08:00:13 Today, the first talk will be given by kg aside from K University.
08:00:19 About effects of final speed on someone dynamic transformations, please.
08:00:25 Thank you very much. mk set of home care University in Japan possible. I'd like to thank organizers for giving me the chance to talk on this title.
08:00:37 And this work was done with important postdoc, Tom bamboo. The result already posted in the archive, so please have a look at this. If you are interested in.
08:00:50 So let me start with very simple point about the sama sama dynamics are the you know the sum of dynamics is built upon the several rows, the first row is about the quiz conservation of energy, and second row is a core into some dynamics, which tells us
08:01:13 are over time in our natures into some random access.
08:01:29 The first one is a change of the systems entropy.
08:01:32 And there's the tension, change of a system entropy given practice using using this channel entropy at the point in time, and ensure time.
08:01:44 The best entropy of the second party the party entropy, the bus entropy is described the practice using the change of the heat inside the boss. The boss is always equilibrium.
08:01:56 And so you can use a standard definition for the study in the studies study conducted family dynamics, using heat.
08:02:07 So, this second law districts are many, some dynamic control.
08:02:13 Why was the most critical most important physical object is heat, heat engine heat engine to second row bounds efficiency from above the upper bound is well known current option she has a not heated turns you were originally studied for the macroscopic
08:02:31 object, but nowadays evil atomic scale or Peter nZi experimentally the most right it.
08:02:39 Now this is another interesting object is is information processing to some dynamics of information process processing is important to understand the commercial engine with boxer demos, and some dynamics of the computation, and so on.
08:02:57 Concerning the thermal dynamics of the computation.
08:03:02 Most important subject, well most important subject is about that information ratio, which is now called at our band.
08:03:12 The computer is now very small scale, using the quantum mechanics. And so,
08:03:18 this other scale is reduced to we need to understand scoring to subject.
08:03:25 The subject, first subject is about, no equal to be on FX because small scale object tends to be affected by external motivation, very easily.
08:03:37 And so the state easily becomes an aquarium state, another subject is a road over quantum mechanics, such as the quantum coherence and the quantum entanglement.
08:03:51 And so, in this context, so far, many subjects was addressed in the heat engines such as thread of relation between the extension power, and a lot of coherence and the point of measurement perspective on so on.
08:04:06 These are very interesting.
08:04:17 Today I don't discuss heat engine, but I focus on the land of punishment in the summertime computation computation, our own designs.
08:04:20 So here I'll actually explain what's the London Bridge police.
08:04:25 This is, this is a second schematic, on the beat on the tape.
08:04:31 After computations, and many types of the configuration of beats appears, sometimes there are sometimes data Wonderwall and so on the respective of the beat, state.
08:04:43 We want to reset using our pics protocol. Here the protocol is a map denoted as denoted by capital Ramadan.
08:04:52 And he had zero is a reset state.
08:04:55 So he said oh beat is Asia we information. The London principles state that the heat Asia.
08:05:02 Later process, inevitably generate heat dissipation.
08:05:07 It was a.
08:05:09 It is a process is the place I started process. And then the heated discussion part one bit. is equal to, kbT local to.
08:05:20 This is a statement by Rhonda.
08:05:25 And the one who can be understood as a consequence of the second to load the changeover the system entropy is a KVTKV it over to because. Step one, and understated Dale equally appears without same probability, number one hub.
08:05:43 And in the quest accepted protocol, the inequality becomes equality and we get that under
08:05:53 there under a bridge pool was experimented the most rated in the group of severity in France, the experimental experiment was performed using a quarter particle system using that drop the potential.
08:06:06 The experiment is in the cluster as you take consider the web the potential to make the state to state that he said state is a state where the particularly in India right well.
08:06:20 using using these peaks the protocol. they showed the polling nice result.
08:06:28 This is a heated displeasure, as a puncture with time duration of protocols update the x axis is a time of protocol and the y axis is a heated discussion.
08:06:43 from this from this figure.
08:06:45 We can make two important observations.
08:06:48 So past observation is that none of our bond is achieved within the quest is that agreement that this last line is that under grace I studied them, it means, time is infinite.
08:07:02 Time is infinite. What very large.
08:07:16 Okay, having this experiment in mind, we can roughly ask the following question. Suppose we want to have the information processing, then the foreign questions are clearly important.
08:07:17 A second observation is that the Asia within a short time, needs more heated displeasure.
08:07:30 The first question is about the effect of a finite time later.
08:07:46 So concerning these programs. There are Devon's box concerns the first questions, namely on the finite time ratio.
