth of that much will just entangle those qubits. 528 00:44:31.000 --> 00:44:41.000 And this is something that actually somehow was not known and somehow to my surprise, I must say, that when we wrote this paper, we found that people actually were using. 529 00:44:41.000 --> 00:44:56.000 Let's say that we're not going with correlation. And so it's something that because you can get stuck in in, you know, barren plateaus and all these technicalities of optimization problems that then give you somehow wrong impression of, you know, what the actual depth is. 530 00:44:56.000 --> 00:45:05.000 And so here we are able to get depth, which really scale with correlation. Very good. Any other questions. 531 00:45:05.000 --> 00:45:15.000 Okay. How much of the resources you need to get? It's just on laptop. It's very simple. Yeah, compared to always a dmrg. 532 00:45:15.000 --> 00:45:21.000 You know, it's hard to kind of quantify like wall clock time, you mean? 533 00:45:21.000 --> 00:45:29.000 Because you know, they kind of work with different ways, but I would say the dmrg is is nominally faster. 534 00:45:29.000 --> 00:45:34.000 So the optimization would take longer. Because it's a classical optimization. 535 00:45:34.000 --> 00:45:45.000 I would depend on epithelium. So the number of layers. 536 00:45:45.000 --> 00:45:50.000 Now, that's a difficult question because I think the, you know, I see grow the number of layers, the amount of entanglement grows. 537 00:45:50.000 --> 00:45:59.000 And so that will then scale with some true or some one dimension of the problem that is involved in representation of the state in terms of matrix product states. 538 00:45:59.000 --> 00:46:06.000 And so, typically, I would think that the one dimension would grow. 539 00:46:06.000 --> 00:46:17.000 Would the complexity would grow as order high cube or something. So that would be kind of the order N cube would be the intuition. 540 00:46:17.000 --> 00:46:24.000 Anything else? No. Okay. All right. So there were a few other models that I played with that we played with. 541 00:46:24.000 --> 00:46:35.000 One of them was actually the model of constrained Hilbert spaces. So here we were looking at models like which could be easily mapped to spin chains, which live in tensor product Hilbert space. 542 00:46:35.000 --> 00:46:43.000 Now, here I was playing with the idea of having what I call restricted solid and solid models where these are models of heights. 543 00:46:43.000 --> 00:46:53.000 You can think of a chain with heights at each site, but what height goes on what site depends on the neighbors. There is some kind of constrained Hilbert space that is allowed. 544 00:46:53.000 --> 00:46:58.000 So I was able to map it to the to the cube itself. 545 00:46:58.000 --> 00:47:07.000 And in terms of projectors. And then from there we can then immediately hook up the machinery that we have developed here and create ground states of these models. 546 00:47:07.000 --> 00:47:18.000 And why would you want to do this? Well, it's because these ground states are actually the ground states are the ground states of the conformal field theories to meet the so called minimal models. 547 00:47:18.000 --> 00:47:28.000 And they give us a very nice toy models. You can perturb them in certain ways. And these are toy models of one the quantum field theories and which are which are very fun to play with. 548 00:47:28.000 --> 00:47:34.000 And they are also ideal for realization and quantum simulator. This is what I will show you later on. 549 00:47:34.000 --> 00:47:49.000 And what is quite exciting is that I found that if you if you have multi-cupid measurements, then then you can actually find signatures of this constraints. And here these histograms actually show you occupation probabilities of heights in the ground state. 550 00:47:49.000 --> 00:47:56.000 And this is the case for for the peoples for which actually corresponds to the tri-criticalizing model. 551 00:47:56.000 --> 00:48:02.000 I'm not going to details here, but just leave it at that if you want to ask me about this. I'm very happy to tell you more. 552 00:48:02.000 --> 00:48:16.000 And more recently we have become interested in chemistry problems. And so this is work in collaboration with PINGU and TNU, and at Brookhaven and Robert Connick in Brookhaven, where we looked at molecular Hamiltonians. 553 00:48:16.000 --> 00:48:30.000 We used our same Euler-Kratan ansatz, the same thing that is behind the conformal theory model, spot models, Schringer models. And now we are now being used to analyze chemistry problems. 554 00:48:30.000 --> 00:48:39.000 So here we compute the ground state of this model, the rhodium cobalt molecule in the context of catalysis. 555 00:48:39.000 --> 00:48:51.000 And we see the precision in all these cases is fairly good with shallow depths, which makes us quite optimistic about implementation on actual quantum hardware. 556 00:48:51.000 --> 00:49:07.000 And we didn't just restrict ourselves to ground states. We also looked at excited states and using more complicated methods. And so there is a very recent work with my student David here, where we analyze some of these models and the excited states. 557 00:49:07.000 --> 00:49:17.000 But that was enough about modernist simulations. And so now at this point, you must be wondering, does any of this work on real quantum hardware? 