 Thank you for being here to see my talk. My name is Jared Hertzberg. I'm with IBM research in Yorktown Heights, New York and I want to say big thanks to the many people who are involved in this work and related work and To IBM for funding of course and for external funding that we received for part of this work. I want to talk about one particular aspect of Scaling up lattices of cubits for larger scale Multicubit quantum processors and Focusing particularly on the kind of architecture that we Have used very often in our work at IBM where we have Fixed frequency transmount qubits that we connect to one another by microwave buses and That we've used for scaling up all the way to the 50 qubit level at this point and where we're particularly employing all microwave cross resonance gate to produce ZX interaction and implement a controlled not gate and the key to this cross resonance gate has been very often discussed is That you have a control qubit target qubit and you're driving the control qubit at the target qubits frequency In order to activate the gate through the the intervening microwave bus Now the fact that you're driving the control qubit at the target qubits frequency gives you the The issue that you can run into degeneracies between the energy levels of these two qubits. All right, so you can have a Degeneracy between the 01 states of two qubits where which are nearest neighbors You could have a degeneracy between 01 and the 02 over 2 between 01 and the 1 2 of nearest neighbors You can have cases where the The frequencies of the control and target are too far apart so the ZX Interaction is too weak to run an effective gate And you also have to consider interactions between next nearest neighbors in the lattice So you could have a degeneracy between the 01s Or a degeneracy between the 01 and the 1 2 of next nearest neighbors And we also have to consider Interactions between three qubits where you can have a two photon excitation that would lead to a degeneracy between Two qubits and another one's 02 state So we we call these so-called frequency collisions or frequency crowding And I've listed here respectively seven types of these These cases that we have to avoid when we set the frequencies for our qubits in a multi-cubit lattice And we have to to define some kind of exclusion range around each one of these Collision types and we've been able to extract that approximately from some work that we've done Theoretically that that some of my colleagues at IBM have done theoretically trying to set a bound where the These frequency collisions would be the limiting case for the For the gate fidelity compared to the typical gate fidelities that were able to achieve We can set some very approximate bounds on many of these collisions So let's think about how that's going to affect The overall Functioning of a lattice right so the the in order to avoid these collisions. We want to try to set a Pattern of frequencies in the lattice that is Where where You totally avoid all those types of collisions, right? So let's say you have the square lattice familiar from surface code If you have five distinct frequencies what you've done is you've set so that no two on the same bus have the same frequency and Also nearest neighbors and next nearest neighbors are not degenerate in their frequencies and but we know that in Setting frequencies of fixed frequency qubits. There's some imprecision in setting those frequencies So we want to try to develop some model for how this will scale and we can do that by treating each of these frequencies as a median frequency with some distribution pardon me and Randomly assign the frequencies drawn from that distribution count the collisions and repeat this is sort of Monte Carlo style to see What how many collisions you're likely to have among the frequencies and then to see how likely or to have a collision-free chip? So Schematically you can think of that as distributions of frequencies that for around each of these Five frequencies and when we run a model on say this type of chip What we can find is that the likelihood of having a collision-free chip can be very Precisely stated in terms of what this precision is that you're able to set the frequencies with So if you look at this plot here You could say well if you can set the frequencies with a 50 megahertz precision in this five frequency pattern Then your 17 qubit square lattice is liable to have oh Say about a 50% chance of having fewer than eight collisions a 10% chance of having fewer than four and a point two percent chance of having Fewer than of having zero collisions So we want to try to apply this kind of statistical model to different lattice types and frequency patterns that we believe to be able to be Evading the the frequency crowding problem. So there's the five frequency pattern at a 17 qubit square lattice a 49 qubit square lattice these correspond to lattice types that could run Say a surface code type error correction at a distance three or distance five We've also begun looking at lattices of a different Connectivity a different layout you can see some work in this recent paper Here is a What we call a heavy hexagon lattice and a three frequency pattern which we we are going to look at In this model for how it it's able to evade the frequency crowding and Here is a what we call a heavy square lattice again with a four frequency pattern that should be able to Be resistant to the frequency crowding issue So when we take all of these different kinds of lattices we run them in that Monte Carlo model and we're going to look for how many Collisions does each type of lattice Develop on average for putting these Three frequency pattern for frequency pattern or five frequency pattern for these different types of for these different types of lattices and what you do see is that the square lattice for the same Size of lattice effective same distance of lattice You're always seem to be having more collisions at any scale and then followed by the heavy square and then the heavy hexagon So Let's look at the what we call the yield That is a fraction of cases in the statistical model that will have be collision-free and that looks like Me like This okay And So What we see is that if we're looking for say a distance five lattice where we can We can operate Without collisions putting these These five frequency or three frequency or four frequency pattern in to evade the collisions We have to be able to achieve Precisions of Setting the qubit frequency in these patterns that that you can read off of this plot here So let's say we were we were going to aim to have 10% of our chips be collision-free and In that case you would need to have You really want to be working with one of the heavy hexagon or heavy square lattices and be able to achieve a Frequency precision of 10 to 20 megahertz So let's say let's get a sense of how What we can do practically to achieve these precisions and how are we doing? Here's a test bed chip where we have 36 qubits that we can look at Frequency statistics on a fairly large scale and Here we know that the frequencies are going to be correlated to the junction resistances of the of the The fixed frequency transmons the tunnel junction resistances and so here's a here's The set of tunnel junction resistances that we measured on this chip And we cool that chip in the fridge and we have a distribution of frequencies Now we're going to try to do is use some techniques that have been discussed the Fair amount in the literature of trying to say selectively anneal the the tunnel junctions with a focused laser beam in order to to Set the frequencies precisely what we're going to try to do for a For a test here is to make a two-frequency pattern For an initial evaluation of this kind of technique and so we do that and We set resistances on this chip and we've made it we've certainly made two distributions of resistances and we can see that they're the spread in each resistance is about about 50 ohms Now if we take this chip and we cool it down in the fridge and we measure the qubit frequencies We see that we do indeed have Two target qubit frequencies and the spread off of those two targets is About 12 ohms a sigma of about a rather 12 megahertz a sigma of about 12 megahertz Off of these two target frequencies So we see this as pretty good progress towards meeting the goals that were laid out In terms of this statistical model for how do you evade the frequency collision problem? So let me summarize we Recognize and we're working hard to quantify the frequency crowding problem in collisions of in in lattices of Q of fixed frequency qubits Where We're trying to avoid frequency crowding in order to to maintain gate fidelity We can use a statistical model to show that the precision of setting the qubit frequencies is really the key parameter In order to be able to predict how well you're evading the frequency crowding We're able to demonstrate statistically that these alternate heavy hexagon type lattices with a three frequency pattern are Much superior to a square lattice in evading the frequency crowding problem But we need a a good precision of setting the qubit frequencies in order to make use of that and we started to try a technique of selective anneal of the junctions in the trans mods in order to achieve Desired qubit frequencies and I'll say thank you very much