Qedma at Q2B 2025 Tokyo – Netanel Linder (Qedma) and Seiji Yunoki (RIKEN) on Quantum-Enhanced HPC Simulations with Error Mitigation

[0:00] [Music] [0:05] Hello everyone. Uh thank you for [0:06] attending. So it’s a great pleasure uh [0:09] to give this talk together with my great [0:11] collaborator uh Yukisan from Ricken and [0:15] we’ll be talking about how to enhance [0:17] HPC simulations using error mitigated [0:20] quantum computers. So let me first begin [0:22] by introducing the problem. The main [0:24] problem with quantum computing at this [0:26] time is the issue of errors and noise in [0:28] quantum computers. We all know that [0:31] noise severely limits the size of [0:33] quantum computations that we can do with [0:35] quantum computers. Um and we this [0:38] problem can be remedied in two different [0:40] ways. One of them is to use a large [0:42] number of extra cubits in order to use [0:44] error correction. These cubits also have [0:45] to be of very high fidelity in order for [0:48] this to be useful. current devices uh [0:51] are don’t have the numbers for making [0:53] error correction uh still kind of use [0:55] useful uh in a practical sense uh and [0:58] the other way uh other resources you [1:00] could use is to use extra QPU time and [1:03] use methods undergoing the name of error [1:04] mitigation um and here the QPU time [1:07] could be large it’s important to use a [1:09] method that is very efficient this is [1:10] what we’re focusing at at KDMA we’ve [1:12] developed a software called Kessum which [1:14] I’ll introduce uh which does this very [1:16] efficiently um and and this uh type of [1:19] methods do not need x any extra number [1:21] uh cubit overhead. Furthermore, uh error [1:25] mitigation can be combined together with [1:28] error correction to give a significant [1:30] extra boost over air correction and can [1:33] also be combined together with HPCs in [1:35] order to boost performance and this is [1:37] going to be the focus on this [1:39] talk. So let me discuss uh the [1:43] possibility of obtaining a quantum [1:45] advantage with error mitigation. So the [1:48] time for performing error mitigation [1:50] scales mildly exponentially [1:53] uh with the uh circuit volume times the [1:57] error rate. Now this exponential scaling [1:59] means that there could not be an [2:00] exponential quantum advantage but there [2:01] could be a polomial advantage of a very [2:04] high degree uh for quantum computing [2:07] versus classical computing. Uh and this [2:09] polomial could be uh of a degree of one [2:12] over the error rate which is very large. [2:14] It could be in the order of a thousand. [2:16] So this very large polomial advantage [2:19] can lead to dramatic qu finite quantum [2:22] advantages. These are the practical [2:23] quantum advantages we’re interested [2:26] in. Um so you know in order to enjoy [2:30] quantum advantage uh using error [2:32] mitigation it’s of course important to [2:34] use an method which is efficient in [2:36] order to reach the largest uh circuit [2:38] volumes possible. But it’s also [2:40] important to use a method which is [2:41] unbiased since in the regime of quantum [2:44] advantage you cannot verify your results [2:45] anymore against classical simulations. [2:48] In fact, using the devices that are [2:50] available today, I’ll show you that [2:52] we’re very close to achieving quantum [2:54] advantage for executing circuits and uh [2:57] with you know next generation of devices [2:59] we’re going to be in the quantum [3:01] advantage regime and furthermore using [3:03] the combination with HPCs our work with [3:06] we can show we can really accelerate the [3:08] timeline for achieving uh quantum [3:10] advantage um already [3:13] today. So let me introduce KSM. Kessm [3:16] stands for quantum error suppression and [3:18] error mitigation. In Hebrew, Kessm mean [3:21] magics. Um it is a few things I want you [3:25] to keep in mind about uh KSM. One of [3:27] them is that it’s based on an unbiased [3:29] method. Meaning that when you execute [3:31] the algorithm, you’re getting results [3:34] from a noise-free quantum computer. The [3:36] only remaining uh sources of noise are [3:39] statistical. This is an inherent part of [3:41] quantum mechanics and could be reduced [3:43] just by running for a longer time. The [3:46] method works for any quantum algorithm. [3:47] We refer to it as being algorithm [3:49] agnostics. It also uh works for a [3:52] variety of different quantum hardares [3:54] and we’ve tested it also uh extensively. [3:57] It also has a very flexible