Q2B24 Tokyo | Pushing Forward for Quantum Avantage with Error Mitigation and HPC | Qedma & Riken

0:00 [Music] 0:05 I’m nanel from kma and uh I’ll be 0:08 sharing this talk together with uh San 0:11 from ricken and we’ll be describing our 0:14 work uh for using aror mitigation and 0:17 HPC to push forward for Quantum 0:22 Advantage can I have the clicker 0:26 working okay so uh we we all know that 0:30 errors and noise really constitute a 0:32 huge problem for Quantum Computing if 0:34 you try to run even on the best devices 0:37 available out there any Quantum circuit 0:39 with appreciable size you’ll see that 0:41 you get very large systematic errors 0:43 that get worse and worse as you increase 0:46 the size of your program now there’s 0:49 several ways to remedy this maybe the 0:51 most known well wellknown way is error 0:54 correction we also know that error 0:56 correction requires a huge amount of 0:58 High Fidelity cubits 1:00 uh which are not currently available on 1:02 near-term devices at kma we’re focusing 1:04 on a different way to eliminate errors 1:06 and this is error mitigation air 1:08 mitigation does not use extra any extra 1:11 cubits it does use however extra qpu 1:13 time and therefore is very important to 1:16 make it as efficient as possible so at 1:19 kma we uh are launching software called 1:22 cassm uh cassm is a software for error 1:25 mitigation and error suppression which 1:28 gives unbiased results 1:30 uh at very large circuit volumes I want 1:33 to also stress that CM can be combined 1:35 with airor correction and in fact this 1:38 shows you that uh the fall tolerance uh 1:41 transition is not a phase transition it 1:42 is in fact a smooth transition between 1:45 full air mitigation and full error 1:48 correction now it’s really important to 1:50 get unbiased and efficient error 1:51 mitigation to actually get Quantum 1:53 Advantage once you run your program with 1:56 kesm you will get uh no systematic 1:59 errors and you’ll get your uh ideal 2:02 values as if you’re running on an error 2:04 free quantum computer and you’ll get 2:06 only statistical error bars which can be 2:08 reduced by running for a longer 2:10 time now an important message I want to 2:13 convey is that error mitigated Quantum 2:15 computation is 2:17 approaching the point of having Quantum 2:20 advantage and by Quantum Advantage I 2:22 mean that the time to execute a circuit 2:25 with error mitigation is smaller than 2:28 the time it would take to to classically 2:30 simulated um today we’re already almost 2:33 at that breaking point and with devices 2:36 that are going to be available very soon 2:38 we’re actually going to be very deep 2:40 into this regime of quantum advantage 2:42 and in fact there is going to be an 2:44 exponential separation between this 2:45 running times and air medicated Quantum 2:48 computation will be performing things 2:50 that are not possible with classical 2:52 computers now uh the second half of the 2:55 talk will be presented by sisan and 2:57 you’ll show you our joint work for 2:59 accelera in this timeline into Quantum 3:02 Advantage so first I want to introduce 3:04 our software in more detail so this is 3:06 the workflow of the software it starts 3:09 with a user sending our system the 3:11 circuit he wants to run the quantities 3:14 he wants to measure the accuracy level 3:16 he demands and the specific device he 3:18 wants to run this on based on this 3:21 information we then run a 3:23 characterization of the uh errors on the 3:26 hardware on the specific Hardware at the 3:28 specific time we’re going to execute the 3:30 circuit this is very important we 3:32 perform optimization of the quantum 3:34 Gates on that Hardware we trans file the 3:37 circuit based on this characterization 3:38 to obtain optimal results and then we 3:41 based on the characterization we also 3:43 compile the circuit into an ensemble of 3:45 qu of circuit which we then execute on 3:48 the quantum Hardware collect back the 3:50 results do classical postprocessing and 3:53 then return unbiased results the user 3:56 unbiased means that your algorithm runs 3:59 as if you’re being as if it’s being run 4:01 on a noise-free quantum computer I want 4:03 to stress that point now cassm is also 4:06 application agnostic meaning that it 4:08 works for any Quantum circuit uh you 4:10 want to run um and it also Hardware 4:13 agnostic meaning it can run on a variety 4:15 of Hardware platforms and I’ll show you 4:17 uh several 4:19 demonstrations two important numbers I 4:21 want you to keep in mind which basically 4:23 quantify the benefits of using cassm for 4:26 performing error mitigation the first 4:28 one is something we we call the Circuit 4:30 volume boost and it goes the following 