08:08:01 Process Pressman, and the co workers, studied on this subject. They considered the crossfire system to understand the experiment that I explained before, using the open up the lines by dynamics, or Southern Cross over the pixel protocol.
08:08:20 They derived.
08:08:23 Following a nice result about that boundary dissipation.
08:08:30 This describes a bond appreciated special. And the second time, after the past the first time is second row and second time is a finite time production.
08:08:44 If the pilot time with the imprint in us. The standard standard and our boundaries obtained when we use a particular protocol. The second term is dominant, which means that.
08:08:57 Additionally, she did this page and is necessary for your answer.
08:09:02 So concerning to take on the question.
08:09:05 There is also nice paper by media and co workers, they arrest cubit to ensure the slow driving Damon.
08:09:17 They assumed that the dynamic is governed by interpret dynamics.
08:09:22 And they, especially focus on the distribution of a heated discussion, using a technical company statistics.
08:09:30 And they demonstrate that
08:09:35 they demonstrated started driving protocol generating quantum coherence shows the distribution of a sheet, like this.
08:09:44 And the event, having estimated three realizes she the dispersion of event can be obtained around here.
08:09:52 This suggests that the quantum coherence induces additional space spacer.
08:10:00 Nice luck. And so now we make questions more in detail.
08:10:08 But, but very general question we asked the following general questions, concerns of us questions, we consider the effect upon a time in the quantum lesson.
08:10:22 And then the quantum religion, we ask is the role of quantum coherence for arbitrary speed.
08:10:32 This is our second question, and these two are clearly important and general questions concerning the second question about a quantum cockiness. I have one remark.
08:10:44 She the engines case.
08:10:52 The law of quantum coherence has already been studied so far.
08:10:53 He turns you he tends is driven by to shoot passes, but Randall case law principles case uses the only Washington.
08:11:01 And so these are different, but it was good to bus mentioning the result in the case of heat engines in heat engines, you can use renewable dynamics to make a general statement in response regime.
08:11:22 The general statement is according to quantum coherence, generally induces two additional his displeasure, And so the work output is.
08:11:30 Do you think that linear response vision, the linear response here means that either driving operations is very small, or driving speed is very small.
08:11:41 On the other hand, in the park along with Caribbean region, surprisingly, quantum computers can help enhancing the output, depending on the protocol.
08:11:56 There are several papers that demonstrated this effect clumsy the studies, we can say that, go to content coherence is not trivial.
08:12:08 This is a very important background on the quantum coherence that we can say from sexy two engines.
08:12:14 And so we can ask, what about Rhonda was case where to only see single sheet capacity skills.
08:12:25 So now, let me explain our setup to answer our questions.
08:12:31 Consider the general General QQBQ the system, composed of with a de de de dimensional space.
08:12:41 The standard JV uses of the quarter. And so you can, you can see that our result is about it for the quarter. In general,
08:12:55 we, we assume that the qV it is a corporate to the summer Reserva berry weekly so that the dynamics of the Justice the matrix is given by the miracle PM, Linda breath dynamics.
08:13:10 And for the integrated this beta, beta, we impose dictated by getting rid of bonus condition.
08:13:21 Here, I don't try to express the expression for the detailed past condition, but imposing the detail bonus conditioned
08:13:31 deliberate dynamics provided thermal dynamically consistent dynamics, because it guarantees guarantees that the positivity of dangle no matter it's element of the testing metrics.
08:13:45 And it also guarantees that the second little second row, can be formulated very easily.
08:13:54 Woody months at a fast pace derivation of the in the broad dynamics.
08:13:58 Using the whole dynamics of the system and the reservoir uses several ad hoc procedures such as medical feminization and second up risk measure and so on, but using their inability exclusionary to Steve useful in the sense that it provides thermodynamic
08:14:16 or consistent dynamics. So, who can expect that it provides deliberate dynamics shows Thompson universal believing these, we proceed the calculation to answer our questions.
08:14:36 So I need to explain additional setup.
08:14:46 The first is about expressed it formulation of the changeover system and therapy, and he did this vision.
08:14:47 We follow the standard upon ratio of a sticker sticker some dynamics.
08:14:52 You go right so she did this phase you're using the time time event and time independent Hamiltonian, and the tema derivative of the matter is called the system.
08:15:01 This is something so the standard sounds are set up is on the inchoate as the metrics to this and let Kavita lambda, the map that stands of course that's today's your protocol that they'll be reset state, then we want to reset arbiter a pure state to
08:15:27 state practice using the fix the protocol.