558 00:49:17.000 --> 00:49:26.000 And the second question, which sometimes is even more important than the first one, is where is the supremacy or advantage of that? 559 00:49:26.000 --> 00:49:37.000 And so here is something that is motivated by a book that I read. It was made into a Hollywood movie. And the question of quantum supremacy can really be made into a nice movie. 560 00:49:37.000 --> 00:49:43.000 I think I'm willing to sell this poster to any Hollywood producer if they want that. 561 00:49:43.000 --> 00:49:56.000 And so the idea is that does any of this work? Yes, this I will show. Well, do we have supremacy or advantage? Well, that's a more difficult question. 562 00:49:56.000 --> 00:50:07.000 And so here is the honest answer. So we have about a hundred qubits in these machines. Now, if you think about it, you will say, well, why not quantum supremacy then? 563 00:50:07.000 --> 00:50:17.000 Because the world record right now to exactly diagonalize and analyze a qubit system is about 40 something qubits. 564 00:50:17.000 --> 00:50:24.000 So why can we not achieve quantum supremacy with hundred something qubits? It's because the qubits are constantly dying. 565 00:50:24.000 --> 00:50:35.000 The qubits are finite lifetimes. The gates are noisy. And so you cannot really create a quantum current state of a hundred qubits and do something useful with it. 566 00:50:35.000 --> 00:50:44.000 Is it possible in the future? Absolutely. And I'll show you results like from from last year and from three years ago where you can see the progress. 567 00:50:44.000 --> 00:50:51.000 And we are really optimistic that we will get there in the not too distant future. 568 00:50:51.000 --> 00:50:59.000 All right. So here are some simple results. We are going to look at two toy models. One is that of icing mason's. 569 00:50:59.000 --> 00:51:10.000 So this is the lattice Hamiltonian. It's a spin chain. There is it's model of a magnet. Okay. So there's the ferromagnetic interaction. There is some transverse field and some longitudinal field. 570 00:51:10.000 --> 00:51:21.000 The ferromagnetic interaction, of course, makes spins a line. This makes spins point in the x direction. And this also is an extra field along the z. 571 00:51:21.000 --> 00:51:29.000 There is a critical point at lambda equals one that separates the ferromagnetic and the paramagnetic phases for h equals zero. 572 00:51:29.000 --> 00:51:43.000 And for h not equals zero, lambda less than equal to one. There is a gap phase where you have coroncot's masonic excitation. You can really think of domain walls that get bound due to this magnetic field right here. 573 00:51:43.000 --> 00:51:50.000 Okay. And as you can see from the reference list, this goes back many, many decades. And this was very well understood. 574 00:51:50.000 --> 00:52:03.000 And it was our first venture into the quantum simulation business where we we try to see if the simplest of simple models can be can be can be analyzed on a quantum simulator. 575 00:52:03.000 --> 00:52:23.000 So this is from a few years ago and these are IBM Auckland and IBM Mumbai machines. We do a simple quench experiment. We prepare all this spins in in a polarized state to pointing to the right. Then we evolve with time and then we make single cubic measurements. 576 00:52:23.000 --> 00:52:38.000 And here are the results. So on the left panel, we see the the power spectrum of the sigma wire measurement. And you can see here the green line is exact computation down on a laptop. There is nothing quantum there. 577 00:52:38.000 --> 00:52:42.000 But it shows the piece where we should be expecting them just to check. 578 00:52:42.000 --> 00:52:59.000 Then these dashed orange lines are the lines that you see that are at a larger time step. So we have to now take larger time steps because we don't have that much freedom on the quantum simulator to take really small time steps and you cannot go very far before all the cubits are deco here. 579 00:52:59.000 --> 00:53:14.000 That's also a classical simulation of the orange lines. It again shows the peaks, but it shows that the peak location of the peaks is is relatively not sensitive, not too sensitive to the to the time. 580 00:53:14.000 --> 00:53:22.000 Now with that in mind, now we can run the experiment on the on the quantum hardware on these two quantum chips. 581 00:53:22.000 --> 00:53:35.000 And what we find is that you see the blue diamonds, they show up as spikes in the quantum data, right. So here at least the lowest spike that you can see quite quite clearly. 582 00:53:35.000 --> 00:53:40.000 And then the others are kind of depending on your level of enthusiasm. 583 00:53:40.000 --> 00:53:50.000 So if you kind of look on the right hand side, this is the summary of our findings. So you can see the lowest maze on, which is the dashed line right here. 584 00:53:50.000 --> 00:53:56.000 And this kind of see it, the you can see and these up and down triangles at different kinds of error mitigation techniques. 585 00:53:56.000 --> 00:54:01.000 But then the upper mazes are again, you know, some of them you can kind of tell, but the others not so. 586 00:54:01.000 --> 00:54:12.000 And this was from three years ago, okay. And so since then like other groups have tried to reproduce this results in some into other platforms and they have gotten better data. 587 00:54:12.000 --> 00:54:21.000 And more recently, there was a paper where they have not only looked at ising chains, but ising labs for similar bound states appear. 