4:32 so you first set the accuracy level you 4:35 want to obtain when you execute your 4:38 program and then you can ask what is the 4:40 largest volume of a Quantum circuit I 4:42 can run on a device as is without error 4:45 mitigation and what is the volume of a 4:47 circuit I can run together with KM and 4:51 obtain that accuracy level if you take 4:53 the ratios of this volume you get the 4:55 circuit volume boost which can for high 4:57 accuracies can reach uh a boost of uh a 4:59 thousand even more high accuracies for 5:02 example required for chemical 5:05 applications um you can also ask you 5:08 know what is the performance in terms of 5:09 qpu time and here we want to compare to 5:13 the competing method for performing 5:14 unbiased or mitigation which is 5:16 probabilistic error cancellation and you 5:18 can see that km performs exponentially 5:21 better and allows uh the user to access 5:24 Quantum circuits that are not possible 5:27 uh to run using PC 5:30 now I want to uh share with you this 5:32 demonstration so these latest 5:33 demonstrations that we performed the 5:35 first one was demonstrate was an ionq uh 5:38 in a collaboration with AWS bracket and 5:41 here we ran a chemical application uh uh 5:44 for uh the O2 molecule uh we’re running 5:48 a vqe uh uh circuit uh with a the 100 5:52 Gates on 12 cubits and you can see in 5:54 red the result we got for the ground set 5:57 energy of that molecule uh if you ran it 6:00 without error mitigation compared to the 6:03 ideal value you would get for this 6:04 circuit uh if you run on a perfect 6:06 quantum computer with no noise in Black 6:09 uh you can also see in blue what you get 6:12 when you run the circuit on iq’s device 6:14 with our error mitigation and you can 6:16 see that indeed you get results which 6:17 are accurately uh correct and within 6:20 statistical error bars with the ideal 6:22 results you can see that this happens 6:24 also so for other quantities like 6:26 orbital occupations and other 6:27 correlations 6:29 now before moving on to the other large 6:31 scale demonstrations I want to introduce 6:33 a quantity which measures the complexity 6:36 of error mitigating Quant circuits and 6:38 also uh the complexity of classically 6:41 simulating them this quanti is called 6:43 the active volume and in a nutshell it’s 6:46 basically the number of two Cubit Gates 6:48 affecting the observable you want to 6:49 measure so if you look at the diagram on 6:52 the left you can see a brial circuit and 6:55 an observable being measured at the end 6:56 and you can see kind of a fan of the uh 6:59 two kbid gates affecting uh this 7:01 observable now it’s very insightful to 7:04 look at these uh active volumes for 7:06 circuits for family circuits uh which 7:09 are often used at Benchmark and also 7:11 simulate the physical model this is 7:12 called the ising model uh and these 7:15 circuits are basically uh repeated 7:17 layers of X rotations ZZ rotations and Z 7:20 rotations applied n times and uh at the 7:24 bottom here you can see how these active 7:26 volumes look as a function of the 7:28 circuit depth and in the generic cases 7:30 the cases I’m going to show you uh these 7:33 uh volumes have uh the shape of what we 7:35 call a light cone so information is 7:37 propagating in circuit with a certain 7:40 velocity now we the first demonstration 7:43 I want to show you uh is a demonstration 7:45 on uh one dimensional model of 40 cubits 7:48 and we uh in this demonstration uh we 7:50 ran deep circuits and we uh measured 7:53 various quantities like two point 7:55 correlations and string operators you 7:57 can see on the plot of the right as a 7:59 fun of the length of the string operator 8:01 we basically access High higher and 8:04 higher uh active volume reaching up all 8:07 the way up to a volume of 8:10 490 2 Cubit gate in a circuit that in 8:13 total had 1,400 Gates and a depth of 7 8:16 to2 Layers okay so this is this is 8:19 probably one of the largest air unised 8:21 air mitigation experiments ever 8:23 performed and uh it’s maybe only rivaled 8:26 by these two-dimensional uh 8:28 demonstrations we did on a full device a 8:30 full eagle device with 190 cubits again 8:33 uh reaching uh volumes of around 400 8:36 measuring various observables and 8:38 basically uh reaching a an active volume 8:41 that covers the full device uses all the 8:43 cubits in the 8:45 device now you can use this results to 8:48 map out uh the uh road map for Quantum 8:52 advantage using kesm by plotting the 8:55 required qpu time to error mitigate uh a 8:59 certain active volume here on the 9:01 horizontal axis and you can plot these 9:03 qpu times for different uh fidelities 9:06 and you can ask when do this line cross 9:09 into the regime