deployment [3:59] that could be used either through our [4:01] cloud, it could be installed on premises [4:03] or could be used through a kitkit [4:05] function uh that we deploy. So let me [4:08] give you a bird’s eye view of how the [4:10] software works. The end user sends our [4:13] system the circuit he wants to run, the [4:16] uh level of access he want to get and uh [4:19] the specific device he wants to run on. [4:22] Then based on this information at the [4:24] time of execution we run a job for [4:26] characterizing in a very precise way the [4:29] noise sources in the device. uh based on [4:32] this we optimize gates we transpile the [4:34] circuit and we compile the circuit uh to [4:37] an ensemble quantum circuits which we [4:39] then execute on the device and by [4:41] classical post-processing we return [4:43] noise free results to the user [4:46] um to quantify the benefits of KM it’s [4:49] it’s important to look at a quantity we [4:50] call the circuit volume boost this is [4:52] the ratio between the largest volume you [4:55] can reach with KSM over the largest [4:57] volume you can reach just by running on [5:00] the device with no error mitigation for [5:02] a given accuracy and this boost for high [5:06] accuracies could become very very large [5:07] on the order of a thousand. Uh again [5:10] this means that you can run a circuit [5:11] that is a thousand times larger than [5:13] what you could do otherwise. Um you can [5:16] also compare KSM to other competing [5:18] method that are unbiased like pro [5:20] ballistic error cancellation and you can [5:22] see that KM runs exponentially faster [5:25] giving you access to uh circuit volumes [5:28] which are significantly larger. [5:31] Um before I’ll show you some results I [5:33] want to uh introduce a quantity which is [5:35] important in order to quantify [5:36] performance and this quantity is called [5:39] the active volume. The active volume for [5:41] a given circuit and observable you want [5:43] to compute counts the number of two [5:45] cubic gates that are affecting that [5:47] observable and this import this quantity [5:50] quantifies all the complexity for [5:52] performing error mitigation since you [5:54] only need to error mitigate gates within [5:57] the active volume. It also quantifies [5:59] how hard it is to do a classical [6:00] simulation. Since you only need to [6:02] simulate the gates within this active [6:04] volume and you know the shape and the [6:07] size of this active volume strongly [6:09] depends on the parameters of the [6:11] circuit. Here we are plotting it uh for [6:13] a family of circuits called the Toronto [6:15] kicked icing model which we’ll be using [6:18] uh in the next slides. So here’s a [6:21] recent result from a herm device. Uh [6:23] here we used 130 cubits uh on IBM [6:27] Marrakesh. Uh we ran this protoerizing [6:30] circuits for uh 13 protoer time steps. [6:33] Uh this is a large circuit. It’s over [6:35] 30,000 uh CZ gates. Uh it is of depth of [6:39] 78. Um and we computed uh you know [6:43] different observables here uh from [6:46] single point correlations to four point [6:48] correlations. We compare them here to [6:50] the ideal results plotted in gray. Um [6:53] the red points are the results you get [6:56] by running on the device with no error [6:58] mitigation. You can see that there is [6:59] very big systematic errors and the blue [7:02] markers are the results we get with [7:04] Kessm which agree very well with the uh [7:07] correct results. On the right you can [7:09] also see how the uh active volume or the [7:12] lite cone evolves uh with the number of [7:14] time steps and you see that eventually [7:16] at at 13 time steps it covers almost the [7:19] full [7:20] device. Um here are some uh uh problems [7:24] we worked on with our uh collaborators [7:27] and partners. Uh this is a group [7:29] focusing on on high energy. Um and they [7:32] used KSM to study uh couplings uh in a [7:36] one U1 lattice gaze theory in two plus [7:38] one dimension. They used the VQE [7:40] approach uh and used Kessm for for [7:43] executing the circuits. Um they also [7:45] used uh KSM uh for a fluid dynamics [7:48] problem in which they measured the [7:50] moments of the velocity field. The [7:52] quantum chemistry group at the [7:54] University of Southern Denmark uh used [7:56] Kessm for performing VQE for the ground [7:59] set of the H2O molecule. Uh and the [8:02] group of softbank used in the QML [8:05] algorithm uh in which uh they computed a [8:08] kernel matrix using KSM and you can see [8:11] here the results. Uh you can see