588 00:54:21.000 --> 00:54:37.000 So it really shows the progress and the next result that I will show you will actually would actually really demonstrate on a hardware, because this this experiment could not have been done about three years ago. 589 00:54:37.000 --> 00:54:44.000 So this is a, this is a different model. This is this is another variation of the quantumizing Hamiltonian where you have different perturbations. 590 00:54:44.000 --> 00:54:53.000 So these are the two terms of the Hamiltonian and I'm again glossing over what the terms really do in detail, but feel free to ask me afterwards. 591 00:54:53.000 --> 00:55:03.000 But the main thing I want you to notice is that the ising chain is tuned to criticality. See this, this number is one year, what I said earlier was a quantum critical point. 592 00:55:03.000 --> 00:55:13.000 And this parameter B is something that just determines the boundary condition. I'm going to say B is either 0 or 1, corresponding to an open chain or a periodic chain. 593 00:55:13.000 --> 00:55:20.000 And then there is a defect term here, which applies on the spins at K and K plus 1 inside. 594 00:55:20.000 --> 00:55:25.000 So you don't have to understand the details, but just notice that there are two picks points that appear. 595 00:55:25.000 --> 00:55:33.000 There's a length scale that is due to the fact that there is a parameter B. So the length scale is determined by E to the 4B. 596 00:55:33.000 --> 00:55:37.000 If L is much bigger than E to the 4V, the defect disappears. 597 00:55:37.000 --> 00:55:42.000 And if L is much smaller than E to the 4V, then there is the Kramas van Yeter. 598 00:55:42.000 --> 00:55:49.000 This is a very prototypical condo type problem. As you can see, we can come to references to many of this was known from many, many years ago. 599 00:55:49.000 --> 00:56:00.000 And was largely done here. And our goal was to see if we can find signatures of this defect on a quantum simulator. 600 00:56:00.000 --> 00:56:10.000 And what I found quite exciting was that this quantum simulator opens doors to new kinds of measurements that would be difficult to do on a solid state setting. 601 00:56:10.000 --> 00:56:24.000 So here what we will do is to prepare the ground state using using a quantum classical algorithm, then we are going to measure two point correlation functions of this of these two operators. 602 00:56:24.000 --> 00:56:28.000 And also measure the expectation value of the defect operator. 603 00:56:28.000 --> 00:56:36.000 Now in a condo matter setting, this would be hard to do because you cannot really create the ground state and then then measure two point functions. 604 00:56:36.000 --> 00:56:46.000 And this is something that the defect operator is often also not known, but even if it's known, it's hard to measure. 605 00:56:46.000 --> 00:56:53.000 Another point that I want to highlight is that this construction is done using integrability. 606 00:56:53.000 --> 00:56:58.000 And so there are some characteristics of the defect that are exactly visible on the left. 607 00:56:58.000 --> 00:57:05.000 So even if you have a very small quantum system, like a quantum simulator, you can exactly see their signatures. 608 00:57:05.000 --> 00:57:10.000 And so this is kind of the motivation and we wanted to see if this is possible. 609 00:57:10.000 --> 00:57:19.000 So what do you expect? Well, if you think of just an open chain for a second, for one second, let's just think that the chain is big. 610 00:57:19.000 --> 00:57:30.000 Then what you would see is that if you look at correlations on one side of the defect, you will get power law decay, which is characteristic of the icing criticality, the exponent is one port, which all of this is well known. 611 00:57:30.000 --> 00:57:39.000 Now, if you look at the other side, again, see the same thing. It's again a power law decay. The defect is not visible. 612 00:57:39.000 --> 00:57:50.000 But if you now look at correlations across the defect, then you see that it starts out as a power law decay, but then the correlation abruptly drops to zero as you cross the defect. 613 00:57:50.000 --> 00:57:57.000 And it is this jump that I'm hoping we could see on a quantum simulator, because this is not a tiny effect. 614 00:57:57.000 --> 00:58:03.000 It's a big jump. So this is what we tried to do. 615 00:58:03.000 --> 00:58:12.000 This is IBM Kingston. It has 156 qubits, but remember that we cannot use all of them because the qubits are deco hearing. 616 00:58:12.000 --> 00:58:14.000 Here is the result. 617 00:58:14.000 --> 00:58:32.000 So for b equals zero, which corresponds to no defect. So that's just the open icing chain. You just have power law decay and you can see the circles are not too far from the process and the distance from the process actually tells you how good the core exists across distances. 618 00:58:32.000 --> 00:58:42.000 Now, if you look at the case when v is forward, now you see that the, the, the, not the diamonds, but the squares, the correlation goes down. 619 00:58:42.000 --> 00:58:48.000 And then as you get to the defect point, the correlation drops abruptly. 620 00:58:48.000 --> 00:58:55.000 And this is something that we found to be true, not just for l equals 12, but also for l equals 16 side qubits and 16 qubits. 