Building the Modern Quantum Architecture—Lecture 6: Balancing the Cost of Utility-Scale Quantum

Added: 2026-04-29

[00:00:08]Hello, my name is Matthias Troyer.

[00:00:11]I'm a Technical Fellow and Corporate Vice President at Microsoft, where I lead the teams working on quantum architecture applications and software.

[00:00:29]Today I want to talk about quantum simulation of chemical reactions, which is one of the most promising applications for a utility scale quantum computer.

[00:00:48]These simulations can be simple quantum models like quantum magnets, can be molecules, can be materials, can be nuclear.

[00:00:57]There are many applications.

[00:00:59]Today I want to focus on chemistry and specifically on chemical reactions.

[00:01:04]They appear in the synthesis of molecules and materials, in catalysis, in enzymes in the body, in the soil and in plants, they appear in degradation and corrosion.

[00:01:23]They are what chemistry is about.

[00:01:26]If I want to understand the reaction, then I have to look at the energetics of it.

[00:01:33]Here is one example of the carbon fixation reaction.

[00:01:41]I want to take the carbon dioxide and nitrogen, and turn it into methanol.

[00:01:50]I simply want to take carbon from the air and turn it into valuable chemicals.

[00:01:57]If I want to just do that, then bring it together, then I have to go to an intermediate state that has a much higher energy than the initial state, and that is determined by the energy barrier through which the molecules have to go.

[00:02:23]It's like a mountain pass.

[00:02:25]When you want to cross the mountains, you have to climb up the pass, and then you walk down again.

[00:02:31]And the rate of the reaction depends exponentially on the height of the barrier.

[00:02:38]Thus, to make it faster, I want to reduce the barrier height.

[00:02:43]We can do that with a catalyst.

[00:02:46]The catalyst is the substance that accelerates the reaction without being used up in it.

[00:02:55]So in this case it's CO2, and hydrogen bind to it, react, do many steps, and they get out the methanol.

[00:03:06]And then the catalyst can bind to the next CO2 molecule.

[00:03:15]And the big thing here is that in that reaction, although it's much more complex with the catalyst, the barriers are all lower, and the rate thus higher.

[00:03:26]And the key thing in understanding reaction and the rate now is being able to calculate these barrier heights.

[00:03:33]And that's where the quantum computer comes in.

[00:03:36]Because as you recall from the first lecture, the more accurately I want to simulate the chemical system, the more expensive it becomes.

[00:03:51]And here I really want to look at the behavior, the reactions.

[00:03:56]So the behavior of the electrons in the reaction, the chemical bonds forming and breaking, and thus I have to go to high levels of accuracy.

[00:04:09]If I do it with Density Functional Theory, then I assume that electrons are essentially independent and I simulate a single electron embedded in the average cloud of the others.

[00:04:25]That works as long as the electrons do not correlate.

[00:04:28]They essentially behave independently.

[00:04:33]And that's not the case during the chemical reactions.

[00:04:39]That's why then we at least go to the Coupled Cluster methods.

[00:04:45]There we capture the correlations between two electrons, three and four.

[00:04:52]So we capture some limited entanglement between a few electrons.

[00:04:57]That can be good enough in some cases.

[00:05:02]When it is not, we have to go to exact methods.

[00:05:07]So calling for a Full Configuration Interaction level of theory where I take into account all the correlations between all the relevant electrons.

[00:05:20]But then the scaling becomes exponential.

[00:05:23]And if we now look at the cost of a classical calculation versus the quantum one, when I need the exact answer, when I need really all the quantum correlations, then the classical scaling of the cost is exponential.

[00:05:39]When it's ten orbitals, it’s still pretty cheap, when it is about 20, it’s thousands of dollars.

[00:05:47]When you get to 30-ish, it's millions of dollars, and 40 becomes billions, and 50 becomes trillions of dollars.

[00:05:53]The cost just explodes exponentially.

[00:05:56]But quantumly, the cost goes quadratically, cubically with the problem size.

[00:06:04]And the goal is to keep it in the range of thousands of dollars.

[00:06:08]And then we can do much bigger systems accurately with quantum hardware, with a range where it's just no longer possible classically.

[00:06:19]And that is important for chemical reactions, not just to get the energies right or the rates right, but if the rates are off, if the barrier heights are off, then I might pick the wrong path in the reaction.

[00:06:37]For example, an ethylene molecule reacting with ozone, I want to know what comes out, what is the product when they react?

[00:06:46]And if I do the calculation of the energy barriers and the rates with Density Functional Theory, then I pick out one path.

[00:06:56]The top one here.

[00:06:59]But if I do it more accurately with Coupled Cluster or with quantum methods, then I get a different path and I end up in a different product.

[00:07:08]So it's even qualitatively wrong.

[00:07:10]I get the wrong reaction path, the wrong products.

[00:07:14]I just get it wrong when I don't do it well enough.

[00:07:17]Hence, we really need quantum computers to be sure that we get the right reaction path.

[00:07:25]But the real chemical reactions are often much more complex.

[00:07:31]So here's one example of a network where we had to do more than a million calculations with Density Functional Theory.

[00:07:46]And we found kind of the 3,000 most relevant configurations.

[00:07:51]We refined those more accurately with Coupled Cluster methods.

[00:07:57]So then we found about 20, where we didn't trust it.

[00:08:02]There we then did the Full Configuration Interaction calculations.

[00:08:12]And for 5 to 10 we would really have loved to run it on a quantum computer to get the right rates.

[00:08:24]Now how do I use the quantum computer?

[00:08:28]As mentioned, we have to calculate the height of the energy barrier.

[00:08:33]And the energy barrier is simply the difference of energy of the intermediate state during the reaction and the initial state where the reactants are separate.