the uh [8:14] comparison between the ideal uh kernel [8:16] matrix uh the kernel matrix you could [8:19] get when you run on the device with no [8:21] error mitigation on the left and you can [8:22] see that there are very big systematic [8:24] errors and you can see on the right the [8:26] results for the kernel matrix you get [8:28] with Kessm which agree very well uh with [8:30] the ideal [8:31] result. So um let me discuss the road [8:35] map for achieving quantum advantage with [8:37] KSM. uh in this plot you can see the [8:40] runtime of KM as a function of the [8:42] active volume for different values of [8:45] the uh fidelity. You can also see how [8:48] HPC state vector simulation scale um as [8:51] a function of this active volume and you [8:54] can see that with fidelities of 99.8% 8% [8:57] uh you can already be in the quantum [8:59] advantage regime for kind of generic [9:01] circuits and you can also see that the [9:04] uh you know the issue of the question of [9:06] when do you cross in the quantum [9:07] advantage regime also depends on the [9:09] geometry of the specific uh active [9:12] volume that you’re looking at. So I want [9:15] now to turn over the stage to Yukian uh [9:18] who told us about really great [9:20] collaboration uh in which we showed that [9:22] the combination of custom together with [9:23] HPCs uh can enhance classical [9:27] simulations already today. [9:35] Okay. Okay. Thank you. Uh so let’s wait. [9:42] Oh, maybe I have to. Okay, at le our [9:46] team is mainly focusing on uh classical [9:49] computations particularly uh tensor [9:51] network based method. uh as a quick [9:54] reminder uh NPO and NO related [9:57] approaches are very powerful classical [10:00] approach to compress data classical [10:05] informations and let’s let’s just assume [10:07] that we have a operator or acting on n [10:12] cqits and in order to represent this [10:14] operator we generally need a four to n [10:18] uh parameters and therefore it usually [10:21] cost you like exponential potentially [10:23] large amount of computational time with [10:26] increasing the number of cubits n uh if [10:30] you want to treat uh this uh uh operator [10:33] numerically [10:34] exactly. However, uh uh the MPO and NPO [10:39] related approach uh provide you uh [10:43] compress uh representation of operator [10:46] or as a product of uh matrices with bond [10:50] dimension kai and the computational cost [10:54] uh for this approach scales uh as the [10:58] kai cube and therefore this is more [11:01] convenient than the numerically exact [11:04] approach and this method is widely used [11:06] in various research fields including uh [11:10] physics, quantum chemistry and and [11:12] machine learning. And in this talk uh [11:16] we’d like to propose our new approach [11:19] which we would like to call a quant [11:21] enhanced MPO computations. And the key [11:24] idea here is to apply simply a cont onto [11:29] a MPO [11:31] uh and measure the expectation value of [11:34] the the resulting the the operator using [11:38] quantum computer with error mitigation. [11:42] So as a use case uh uh use case example [11:47] uh we consider quantum dynamics that is [11:52] uh split between quant and classical [11:56] computations. More precisely uh we uh uh [12:01] uh divide the total evolution steps uh [12:05] large t uh into uh two segments. The [12:09] first part first segment is performed on [12:12] a class and on a quantum computer while [12:15] the second segment is handled uh using a [12:19] classical computers by uh back [12:22] propagating the operator or for a time [12:26] steps tab uh using [12:29] MO. And this approach allows you uh to [12:34] uh to to to evaluate the expectation [12:37] value of the operator or of [12:41] tow over a time evolved state outside of [12:45] small t uh by running the first part of [12:49] the time steps using quantum computer. [12:53] So to demonstrate our approach here we [12:56] consider a one-dimensional kickizing [12:59] model on 75 cubits [13:03] uh with this particular parameters [13:06] uh where uh you can find discretion [13:09] crystal and we measure a magnetization m [13:13] over the entire uh [13:16] cubits and for all the experiments uh we [13:19] used IBM two systems. [13:23] uh uh and we set the classical uh [13:27] evolution time to uh uh equal 10 [13:32] steps. And without error mitigations, [13:36] the estimated magnetization [13:39] uh [13:41] uh here [13:44] represented by red stock here [13:48] uh deviate significantly from the ideal [13:50] values shown in the gray. [13:54] However, after applying