621 00:58:55.000 --> 00:59:07.000 And that's something that's quite promising and shows that you really can, can prove these kinds of defects on quantum simulators on such small simulators. 622 00:59:07.000 --> 00:59:22.000 The other thing is the expectation value of the defect operator. This is again to be maybe be technical and so just as a statement that these defect operator expectation value gives determines the sort of a g function of the defect, which uniquely identifies the defect. 623 00:59:22.000 --> 00:59:29.000 It's well known in this case in square root of two, you know, in the icing model is either two or square root of two or one. It's nothing else can ever happen. 624 00:59:29.000 --> 00:59:34.000 But so, so in this case, you have in square root of two here. 625 00:59:34.000 --> 00:59:41.000 And so we are going to measure this function. Traditionally, in a condensatory experiment, you would make thermodynamic measurements. 626 00:59:41.000 --> 00:59:50.000 You would look at change in the entropy, thermal entropy, and you would get the difference in the D function as the log of the D function would determine the change in the entry. 627 00:59:50.000 --> 01:00:00.000 And here we don't want to do that. We want to do it differently. So here we prepare the ground state of the of the icing chain periodic icing chain. 628 01:00:00.000 --> 01:00:08.000 Then we apply these controlled unitary rotations. These are the operators that build up the defect operator here. 629 01:00:08.000 --> 01:00:13.000 And then we measure using an and silacute. 630 01:00:13.000 --> 01:00:18.000 So this is something that is similar in spirit to the hardware test in quantum computer. 631 01:00:18.000 --> 01:00:25.000 And this approach then gives us the data that you see that was obtained from the quantum simulator. 632 01:00:25.000 --> 01:00:31.000 The circles are the experimental data. And you can see the crosses are perfectly on the square root of two. 633 01:00:31.000 --> 01:00:38.000 That's because the defect is perfectly realized on the lattice. So that's that's the that's the result. 634 01:00:38.000 --> 01:00:48.000 All right, I think it's over time. So let me just finish here. So I show you some results and noise less and then also some quantum accumulation results. 635 01:00:48.000 --> 01:00:55.000 And so where are what where do you think? Well, so let's look at the south bridge that goes up to Mount Everest. 636 01:00:55.000 --> 01:01:08.000 So if we'd imagined that the that the top is really fault tolerant universal quantum computation and let us say that this is where we were in fall 2021, which coincidentally happens to be the year I started at Rutgers. 637 01:01:08.000 --> 01:01:14.000 And then I would say that we moved quite far and we are about here. 638 01:01:14.000 --> 01:01:27.000 Where we are, let's say 40% there doesn't mean it gets easier. So next we are thinking of doing two plus one dimensional quantum models and chemistry molecules and here we have made a lot of progress. 639 01:01:27.000 --> 01:01:37.000 There was a recent work where we found new ways to do quantum simulation classical and quantum simulation by by conservative engaged symmetries in lattice case theories. 640 01:01:37.000 --> 01:01:52.000 And the work below talks about how to how to do quantum state preparation using automatic differentiation. These are all like technical works that are that have come out in the recent years and we are pretty optimistic that we are ready for the next step. 641 01:01:52.000 --> 01:01:58.000 And another step that we have to go through is the error corrected simulation right now. 642 01:01:58.000 --> 01:02:04.000 I never talked about error correction and error correction is crucial for doing something in scalable and also fall tolerant. 643 01:02:04.000 --> 01:02:12.000 And so here I'm excited about some recent work that I'm finishing up where we have some autonomous error corrected scheme for quantum simulation. 644 01:02:12.000 --> 01:02:19.000 So this is all that I want to say today. This is the pretty much where we are at. Let me thank my collaborators. 645 01:02:19.000 --> 01:02:29.000 So we first the group members. It's a current and former group members. These are the listed here and then ones who are highlighted are the ones who have contributed to the works I have shown. 646 01:02:29.000 --> 01:02:36.000 And on the right hand side, there are mentors and collaborators who have helped me in a step up the way. So these are these are listed here. 647 01:02:36.000 --> 01:02:45.000 And in some way or the other, the most of my work is funded by the Department of Energy and there's some small part from the scientific. Thank you. 648 01:02:45.000 --> 01:03:02.000 I really thought some mine as well. There's a lot of applause coming down. Yeah, you see it. 649 01:03:02.000 --> 01:03:11.000 So hopefully this error is a timescale not more. Yeah, you know, and one will one will see, but you know time will tell. 650 01:03:11.000 --> 01:03:16.000 Yeah, but so you believe that in principle. 651 01:03:16.000 --> 01:03:27.000 So it's a reasonable time to, I say, ultimately, quantum field theory to to a small way down the quantum computer without technological breakthrough. This is not going to happen. 652 01:03:27.000 --> 01:03:41.000 So, yeah, but, but you know, in five years, yeah, well, well, you know, I think what is kind of impressive, I think is the fact that when I was a graduate student, I graduated 2016. 