08:15:33 Actually that there are many there are many variation, or there are many input state, which is, it should be deceptive.
08:15:42 Because any input state is really set to tell the ensemble over the input state also equal to tell like this you can do it this way.
08:15:52 Now, lambda, lambda is a linear map and so ensemble average and breaking them up into comfortable. So you can you can get this expression.
08:16:04 So, inside the bracket, the average over the input state appears, and the average of the inputs team but state should be maximally make the state.
08:16:16 So, we know a general statement I mean I make the general statement about initial state.
08:16:28 Actually to
08:16:28 maximize mix the state is enough. As I stated to discuss the ability to displeasure, you can, we can show the following them easily. Then we give the final state state, starting from the maximum the mix of days is close to the decent state within that
08:16:51 era, epsilon, then you can say that the final state, starting from arbitrary pure state is also close to the desired state like this.
08:17:01 So now, let me explain.
08:17:09 Concerning the past question. So first question was, I effect of spinal tap into your process.
08:17:17 We get the horn seldom
08:17:22 on this.
08:17:23 As I explained in the previous page. I said, the maximally mix of state, are they interested to course the ability to dispersion.
08:17:40 And the second term is additional bound,
08:17:45 which is a collection of pilot time.
08:17:49 Here the numerator.
08:18:05 In the numerator, thrice distance between the initial state and a pilot density model appears, and in the denominator, gamma bar is his average Joe average dynamic or activity like this dynamic or activity is very standard on the physical quantity in
08:18:13 the group yes that's got physics. It quantifies it quantifies hopefully creatively the transition occurs.
08:18:23 Second time because it's crucial if, if, fast, raise your protocol is children.
08:18:30 Suppose that we can choose the protocol, where, where the state is completely reset to zero, namely the final days the market is, is equal to the desired state, then this.
08:18:55 And the second term is a finite time correction, and the second time visibility same content dynamically activity.
08:19:08 So, now we want to explain the result for the second the questions, sit on the question was on the road of quantum coherence for arbitrary speed to the to this and we need, we need to define the quantum Casitas.
08:19:26 There are several definitions to quantify the quantum proceed and such as Edwin normal coherence, where are the pressure, measuring, and the data to be entered the coherence and so here we use to Edwin little coheres that introducing this paper to head
08:19:44 one little more coherence a summation of publicity to barrios have offered another element in the density metrics, when we write the tasty matter It was instantaneous basis of the Hamiltonian,
08:19:58 this can be given for arbitrary time key.
08:20:04 Then, we define the total amount of quote unquote sheet as like these by intimidating.
08:20:12 Over time, this quantity is city Cheeto is crucial in our result.
08:20:21 So, we know make a statement for the second the questions.
08:20:26 Remember that marks Money makes the state is ensemble of many inputs, pure state.
08:20:32 Not that much money makes the state has zero coffee Yes.
08:20:35 On the other hand, each input a pure state should have very radical healers.
08:20:41 We want to see the coherence for the whole time regime, including the initial state. So here we use arbitrary Interstate, so that we can discuss Kochi as a practice our deliverable at the microscopic level.
08:20:58 The state maintains our opponents. What, any issue input state to heated this Beijing is bounded from both using the practice, up to the first term is a standard standard all the finite time correction is with a with a term of quantum coherence FL, is
08:21:16 Gamma Toba is given this expressions which expresses the opportunity for relaxation, but at the detail detail, it doesn't matter.
08:21:30 What matters is that this, this quantity is non narrative.
08:21:38 And can the cheetah Cheetah is a quantum both ends that I explained in the previous page. And this time, enter in the numerator, with a squared form. This implies that the quantum question is always generate Jesus dissipation.
08:21:59 A note that these boundaries.
08:22:01 Buried for any interested.
08:22:06 So I explained in Mary's out so far about finite time pilot and can finish in like two three minutes because we need time for questions.
08:22:18 Ok, ok, ok, I hurry up speed up.
08:22:23 I show you the numerical calculations that quantum computers in a generator patient, be considered a cubit system where the dynamics is given by an integral here, we points the time independent Hamiltonian HD practice Chiang Mai is a party mattresses,
08:22:47 can control. Keep Shaun T and acidity in this hard to be independent operator are set like this, using the instantaneous Hamiltonian, you know, we want to discuss the two protocols that is the same.
08:23:00 It is, it is accuracy, so forth, bro protocol is the ultimate optimal protocol that is derived by optimizing, not only accuracy, but also minimizing the heated discussion.
08:23:11 This can be achieved with numerical evening, minimizing the following March objective function.