the testing for [13:57] the error mitigation, the results shown [14:00] in blue [14:02] uh agrees quantitatively [14:06] uh uh uh wi with the ideal value or [14:10] within the statistical accur statistical [14:13] error bars. [14:17] More importantly that the time required [14:20] to obtain this error mitigated uh uh uh [14:25] uh magnetization is [14:28] uh is only 8 minutes here [14:32] uh for the total time steps [14:34] 15 with uh classical time step 10 10 [14:38] time steps. [14:40] Uh in contrast, if you use uh quantum [14:43] computers alone [14:46] uh to achieve the same statistical [14:48] accuracy, [14:50] uh the estimated uh the the required QPU [14:54] time would be uh increased up to like [14:59] 240 [15:00] minutes. And the benefit of our approach [15:04] becomes more pronounced for a longer [15:06] time steps such as 25 time steps where [15:12] the required QP time reduces from 17,000 [15:16] minutes to 120 [15:19] minutes if we use our approach. [15:26] So uh using a very simple math with uh [15:29] some reasonable assumption uh one can [15:33] estimate a QPU time required [15:36] uh uh scales uh according to the [15:40] expression shown there up there. there [15:43] uh uh kai in is the bond dimension of [15:48] the mo that is calculated using [15:52] classical [15:53] computers and if is the infidelity of [15:57] the quantum computers employed in your [16:00] experiments and small t uh is the the [16:05] portion of the uh quantum portion of the [16:08] time steps [16:10] uh that that that that you do in a [16:12] quantum [16:14] computer. Uh indeed our experiments [16:17] shown in the previous viewraph [16:20] uh scales very nicely [16:23] uh according to this scaling uh form [16:26] indicated by this straight lines [16:29] here. Since the classical runtime [16:32] required to extend [16:35] uh the evolution by another uh time step [16:39] small t scales exponentially. Uh there [16:42] is a very uh strong uh potential [16:46] to realize quant advantage provided that [16:50] the infidelity of the quant computers uh [16:53] is sufficiently small. [16:58] So finally uh let me give you uh uh the [17:03] concrete example uh by estimating the [17:07] actual runtime. Let’s just assume that [17:10] we have a MO with bond dimension [17:14] 10,000 which is given in this estimate. [17:19] So extending the evolution for another [17:22] five time steps [17:25] uh [17:26] would would require approximately 276 [17:31] hours if you use one of the NVIDIA [17:36] system. In contrast [17:39] uh uh the the required time the QPU time [17:43] in our approach is just 30 minutes. [17:47] Note that here also we have additional [17:49] classical time 17 hours to decompose the [17:53] the mo with bond dimension [17:57] 1000 and the advantage of approach uh [18:00] becomes more clear uh for uh when the [18:04] time step is extended to like 10 steps [18:08] over there [18:10] here the required I if you use a quant I [18:14] mean classical approach [18:16] it it it requires like more than 3,000 [18:20] hours whereas our [18:22] approach can still complete in just [18:26] three [18:27] hours and then even more interesting uh [18:30] if the content computer reaches like a [18:33] fidelity of [18:36] 99.9% the uh the required QPU time uh to [18:41] simulate up to like a 50 time step is [18:44] only 3 [18:48] hours. So these estimates strongly [18:51] suggest that the content advantage may [18:54] be achievable uh much sooner than uh [18:57] previously expected [18:59] uh well before the full FTPC [19:01] era. So please stay tuned because more [19:06] interestingly that are coming soon. [19:08] Thank you. [19:15] Thank you very much. I think we have a a [19:17] question for Netanau, I believe. Um it’s [19:20] in Japanese, but I’ll um translate it. [19:22] Um so um it’s a two-part question. Is uh [19:27] Kessum a solution that is deployed on [19:30] software and second part is is it um [19:34] reliant or upon IBM hardware. Thank you. [19:38] Yeah. So KM is a software solution. uh [19:40] you know it could be accessed through [19:42] our own cloud. It’s also integrated as [19:44] in the Kiskit function in IBM but it is [19:47] not uh you know specific for IBM [19:49] hardware. Uh we’ve tested it on uh [19:52] variety of different hardwarees uh [19:54] including IMQ and uh and IQM and other [19:57] hardware. So you know it it could be [20:00] used on any hardware uh and it needs [20:03] just some adaptation in terms of the [20:05] characterization part of the software. [20:07] Okay. Thank you very much. Thank you [20:10] again both to Yoan and Netanel. [20:16] [Music]