653 01:03:41.000 --> 01:03:50.000 And at the time, nobody even believed that you would have more than five. There was this quantum chip in 2018 or so that a five. 654 01:03:50.000 --> 01:04:02.000 And then in the last 10 years, we have now we are now realistically accessing 156 qubits and the lifetimes have gone up from 100 microseconds to 300 microseconds, sometimes even more. 655 01:04:02.000 --> 01:04:12.000 And I'm sure what symbol have more to say about that. I think there's a lot of experimental advancement that is that has happened and is still needed to get to the goal. 656 01:04:12.000 --> 01:04:29.000 We are, I would say it's not impossible. There is nothing fundamental that stops us. That's what I guess. How about speed? You think that the quantum computers will be ever able to be sufficiently fast. 657 01:04:29.000 --> 01:04:39.000 That's, of course, the question about if you can really make it fast and not just fast, but you can also have to have this communication between quantum and classical. 658 01:04:39.000 --> 01:05:01.000 That has to be very rapid, right? The natural man's exactly exactly. But this is this is this is work that is that is currently being done. We are kind of conceiving schemes where we how can we embed this quantum computer on a classical setup and and how can we really make the speed faster and so these are, you know, I cannot say that this is absolutely clear that this is possible. 659 01:05:01.000 --> 01:05:18.000 But we are at least trying. This is a couple of questions online. Greg, would you unmute and ask your question? Yeah. So, so I realize this question is really very naive, but I want to ask it anyway. 660 01:05:18.000 --> 01:05:29.000 So why do we need quantum simulation? I mean nature is quantum mechanical and doesn't nature simulate itself? 661 01:05:29.000 --> 01:05:42.000 I guess the question is about controlled quantum simulation. So we would like to have some kind of predictive power where we kind of systematically isolate different effects and then then analyze the problem. 662 01:05:42.000 --> 01:06:05.000 Control is something. But what you say, you know, there's this idea of about analog quantum simulation where you kind of tailor a quantum system and then do the natural time evolution to do its job that kind of kind of hits both points where you would you would like to engineer a quantum system that has only the desired interactions, but then you would evolve in time just letting nature do the job. 663 01:06:05.000 --> 01:06:18.000 This is different from digital quantum computing, which is what I showed today. So the problem is, for instance, if you wanted to do the short factoring algorithm, how would you do it? 664 01:06:18.000 --> 01:06:24.000 And then you need something that really acts on qubits. Is that make sense? 665 01:06:24.000 --> 01:06:35.000 Yeah, okay, but you were you were finding a grandstates of Hamiltonians and so on. So I have a related question. So you're using DMRG is a benchmark. 666 01:06:35.000 --> 01:06:43.000 So what's the advantage of what you do? I mean, why not just use DMRG to answer the questions? 667 01:06:43.000 --> 01:06:53.000 Oh, absolutely. So it's for the one plus one dimensional models that I've shown here. There is no quantum advantage because I can use DMRG and that's what I'm using to compare actually. 668 01:06:53.000 --> 01:06:57.000 So it's just a test of the it's a test of your methods. 669 01:06:57.000 --> 01:06:58.000 Exactly. Exactly. 670 01:06:58.000 --> 01:07:04.000 The idea is that we can then use, for instance, time dynamics or high dimensional models where DMRG would not work so. 671 01:07:04.000 --> 01:07:15.000 Okay, thank you. There's another question online unless we can take one of the room. 672 01:07:15.000 --> 01:07:22.000 Here's all read it out. Can you say anything about the future back to AI on the field of research? 673 01:07:22.000 --> 01:07:31.000 So that's a that's a very good question and there is actually several sides of it and there is varying levels of animosity that goes with it. 674 01:07:31.000 --> 01:07:35.000 I think I will not try to provoke people here, but. 675 01:07:35.000 --> 01:07:46.000 So there was an initial idea that there are some quantum algorithms that could actually speed up algorithms for quantum for artificial intelligence. 676 01:07:46.000 --> 01:07:58.000 This is something that is still kind of unclear how they put pan out and if it is really true or not, what is clear is that AI is right now benefiting quantum computing because in terms of circuit optimization. 677 01:07:58.000 --> 01:08:04.000 In terms of, for instance, coming up with architectures, AI is actually helping us a lot. 678 01:08:04.000 --> 01:08:13.000 For instance, the concrete example is that of the. 679 01:08:13.000 --> 01:08:22.000 In this kind of setup that we that I showed about. 680 01:08:22.000 --> 01:08:27.000 So in this kind of setup of circuit optimization that I showed here. 681 01:08:27.000 --> 01:08:31.000 You can imagine well, what tells me that this is the best answers, right? 682 01:08:31.000 --> 01:08:42.000 So what if I create enough data that would be real with these answers and then train the train a model that would then come up with his own answers. 683 01:08:42.000 --> 01:08:47.000 It's not just about coming up with solving the optimization problem where I fixed the answers. 