where this circuits are 9:11 no longer simulatable okay so and you 9:14 can see from this plots that with 9:16 already with uh Fidelis of 39s uh will 9:19 be able to provide Quantum Advantage uh 9:22 uh will be very deep in this Quantum 9:25 Advantage regime and sisan is now going 9:28 to show you that by combining uh hpcs 9:31 together with error mitigation we can 9:34 actually push uh uh uh this lines 9:36 forward and actually uh considerably 9:39 accelerate uh the timeline for obtaining 9:42 quum Adventure so SG the floor is 9:48 yours okay thank you 9:51 Nel okay thank you uh uh one of the um 9:55 one of the most promising applications 9:57 that may have a Content advantage 9:59 is a Content Dynamics here here very 10:02 recently in in in in in our our archive 10:06 paper we 10:08 explored dynamics of kick diing model on 10:11 the two dimensional hexagonal heavy 10:13 hexagonal L this using IBM quent 10:17 computers uh which shows uh so-called 10:20 discrete time Crystal discrete time 10:22 Crystal DTC is a non equilibrium state 10:25 with spontaneously broken discrete time 10:27 translational symmetry starting with uh 10:30 a strip like uh State uh as the initial 10:34 State shown in the left 10:37 panel uh we studied a pro Dynamics 10:40 determined by uh uh unitary operator UF 10:44 which already introduced by 10:47 Nel uh and of course we fix ZZ rotation 10:51 angle at particular value so that the 10:53 Dynamics is completely determined by the 10:55 two parameters Theta X and Theta Z 11:00 and one thing that one should notice is 11:03 that when Theta X is pi Dynamics uh 11:07 shows a trivial 11:09 DTC uh because the uh the Fate Dynamics 11:12 is completely dep determined by the a 11:15 product of part operators and therefore 11:18 Dynamics evolves in time uh from 0000 to 11:23 111 and go back to z z State and so on 11:27 and so forth 11:30 and and and showing the uh uh uh period 11:34 of two time steps therefore it breaks 11:37 the uh uh uh discrete time symmetry in 11:41 time in time 11:43 domain uh in order to mitigate errors 11:46 and noise in the in the real devices we 11:49 also introduced a a holistic scaling 11:52 error mitigation method which is simply 11:55 by dividing the L experimental low data 11:59 by by those uh taken at the Theta xal Pi 12:04 where trival DTC is 12:06 expected the experimental uh results 12:09 with this simple rcing ER mitigation is 12:12 shown over there uh by uh yellow uh 12:17 diamonds uh that that for obtained for 12:23 for 28 Cubit using IBM toino 12:26 device and there also we compare 12:28 experimental result with the classical 12:30 State Vector method you can see that the 12:33 agreement is extended up to like 50 time 12:37 step uh which is already uh uh 12:40 significant and even more uh we did a 12:43 similar comparison using uh a much more 12:47 system uh uh of 133 cubits uh uh using a 12:53 whole device of IBM 12:56 Torino and again the Diamond shows the 13:00 experimental result with this empirical 13:04 rescaling era mitigations are now 13:06 compared with the two dimensional tensor 13:08 Network method with different point 13:10 Dimensions suggesting that the 13:12 convergence of the classical 13:13 calculations is good enough and again we 13:16 achieved excellent agreement between 13:18 experiments and uh classical simulations 13:23 which is uh is really extraordinary 13:26 because the size of the uh system is is 13:29 now more than 100 13:33 cubits however there are cases where 13:36 this uh simple error mitigation method 13:38 does not work depending on the 13:39 parameters and the the depth of the 13:42 circuit that you use for instance in up 13:44 there uh for this 13:47 parameter uh the the disagreement 13:49 between uh uh experiment and state 13:52 Vector method uh are much enhanced 13:56 especially at uh especially when the the 14:00 uh time is long 14:04 enough so here in this experiment uh we 14:09 choose a particular set of parameters 14:11 with the initial the fully polarized 14:14 state of the initial State uh a case 14:17 where the this simple eror mitigation 14:20 does not 14:22 work and and the in this plot we measure 14:27 a whole uh the the average of the 14:29 magnetization of whole of 28 cubits 14:34 using IBM Kawasaki and IBM 14:36 Torino and red uh are the experimental 14:40 low data and greens are the experimental 14:43 data with this simple raling a 14:46 mitigation which clearly deviate from 14:48 the exact values uh even four times step 14:52 like five time step already they they 14:57 disagree however uh when we use uh 15:00 unbiased ER mitigation developed by kma 15:05 uh uh the the we can successfully 15:07 reproduce this exact values are 15:09 indicated by gra uh uh 15:15 circles now how we can 15:17 