 Very good. Thank you So the title is parody protected Johnson cubits and you see my collaborators But let me start with really important things and It's a great pleasure To be here on such a wonderful occasion. I know warrior for a good third of a century and And I tried to find the earliest photos in my archive and that was from year 1987 and The site was Duchamp Bay, which is a capital of Tajikistan And the occasion was a big cost of school on condensed matter physics I want to emphasize two things a Boris is easily Identifiable on all photos Which means that Over the last 30 years. He hasn't changed much The second thing is that Boris always attracts people Just because he is a great guy, but also he is a generator of new ideas and Over the years of those interactions and attractions Significantly increase his polyronic mass At the same time he got delocalized So Warrior many happy returns now back to By the way, I like this look right Back to superconducting kids So I will start with a very brief introduction that emphasizes still the search for new approaches to individual cubits So theoretically cubit is just a simple two state system For example spin one half in some fictitious magnetic field In reality if the spin if the cubit is made of macroscopic solid state system It's a complicated spectrum. I cannot see that. It's there is a dot and the lowest to energy states are Used in logical operations, it's zero in one the spectrum should be non harmonic to Be able to address this transition and not excite all the other ones and this and the harmonicity is an important parameter because it sets the scale how quickly you can talk to a cubit because the Shortest operational time of the cubit is inversely proportional to the harmonicity now The cubit is a quantum system with a decoherence rate and it's important to realize how good the cubit should be for Being a part of quantum computation So the cubit is characterized by this ratio the so-called error rate where t naught is the time of the longest iteration and Typically, it's two cubit rotations and t2 is the decoherence time Now to implement the error correction codes It's a common agreement that we need the error rate Smaller than 10 to minus 4 and if you think that for simplest rotations For example for a rabbi-flop you need to wait for Something like 100 periods of fundamental frequency of the cubit Right that means that if you consider cubit as a non-linear Oscillator the q-factor the quality factor of this oscillator should be greater than a million Which is a very challenging task Now what is the current state of art This is the plot The horizontal axis is years The vertical axis is the cubit lifetime and the right vertical accesses operations per air And you see that over the last 15 years from the first seminal experiment in doctor's size group in succuba to the present day There was a dramatic increase in cubit lifetime This is the so-called Morse law for superconducting cubits We see that the threshold I was talking about which is the error rate 10 to minus 4 Perperation is almost realized For single cubit operations if we look at two cubit gates you see that This epsilon is still Roughly in order of magnitude Greater than what we need And these are probably the best data At present So the state of the field is that from Single physical cubits the field is ready to Go to the next stage which is a logical cubit would that would live forever By running the error correction code, but we are not there yet And though Martinis Who is a one of the leaders in the field described that that we are somewhere between the invention of the transistor and the invention of the integrated circuit In my mind when not there yet because a transistor in this language is probably logical cubit and not a physical cubit However, despite all those difficulties Finding is already in hundreds of million We have many hundreds of people involved in this field in industry now, but it's clear that though most of the groups are Focused on Transmount type structures to the most popular cubits. There's a need for improvement of individual cubits and one of the One of the approaches to this Was design of parity protected Josephson circuits what this is about I'll be talking about two types of circuits and again because of time constraints. It will be very brief discussion a Parity will mean two things In the first circuit, I'm talking about two Josephson funny Josephson Squeeds attached to a single small island and I'll be talking about the number Parity of the numbers of Cooper pairs on this island By the way this funny squid interrupted by four junctions I'll be referring to as Josephson rhombus Now this element is a kind of non-trivial Josephson element, which is cosine 2-5 periodic in the phase across the element Now the second Circuit that I will be talking about is a key prepare box Which is shunted by a very large inductance And in this case the parity refers to the number of flux quanta flux on in the superconducting loop Which contains those two elements in the first case parity is protected by a run of bomb Deconstructive in destructive interference for transfer of single two pairs. Let's take a look. So we have two arms If they're identical the amplitude of This tunneling is the same for both arms But if the rhombus is penetrated by the magnetic flux, which is a half of the flux quantum the phase between those processes is pi and Deconstructive interference kills this tunneling and in this case the Parity of the number of Cooper pairs is protected. No, please that the transfer of Correlated transfer of two Cooper pairs is allowed for this process the Phase is 2 pi Now in the second device One can introduce the amplitude of flux flux on tunneling In the loop or out of the loop and this