684 01:08:47.000 --> 01:08:59.000 And train the neural network to to come up with his own answers. And so there is a work that that has that was against some interest actually this is called. 685 01:08:59.000 --> 01:09:04.000 There is instead of VQE which stands for variational quantum Eigen solver. 686 01:09:04.000 --> 01:09:10.000 There is something called GQE, which is generative quantum Eigen solver and this was pioneered by the ended year group. 687 01:09:10.000 --> 01:09:20.000 So far it has not really been able to go past what we can do, but there is a good chance that there is something that that. 688 01:09:20.000 --> 01:09:34.000 That can happen through AI and I should say that some of the recent interest in the Genesis mission from the Department of Energy was very much leaning towards these kinds of words. 689 01:09:34.000 --> 01:09:39.000 Does that answer the question peers. 690 01:09:39.000 --> 01:09:45.000 Yeah, thank you. That's a great answer. 691 01:09:45.000 --> 01:09:57.000 Yes. Thank you for a beautiful talk. Can you give us a flavor of your thinking about error correction because that's of course what elephant in the room here. 692 01:09:57.000 --> 01:10:05.000 And and and you'll be I was going to ask it. You did put it up at the very end, but you certainly didn't give us enough time to. 693 01:10:05.000 --> 01:10:14.000 Yeah process. So so the idea is you know and so to give some context and if you if you think about the error correction in the classical computer. 694 01:10:14.000 --> 01:10:21.000 Like your laptop doesn't need air correction because the software will crash away before any errors happen at the level of transistors. 695 01:10:21.000 --> 01:10:27.000 But if you look at servers points in there you would need some air correction and that for instance there is a notion of air correcting memories. 696 01:10:27.000 --> 01:10:37.000 And now that's that's for classical systems which have like error rates of 10 to the minus 15 whereas for quantum systems as we saw the error rates of 10 to the minus three. 697 01:10:37.000 --> 01:10:47.000 And so we really need error correction and there were a lot there was a lot of progress that was done and so Peter Shore in 1995 actually came up with the world's first error correcting code. 698 01:10:47.000 --> 01:10:57.000 And then Kitai came up with the family of codes in 97 and so we do know a lot of ways to correct errors. It's the implementation that is hard. 699 01:10:57.000 --> 01:11:08.000 So for instance the simplest error correcting code that you could do is probably the steam code which has seven physical qubits and six measurement qubits that's a factor 13. 700 01:11:08.000 --> 01:11:20.000 So now if you want to implement let's say the same thing that I just showed you which would these with these kind of variational algorithms. 701 01:11:20.000 --> 01:11:31.000 If you look at the number of qubits here multiply the number by 13 for every qubit you need 13 qubits and that's a huge overhead. 702 01:11:31.000 --> 01:11:44.000 But but the statement is it's not it's not something that we can import and we have to get there and the large of the interest in in these kind of rare correcting codes is that we can maybe come up with different codes like. 703 01:11:44.000 --> 01:11:57.000 I think I'm passing like Sposonic codes people that continue like the the iceberg codes their names are everywhere so you know you cannot avoid them in quantum computing that they come up with names for every little thing. 704 01:11:57.000 --> 01:12:10.000 But for instance the IBM group likes for instance the the family of NDPC codes which are generalizations of stabilizer codes that we have known for a long time to works of Kitai and so. 705 01:12:10.000 --> 01:12:21.000 There is a good reason to to kind of push in that direction and right now that is one of the biggest bottlenecks and so somehow the. 706 01:12:21.000 --> 01:12:29.000 Yes so it's a bit difficult because right now we seem to kind of think as a community that we need about what can we do with the hundred qubits. 707 01:12:29.000 --> 01:12:48.000 But if you think of many body problems with their correction then you know the hundred is divided by 13 then this is what seven so that's not that's few what right so I think we need to get past 100 we need to get towards the thousand mark then we can really do something and. 708 01:12:48.000 --> 01:13:01.000 There is progress in if you look at road maps they all put out road maps that are that are very bold and and and very very enthusiastic so if we whether they can meet that or not is that's another question. 709 01:13:01.000 --> 01:13:04.000 Thank you. 710 01:13:04.000 --> 01:13:20.000 Yeah looking back at the IBM experiment yeah can you explain the deviation from the exact result from the experiment result just like human to go here and search you have a model for it. 711 01:13:20.000 --> 01:13:32.000 So here sorry the the next one. 712 01:13:32.000 --> 01:13:52.000 We did not we were we were not able to do the corresponding noisy simulation by systematically isolating the different channels of the coherence and this is something that that had proven to be an obstacle for us because noisy simulations are very computationally intensive and we cannot really go beyond six sides. 