[00:08:45]And thus I need to calculate the energy as the atoms undergo the chemical reaction.

[00:08:53]And the good news is that is pretty simple, because all I have to do is calculate the ground state energy in different configuration of the atoms.

[00:09:03]First they act in separate, and then I want to calculate the energy of the electrons in the intermediate state.

[00:09:13]So in both cases I just calculate the ground state given that specific location of the nuclei of the atoms.

[00:09:23]Hence I can map it all to the calculation of ground state energies, which as we discussed last time, we can do with quantum phase estimation.

[00:09:34]When I’m in the ground state of the molecule, and the wave function as evolved in time picks up a phase, that is the energy times the time.

[00:09:45]Nothing else has changed, it just picks up that phase.

[00:09:48]And if I could measure the phase, I would know the energy.

[00:09:51]The excited states also pick up phases proportional to the excited state energy.

[00:09:59]Thus, if I want to measure the energy, all I have to do is measure the phase the wave function picks up in a certain time.

[00:10:10]For that, I'm writing a quantum program, written here as U(t), that is the quantum program that propagates the wave function in time.

[00:10:18]And then I want to measure the phase.

[00:10:21]Now while it's not that simple, because I can not observe the phase of a wave function.

[00:10:28]But what I can do is I can observe phase differences.

[00:10:31]Hence let me add another control qubit.

[00:10:35]The control qubit is zero, I don't touch my wave function.

[00:10:38]It stays as it was.

[00:10:40]But if the control qubit is one, I propagate it in time and it picks up the phase.

[00:10:46]Now I put the control qubit into a quantum superposition of zero and one.

[00:10:51]That means if the control qubit is zero, it picks up no phase.

[00:10:56]But if the control qubit is one, the control qubit picks up the phase, but it is proportional to the ground state energy times the time.

[00:11:04]And if I now measure the control qubit, well, then from there I can deduce the ground state energy.

[00:11:13]That is, in simple terms, the idea behind quantum phase estimation.

[00:11:19]So if I start from the ground state wave function, I measure the phase and thus the energy of the ground state.

[00:11:27]If I start in the first excited state, I get the energy of the first excited state, and so on.

[00:11:33]But I don't know the ground state.

[00:11:37]Hence, what can I do?

[00:11:38]If I knew the ground state, well, then I might have solved the problem already.

[00:11:42]I don’t know it.

[00:11:44]So let's try to start from a random state.

[00:11:46]If I do that and I measure a phase, then just like a qubit, when it's measured, I get either zero or one randomly.

[00:11:57]Here, when I measure the phase, I randomly get the phase of one of the excited states or the ground state.

[00:12:05]It might be the first excited state.

[00:12:08]Okay, I can try again.

[00:12:09]Next time, it might be the second excited state.

[00:12:13]Because there are exponentially many states, it might take me exponentially long until randomly I hit the ground state.

[00:12:23]Now that will not work, of course.

[00:12:25]So what can we do?

[00:12:27]We don't know the ground state, and we don't want to start from a random state.

[00:12:34]But here's the solution.

[00:12:35]If I can prepare a good approximation to the ground state, maybe 90% of the amplitude is in the ground state and the bit of the rest elsewhere, then that is good enough, because now most of the time when I measure, I will measure the phase, and thus the energy of the ground state.

[00:12:57]And the wave function then collapses to the exact wave function of the ground state.

[00:13:01]So I have that as well.

[00:13:03]Thus the problem now becomes not knowing the ground state, but knowing a good approximation, good enough to 90%.

[00:13:11]And it turns out that is not too hard for almost all molecules.

[00:13:16]So we have good classical methods, approximate ones.

[00:13:20]They're just not good enough to give us the accurate energy.

[00:13:25]Because to get the energy accurately with an error that’s small enough, I need to know six stages and more of the energy.

[00:13:34]That means I need to have the wave function be precise to more than six digits.

[00:13:41]And that I just can't do.

[00:13:43]But getting it accurate to 90%, that's doable on classical computers, and hence a combination of a good classical trial state approximate wave function with quantum phase estimation is what leads to success.

[00:14:02]And this is a great example of a problem where quantum computers will have impact, because I need only small data, just the coupling constants of the molecule.

[00:14:18]Then I have a big computation that classically would take exponential time.

[00:14:23]And then I get out very little data, and just measure the energy.

[00:14:28]So small data in, small data out, big computation.

[00:14:32]Perfectly suited for quantum computers.

[00:14:35]But I need more than a quantum computer.

[00:14:37]Because the real question I’ve asked, how does a certain material corrode?

[00:14:41]How do I make a certain molecule?

[00:14:44]How does a reaction work?

[00:14:49]That takes many steps.

[00:14:50]I need to look at all the possible structures during the reaction.

[00:14:55]I need to generate it, calculate it classically, find out whether the electrons are correlated, are entangled.

[00:15:04]If they're not, then I solve it classically, apply corrections due to the final temperature, and model the reaction and get the answer.

[00:15:17]But if the electrons are highly entangled, then I extract the subspace of the entangled electrons.

[00:15:26]I simulate entangled electrons in the so-called active space on the quantum computer.

[00:15:34]Once I have the solution I embed the quantum solution back into the full system and then do the rest of the processing.

[00:15:47]So the full workflow will combine AI, classical HPC, and quantum, and all three will be important.

[00:15:58]And with it then we can answer the many questions in synthesis and catalysis, in enzymes, in biochemistry, for corrosion and degradation of materials.

[00:16:11]With this you can now see how quantum computers will really radically transform chemistry.

[00:16:19]And that will then be the start of a new golden age for chemistry.

[00:16:27]Thank you.