combine uh classical and Quantum 15:21 computations uh to increase the number 15:24 of steps that we can reach to uh to to 15:28 to make average 15:29 of expectation I mean to take 15:32 expectation value uh with uh given 15:35 desired 15:37 accuracy our main idea is very simple to 15:40 divide a total Evolution time l t into a 15:43 two parts the first part is uh treated 15:48 using uh uh class and content 15:51 computers and the second half of of 15:54 quent Dynamics is treated classically 15:57 using HBC 16:00 and all we have to do class car is to 16:03 back propagate the operator or for time 16:07 steps T and the measure of 16:11 T over 16:13 the uh time evolved quent State side of 16:17 T in quent 16:20 computer and here is the demonstration 16:23 of hybrid classical Quantum computation 16:25 for kiing model on a one dimensional 16:27 system of 2 cubits and and and the 16:31 horizontal axis is the total Evolution 16:33 time divided into a classical and Quant 16:37 Evolution 16:39 time and in Quant computer we use uh IBM 16:43 kavasaki and IBM toino and cassal uh 16:46 calculations we use aens Network method 16:49 to back propagate the average of the the 16:52 expectation value the operator you know 16:55 should 16:56 St and uh uh and the red the yellow is 17:01 the experimental value of the 17:06 magnetization so which which is still uh 17:09 uh away from the exact value denoted by 17:13 gray circles however if we use uh 17:17 unbiased error mitigation method cust uh 17:21 one can again reproduce exact values 17:24 indicated by 17:27 Blue so what is most beneficial in 17:30 combining class Quantum 17:34 computations is uh we can significantly 17:37 reduce the qpu time required to to to to 17:42 to to measure observable with uh given 17:45 statistical 17:47 error uh do uh doing a systematic 17:51 experiment for smaller systems are using 17:55 different IBM computers denoted by solid 17:58 CES in the left panel uh we can estimate 18:02 with some confidence uh the uh required 18:06 qpu time at function of active volume VA 18:09 in the quent circuit over there so uh uh 18:14 blue uh is the required qpu time when uh 18:20 you use uh no Quantum uh sorry classical 18:25 computations while this rate indicates 18:28 the uh required qpu time when you use uh 18:33 uh classical computers with time time 18:36 Evolution like t t equal to 18:40 20 although that acquired qpu time 18:44 increase this post 18:46 exponentially the active volume that 18:49 enters in the exponent down 18:51 there uh reduces as much as what you uh 18:57 treated in class and therefore the 18:59 required qpu time 19:03 reduces just give you the uh the example 19:07 let let us assume that we have a total 19:09 Evolution time T 30 and if we if you 19:13 don’t use any classical computations it 19:17 requires over uh 800 minutes over there 19:21 assuming that uh U you averaging 19:25 magnetization with the stat statistical 19:27 error of 5 19:30 per however if you uh use qu classical 19:35 computers with 20 uh time steps this uh 19:39 required 19:40 cont uh uh qpu time reduces 19:43 significantly down to TW down to 19:49 40 so this clearly demonstrates that 19:53 combining uh 19:55 unbias unbiased err mitigated quantum 19:58 computer along with the classical 20:02 HBC can reduce it required qpu 20:06 time uh indicated originally by a uh 20:11 yellow solid line to a yellow Das 20:14 line and therefore it it can accelerate 20:18 achieving the content Advantage much 20:21 sooner uh than later before entering the 20:24 fqc era so please please stay tuned 20:28 because more Advent will be 20:31 coming thank 20:36 you um thank you to both speakers if 20:40 there are any questions uh please again 20:42 uh put it on slido um I don’t think we 20:44 have any yet and we’re a bit behind 20:45 schedule but I do have one question for 20:47 the both of you I think one common theme 20:50 today from multiple speakers has been 20:52 the idea of crossboard collaboration 20:54 multi-party collaboration and I I just 20:56 wanted to ask both of you to maybe speak 20:58 to what that experience has been for you 21:02 um and how important it has been for you 21:04 to work together as across 21:06 organizations so yeah go ahead yeah I 21:08 think it’s very important for us to 21:10 understand uh you know what uh are our 21:14 clients you know what do they really 21:16 need what is important for them and 21:19 finding kind of the joint research 21:22 project that would be aligned directly 21:25 with with uh what they’re aiming for and 21:27 this collaboration has been super 21:29 insightful uh for doing that yeah so in 21:32 order to use content computers very 21:35 efficiently we we need someone like you 21:38 I me know to to to get good results 21:42 [Music]