713 01:13:52.000 --> 01:14:21.000 And so I actually have made some progress that last slide had some made some progress here but I can now do it better but but I at the time we did not know what was really causing the difficulty and I should you know clearly point out that reproducibility is an issue with quantum systems right now so for instance if I ran the same if if Chris my quantum simulator simulation expert would run the same experiment. 714 01:14:21.000 --> 01:14:38.000 Again tomorrow that time translation is absolutely broke there's no way that you are going to get the same results tomorrow because you know quits die and you know it better than I and so in the experiment is a very complex experiments and so. 715 01:14:38.000 --> 01:14:56.000 Yeah so I could not say a bit better but but I am with the progress in in this analysis of this noisy simulations so yeah good yes thanks for last time I was well I enjoyed I understand this better so in this case you you prepare the ground state. 716 01:14:56.000 --> 01:15:07.000 Without the defect well with the indiscated with the itself but the first step of it was to prepare the ground state without the defense or with with also here this is an open system with the defect there is a ground state. 717 01:15:07.000 --> 01:15:35.000 And we just prepared the ground so and this statement is that if you prepare the ground state of this model with with the defect and the defect also had two fixed points you said like and that depends on the parameters so we fix V here the V is fixed to be 4 or 0 so these are the two curves so V is 0 or 4 they correspond to two different Hamiltonians and then I would just prepare the ground set of those two and then you if you measure the correlation function there are the rest of the defect which is just exactly. 718 01:15:35.000 --> 01:15:43.000 Then any one that you can do if you use a kind of flow K problem very switch between between the two ground states. 719 01:15:43.000 --> 01:15:53.000 Yeah I think we haven't played with that but there was an earlier work of Aditi Betra and when you found why and and so they were they were looking at these kind of flow K models and one of my students 720 01:15:53.000 --> 01:16:07.000 Matav Sina who kind of pushed a lot of the defect work during his PhD is now is now postdoc with Aditi and he tells me that he is doing that exactly what you're so that's something I can say. 721 01:16:07.000 --> 01:16:22.000 One thing I should say is that you know this is a critical quantum system so the ground state has algebraic correlations and so the depths are not short for the circuit of a 12 qubit we have at least like six layers of unitaries that's why the results are not great. 722 01:16:22.000 --> 01:16:25.000 But you know three years ago it would be complete stretch. 723 01:16:25.000 --> 01:16:32.000 And when you say six layers of unitaries you mean six layers of SC4 of the layers yeah the ones that I should use SC4 as absolutely. 724 01:16:32.000 --> 01:16:42.000 Well actually we have a different parameterization but you know something like that's something like 18 CNR gains per like per pair of qubit. 725 01:16:42.000 --> 01:16:43.000 Something like that. 726 01:16:43.000 --> 01:16:51.000 It's quite deep a circuit is quite deep and yeah we have all we always have to we get our quantum computing access through 727 01:16:51.000 --> 01:16:57.000 through Oak Ridge National Lab which which has this kind of access and they're often astonished at how much we need to expect. 728 01:16:57.000 --> 01:17:00.000 And you do like any of these error mitigation tricks itself. 729 01:17:00.000 --> 01:17:02.000 We do and so here this is done. 730 01:17:02.000 --> 01:17:09.000 So using proper ballistic error cancellation and maybe Z&E Chris do you want to verify that. 731 01:17:09.000 --> 01:17:13.000 The correlation functions were done without any error mitigation so we. 732 01:17:13.000 --> 01:17:17.000 Okay behavior so we could see it but that's why there's still a ship. 733 01:17:17.000 --> 01:17:24.000 So when we did the have a lot of signature operator that was using Z&E and then on the quantum chemistry for music. 734 01:17:24.000 --> 01:17:29.000 So this is the error cancellation will react to the number of inverted pair of circuits. 735 01:17:29.000 --> 01:17:32.000 Thank you Chris. 736 01:17:32.000 --> 01:17:36.000 Any other questions? 737 01:17:36.000 --> 01:17:45.000 Yeah I'm wondering about simulations with qubits that are hard to do with qubits. 738 01:17:45.000 --> 01:17:51.000 You know it's a it's a thing that you know either you either you love it or you hate it kind of thing. 739 01:17:51.000 --> 01:17:55.000 So I personally don't think that we should. 740 01:17:55.000 --> 01:17:59.000 That they're let's say that people this way qubits are harder. 741 01:17:59.000 --> 01:18:05.000 And not because they're not physical systems that have D levels that you can access. 742 01:18:05.000 --> 01:18:10.000 Not because they aren't those systems but it's because if you do error correction. 743 01:18:10.000 --> 01:18:19.000 If you think ahead and think of doing it in an error corrected way it's it's really hard to to understand error correcting codes for qubits. 744 01:18:19.000 --> 01:18:24.000 So so far you know I have I have that can counter qubits and qubits codes. 745 01:18:24.000 --> 01:18:28.000 But if you go to like higher levels it's not clear what you're gaining. 