08:23:18 The queue is actually the displeasure on the average fidelity between the final state on the desire to reset state. If ratio is a perfect these facilities upon the lambda is a weight faster if we take the number one and only heated discussion, either
08:23:44 If we take the wrong vehicle they'll only raise your accuracy optimized. We use somebody over lambda between zero and one. And another protocol is not optimal output protocol, where emotional T and the sheet that he didn't like this.
08:23:52 And we can find that to protocol have the seminar, raise your accuracy, using appropriate areas of optimization.
08:24:00 In this figure, optimal protocol shows tired abundance in the quantum control parameter practice, and no optimal protocol shows this behavior control parameter, the trajectory of the state will optimum case with like decent profit surface.
08:24:24 And like this, and the know optimal case.
08:24:27 I'm sorry.
08:24:28 no particular case shows this behavior.
08:24:32 So you see that the initial state starts the same, same price. And the final state, also the same. This means that data accuracy the same between these protocols.
08:24:45 So using this to proper protocol.
08:24:49 We can discuss the dispersion, and amount of quantum coherence.
08:24:56 As I said, optimal protocol minimises heated discussion. So in this, in the left for your, you see that the heated discussion case.
08:25:15 In the right here, you can see the amount of quantum coherence, he can find that no automatic protocol has a lot of quantum computers were optimal pace optimal case has very small confidence.
08:25:17 In optimal protocol case, minimize is likely to dispersion until the heat dissipation is much more eyes on no particular case.
08:25:32 This demonstrate that small dispersion deploy small quantum casita
08:25:36 sola.
08:25:38 See, let me summarize, i.
08:25:42 So we discuss the point item, London police police quantum case within the random within the Linda broad dynamics, we derive the two, you know, quality, like this.
08:25:54 Thank you for your attention.
08:25:57 Thank you very much.
08:25:59 Very nice talk.
08:26:01 So we have time for questions.
08:26:06 Maybe while people are thinking, can I ask I got a couple questions myself one is sort of clarifying. So usually if you have if you did measurement we sort of have information about the output and then, in principle should be possible to raise it without
08:26:23 any heat right because I'm just trying to understand what's the setup because if you know this particular string, there are no limitations on, maybe I'm wrong.
08:26:39 What we, we know, is about a decent state that I can also measured.
08:26:47 We don't make that assumption that we don't know how would I say.
08:27:02 what sequence of zeros and ones we have, there should be no cost right and.
08:27:09 So, you're raising something you know usually right so
08:27:15 again. But, But if we know the initial state.
08:27:23 We use a feedback comparable to resets the state that we want to use.
08:27:39 We want to use a fixed protocol to reset. Yeah. Okay, I understand. Yes, it is the one with an instant.
08:27:49 That's a point. Maybe I had like another quick question. So you're talking about quantum coherence but if I have like I know completely classical setup I can have coherence also there.
08:27:58 So is the same like formalism apply so easier extra bound depends on age bar that's it the virtual wizards bar to zero or what interest question, actually, we can, we cannot discuss that one, because the way we can find ourselves into discrete dynamics.
08:27:59 Okay, em up that deep into that doesn't.
08:28:20 So, we cannot take the edge back to their limit.
08:28:35 That's the unfortunate situation, but it's a very differently differently very interesting questions
08:28:45 Any other questions. Okay, so there is one more question, please do. We're sorry if I mispronounced. It did a nice talk so I have a question. Gentlemen one.
08:28:49 It seems like there is a relation between what you're describing to the general objective to cool the quantum system let's say to the ground state or any other state.
08:28:57 Can you discuss this relationship life My objective is just to.
08:29:01 You have to call my system. Is it the same type of problem.
08:29:07 Okay so true.
08:29:12 Because you reach a certain we are resetting essentially getting to either ground state or any other state of your system,
08:29:27 don't control the temperature, time, and we don't we don't use to raise the bar, and so i i don't think that this race, this bond is related to the queen.
08:29:40 I may be wrong but I think
08:29:43 that no deviation exist between this and the coding.
08:29:49 I mean, freezing according to general objective, but I have a state and I would just like to direct it to translate the transform it into the grams didn't ask myself about how much heat I need to invest in order to reach that way.
08:30:07 When they're available ability to.
08:30:11 But, yeah, slightly, slightly dated, because the sheet is generated to the best. And we, we make, make a controlling the system.
08:30:25 But I don't I don't know, I don't know, it's not clear about the duration.
08:30:28 Thank you.
08:30:29 Fight We both are madly in very interesting.
08:30:34 All right, I think time is up. So let's sing Kj again for very nice talk.