is this it's similar to the facelift sent facelift process in one of the junctions because of a run of cash or phase the Phase the phase difference between those two processes depends on the charge on the central island and when this charge is Elementary charge e or one half of the Cooper pair again because of destructive interference tunneling of individual flux zones is Forbidden but two flux zones can tunnel at the same time More mathematical description of the idea of protected cubits as shown here. We have some Oscillator This parabolic confinement corresponds to the potential term K is discrete and In one case, it's the number of two pairs in the other case. It's the number of flux zones in the loop The Kinetic term is funny It contains only the terms that mix that mix K and K plus minus two And there are not terms that mix K with plus minus one which Signifies parity protection Now for such a system If you look at the lowest energy states in the system, you can construct two Gaussian envelopes One of them will contain only odd case and another one only even case Now, what's the advantage of dealing with those two wave functions? If the parent is protected those two functions cannot be Converted in one into another right Which means that in the language of cubits t1 is infinitely long. There is no energy relaxation those two states are almost Degenerate in energy it depends on how many components we have in this envelope and If the parent is protected t1 is infinitely long now those states are very difficult to Distinguish from the viewpoint of the invard and if the number of components is large that means that T2 is very long as well And there is also some advantage that for Such a qubit we can think of full tolerant rotations, but that's outside of this talk Let me briefly describe the the experimental results that we have Indy How many minutes I have? Okay. Thank you So let's start with charge pairing devices and let me show you how Well, that's basically the same idea. We have our own one phase Which is gained by when you move a charge around the flux magnetic flux and parity protected Here because if those two arms are symmetric and the rhombus is penetrated by half of flux quantum then we have Transport in the system the system has a critical current which is due to the Flow of 4e charges correlated pairs of cupid pairs, but there is no critical charge due to conventional single cupid pair transport and that was shown in our experiments in some time ago Fabrication All the qubits I'm talking about will be made of aluminum There are new ideas that came from Charlie's lab on Novel structures that are controlled by Electrical gates, I just briefly mentioned about that at the end of my talk But all the results that I'll be talking about are just conventional aluminum junctions so you see For example, this is a rhombus. There are four Joll's injunctions at intersections of aluminum strips This is the device and the readout that I'll be talking about it has a little bit more complicated topology, I won't Discuss this so but you can Identify to Romby With now a little bit more junctions. That's the central island which charge I'll be talking about and this qubit is coupled to the lumped element microwave resonator and The state of the qubit will be detected by the shift of the resonance line of the LC resonator so the microwave impedance of the qubit in states 0 and 1 is different and this impedance being recalculated into the Resonator shifts the line of the resonator In the experiment we have two nodes We can either change the phase difference across the qubit by changing the flux in this loop Now this loop is very large. So without Deviating from the condition that flux in one of those or each Rhombus is should be half a flux quantum. This loop is About 100 times bigger. So We can change the flux the phase across the qubit by many pies without violating this condition and the second knob is the charge on this island, which is controlled by the Gate capacitor This is the micro Microwave circuit that I will probably skip Uh spectroscopy Shows that the spectrum of this system is Very close to what one can predict For reasonable parameters for example for charge on the central island, which is zero in those units This is a spectrum which is shown in red as a function of the global magnetic field if The charge is One half ideally The spectrum should give us straight line at zero But there is a small asymmetry between upper and lower arms and from this spectrum. We can estimate all Parameters that we can use for Simulation of the properties of the qubit. So the Jowson energy which Controlls the transport of pairs of cupid pairs is 10 times greater than the residual E1 that controls the Transport of single cupid pairs ideally that should be zero, but We're dealing with a nanoscale Jowson individual junctions and typically the Reproducibility of those junctions is something like 5-10 percent So that's that's the reason why it cannot be easily done much better So the main result is that if you are far from the optimal point This system has T1 which is about one microsecond And that's typical for not so good Cubids now if we approach the sweet spot which means that the Flux in each cubit is 5-0 over 2 right and the charge is correct on the same island T1 increases by 2 ores of magnitude and it's close to 100 microsecond Right at the same time T2 is not that great because if you count how many Individual K components we have in the envelope Instead of many many we have four as the result T2 Which can be further optimized later on is only a couple of microseconds Right, so this is the Promising design which can be improved we know how to improve it But let me switch gears and Discuss this flux on pairing device Which is also a very interesting approach So now we have a cupper pair box Shunted by a very large inductor Because of our own catcher effect we want to suppress tunneling of individual flux on in the loop and leave only Significant rate of tunneling of correlated flux on What are the conditions and the conditions are challenging to Optimize this thing So if you look at the Hamiltonian of this structure the last term which in this case is a parabolic confinement term Has e sub L Which is inversely proportional to the inductance of this so-called super inductor So what we want to realize that because of tunneling of pairs of Fluxons You see that those minima are localized at 0 4 pi 8 pi and so on and so forth Because of the tunneling between those minima are the states have a finite width and The displacement of those states because of this parabolic confinement should be much less than the width of the level This is the condition In this case the state is delocalized or many minima and we have many components in this Gaussian envelope and that's the condition to realize long t2 Now if you look at the numbers You need a super inductance of The order of 10 micro Hendrick It turns out that in two dimensions If you do not use some tricks and use just wires The inductance is basically limited or impedance. Let's put it this way The impedance is limited to the impedance of this free space, which is 377 ohm So we cannot rely on geometrical inductance We have to use kinetic inductance of superconductors or joseph inductance and it's a challenge to realize such a large inductance without Reducing the impedance of the circuit because of parasitic capacitance associated with the Apology of the circuit and the second requirement is that in order to have large width of the levels we need a high rate of double phase slips Which implies that the ratio of the Jollison energy to the charging energy of Those junctions in the key prepare box should be much less than unity The design of the super inductor in our experiment follows the our earlier work It's a chain of asymmatic squids frustrated by the field So basically there are two approaches either this approach based on one-dimensional chain of squids or just Serious connection of many many Jollison junctions and that's the approach that Yale people use for their so-called flock flux on him the advantage of our approach is that this inductance is tunable and It's non linearity is tunable as well And currently this approach gives the inductive inductance which is about in order of magnitude greater than the inductance of the chain of linear chain of Jollison junctions so the the design of the Device is shown here We have a Cooper pair box These are two small junctions It's flanked by super inductor There are two halves of the super inductor each is three segments of six unit cells each and this is a coupler that couples the System to read out resonator and the read out resonator is coupled to the microwave feed line So what one should expect in this circuit if we forget about any flux on tunneling The system is very simple. It's represented by a fixed number of flux on in the loop and then each level is just a parabolic Curve that corresponds to a fixed M M stands for the number of flux on in the loop Now if we allow some single flux on tunneling processes We open the gap here Which means that yeah, and if Step back if we forget about flux on tunneling the difference between those two levels So this is zero and this is one The difference between two parabolas shifted Horizontally is just a linear function and you expect a zigzag line with a zero intercept Which signifies that there is no avoided crossing between those two parabolic shapes now Ideally we want to realize the situation that we have zero avoided crossing here and significant Yeah that Corresponds to correlated tunneling of two flux zones in the loop. This has not been realized that but Probably for the first time we clearly observed a run of casual effect in superconducting circuits And by clear observation, I mean that it's a spectroscopic evidence where all the charges are controlled and You see that if I Look at blue dots that represent zero to one Transition in the spectra of the qubit For technical reasons, we cannot approach zero, but you see that extrapolation gives us a very nice evidence that Because of destructive are a run of cash or interference. We have almost 100 percent suppression of the Tunneling of single-cube repairs. I'm sorry flux zones and And there is a kind of reasonable gap, but not optimized gap due to the correlated tunneling of pairs of flux zones All right, the last slide refers to the new yes, Andy I'm done to the new approach that We hope that soon there will be a new platform which has for parity protected qubits that have that has several advantages in Comparison with the conventional Johnson junctions in Marcus lab in the University of Copenhagen The High-quality structures that contain nanowires Now and Semiconductor nanowires, which can be epitaxially covered with aluminum are developed And this is a tunable electric electrically tunable Johnson junction so in this case you can is see to Symmetrize the circuit right with a high precision Which is important for all those Circuits protected by the symmetry between the junctions and The second advantage for full total interpretations this circuit can be Controlled by fast electric pulses, which is also a great advantage Okay, let me rev it up. So there are several approaches to so-called parity protected qubits if they're made correctly There is a hope that T1 and T2 can be further improved There are several steps towards realization of those circuits It's a long way to go There are several important challenges But there is an optimism Thank you for your attention