746 01:18:28.000 --> 01:18:36.000 And so it might in my experience and that's a very perhaps limited experience but in my experience I have found qu. 747 01:18:36.000 --> 01:18:48.000 Mapping to qubits is much more efficient than and doing error correction on them or doing algorithms on on those mapped models is much better than. 748 01:18:48.000 --> 01:18:55.000 Then doing you did algorithms and as a simple example this actually is a prototypical model. 749 01:18:55.000 --> 01:19:01.000 Of these height models that I have here. 750 01:19:01.000 --> 01:19:07.000 So in these heights you see the number p right and so that's actually the how many levels are there at each site. 751 01:19:07.000 --> 01:19:16.000 So in the actual model the height model the number of levels are actually 4 5 6 7 or 8 but I need up to 3 qubits per site. 752 01:19:16.000 --> 01:19:25.000 So that's kind of what I I mapped the model to qubits when the hope that error correction will help me do this in the future on a noisy machine. 753 01:19:25.000 --> 01:19:34.000 But this is an escape and saying if you have a Qtrate and you're assuming that the Qtrate or the Qtate has has that many independent errors right. 754 01:19:34.000 --> 01:19:47.000 So yes exactly so here that would be the same and I would say you know this this question is still open because not a lot is known about Qtit error correcting codes to kind of really compare apples to apples. 755 01:19:47.000 --> 01:19:51.000 I think that would be my mistake. 756 01:19:51.000 --> 01:20:06.000 Okay, given the hour I'll let somebody can end it for a bit. 757 01:20:06.000 --> 01:20:21.000 Yeah, it's really nice. 758 01:20:21.000 --> 01:20:27.000 I had lots of questions and I didn't think they were relegated. 759 01:20:27.000 --> 01:20:56.000 Thank you. 760 01:20:56.000 --> 01:21:05.000 It's not surprising that nobody else had tried. 761 01:21:05.000 --> 01:21:10.000 Yeah, I mean you explained it very well. 762 01:21:10.000 --> 01:21:27.000 So I guess is that is a valid question to try to find the optimal solution that would really come to the question of one. 763 01:21:27.000 --> 01:21:45.000 Maybe you said that. 764 01:21:45.000 --> 01:22:00.000 Yeah, that's a case where I mean to be observed in a quality is not fine. 765 01:22:00.000 --> 01:22:17.000 So I don't know how to do that. 766 01:22:17.000 --> 01:22:46.000 I don't know why. 767 01:22:46.000 --> 01:22:56.000 Yeah, yeah, yeah, yeah. 768 01:22:56.000 --> 01:23:16.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 769 01:23:16.000 --> 01:23:31.000 Yeah, yeah. 770 01:23:31.000 --> 01:23:57.000 Yeah, yeah, yeah, yeah, yeah, yeah. 771 01:23:57.000 --> 01:24:24.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 772 01:24:24.000 --> 01:24:29.000 But I thought this can be easily detected because of the local and the element stuff. 773 01:24:29.000 --> 01:24:35.000 So like if somebody is intercepting they can't like create the exact same function. 774 01:24:35.000 --> 01:24:37.000 Then get caught, right? 775 01:24:37.000 --> 01:24:46.000 If somebody is trying to do. 776 01:24:46.000 --> 01:25:05.000 But there's an error to it. 777 01:25:05.000 --> 01:25:09.000 So you don't know if it's error or somebody is dropping. 778 01:25:09.000 --> 01:25:19.000 The question is, what kind of error do you want to tolerate? 779 01:25:19.000 --> 01:25:37.000 So I don't know if it's error or if it's error or if it's error. 780 01:25:37.000 --> 01:25:55.000 The question is, what kind of error do you want to tolerate? 781 01:25:55.000 --> 01:26:14.000 Like they can have some problems like if one cubit just dies. 782 01:26:14.000 --> 01:26:34.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 783 01:26:34.000 --> 01:26:54.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 784 01:26:54.000 --> 01:27:12.000 Yeah, yeah, yeah, yeah. 785 01:27:12.000 --> 01:27:29.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 786 01:27:29.000 --> 01:27:58.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah. 787 01:27:58.000 --> 01:28:07.000 Yeah, yeah, yeah, yeah, yeah, yeah. 788 01:28:07.000 --> 01:28:34.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 789 01:28:34.000 --> 01:28:58.000 Yeah, yeah, yeah, yeah, yeah. 790 01:28:58.000 --> 01:29:18.000 Yeah, yeah, yeah, yeah, yeah, yeah. 791 01:29:18.000 --> 01:29:36.000 Yeah, yeah, yeah. 792 01:29:36.000 --> 01:29:56.000 Yeah, yeah, yeah. 793 01:29:56.000 --> 01:30:20.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 794 01:30:20.000 --> 01:30:35.000 Yeah, yeah, yeah, yeah. 795 01:30:35.000 --> 01:30:55.000 yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 796 01:30:55.000 --> 01:31:10.000 Yeah. 797 01:31:10.000 --> 01:31:25.000 Yeah. 798 01:31:25.000 --> 01:31:45.000 Yeah, yeah, yeah. 799 01:31:45.000 --> 01:31:55.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 800 01:31:55.000 --> 01:32:15.000 Yeah, yeah. 801 01:32:15.000 --> 01:32:39.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 802 01:32:39.000 --> 01:33:04.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 803 01:33:04.000 --> 01:33:14.000 Yeah, yeah. 804 01:33:14.000 --> 01:33:34.000 Yeah, yeah, yeah, yeah, yeah. 805 01:33:34.000 --> 01:33:54.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 806 01:33:54.000 --> 01:34:22.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. 807 01:34:22.000 --> 01:34:33.000 Yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah.