Nearly 80% of the nitrogen found in the human body is man-made and can be traced back to the Haber-Bosch process (Howarth 2008). This nitrogen, which builds proteins, DNA and other essential molecules in the body, comes from the ammonia in the fertilizers we need to support crop growth worldwide. However, Haber-Bosch contributes to about 3% of global carbon emissions, because of the extremely high temperatures needed to synthetize ammonia. Yet, to this day, it remains the best solution to make this ammonia industrially.
Plants, however, don’t burn fuel to fix the nitrogen they need to grow. Instead, microbes in the soil use a molecule called FeMoco to convert nitrogen into ammonia much more efficiently. Biologists have been researching FeMoco for decades in the hope of improving how we produce fertilizers, but to no avail.
Meanwhile, Biochemists have also tried to improve their understanding of another industrially relevant catalyst: P450. P450 enzymes are crucial for drug metabolism and the production of important molecules like cholesterol, vitamin D, and steroid hormones. P450 and FeMoco are both hard to study. Indeed, simulating precisely very complex molecules using the classical computers we have today or will ever have, regardless of how large and powerful, is a very difficult task.
In this blog post, we present how, with a fault-tolerant quantum computer based on cat qubits, we could simulate FeMoco and P450 using “only” 99 000 cat qubits — 27 times fewer compared to other superconducting architectures.
FeMoco and P450: Benchmarks for Molecular Simulation
FeMoco and P450 make promising candidates for quantum molecular simulation. They are notoriously tricky for classical computers to handle, and have very impactful potential applications in medicine and the chemical industry, so are considered excellent benchmark molecules in quantum chemistry.
FeMoco is a metallocluster that plays a key role in biological nitrogen fixation, but its exact workings continue to elude us. In biological nitrogen fixation, microbes naturally convert atmospheric nitrogen into ammonia, the form that plants can readily use for growth and photosynthesis. The issue is that this natural process, while much more efficient than its industrial counterpart Haber-Bosch, doesn’t produce nearly enough ammonia to meet global food needs. Instead, we rely on Haber-Bosch-made ammonia to feed half of the world’s population. Understanding the mechanisms of FeMoco with greater precision could equip scientists with new tools as they search for more cleaner alternatives to industrial fertilizer.
Cytochrome P450 enzymes are also highly promising candidates for quantum chemistry applications. Quantum chemical studies of P450 are valuable to the pharmaceutical industry because of the central role these enzymes play in drug metabolism. Understanding how P450s interact with drug candidates at the molecular level helps predict metabolic stability, potential drug-drug interactions, and the formation and persistence of toxic metabolites in the human body. Quantum chemistry enables detailed modeling of the enzyme’s active site and how its reactions happen, which could help in the design of safer and more effective drugs by allowing scientists to optimize compounds for favorable metabolic profiles early in development.
Quantum Chemistry: A Promising Area for Early Quantum Advantage
When useful, large-scale quantum computing becomes a reality, quantum chemistry is set to be one of the first areas of impact. This is because simulating complex molecules quickly becomes an intractable problem for computers today, whereas quantum computers map naturally to molecular simulation.
Quantum chemistry shows tremendous promise to give groundbreaking new tools for scientists, but to unlock them quantum computers must scale effectively, which means overcoming the fundamental challenge of quantum computing: dealing with the intrinsic errors in quantum computers.
To do so, our best option is quantum error correction, a technique which involves combining several noisy qubits to create logical ones with reduced noise. The challenge is the huge number of physical qubits we have to add to make it work — in standard architectures, we are looking at hundreds of physical qubits to make just one logical qubit — and the huge hardware overhead this requires.
The good news is that scientists are making rapid progress on hardware and software, meaning that the point at which it’ll be practical to run useful algorithms on quantum computers only gets closer. And quantum chemistry is no exception.
Indeed, in the past few years, we’ve seen great progress on the main algorithm for molecular simulation: Quantum Phase Estimation (QPE). According to current estimates, we’ll start seeing the first use cases of QPE for quantum chemistry once we scale to around 1500 logical qubits. But what do such figures mean in practice?
Cat Qubits: Hardware Efficient by Design
At Alice & Bob, we don’t use “traditional” transmon qubits. We use cat qubits. Cat qubits have the special property of being less sensitive to one type of error: bit-flips. They can be engineered to resist bit-flips at an exponential rate, for the favorable cost of a linear increase in phase-flips. Since we “just” have one error to correct, we can use the simpler repetition code instead of the more complex surface code required by transmons. In the repetition code, we use a linear chain of physical qubits compared with the 2D grid configuration needed for the surface code, and this requires far fewer physical qubits for every logical one.
For Precise Molecular Simulation, We Need the Ground State Energy
To predict the probability of a chemical reaction occurring, we study the energy levels of the molecules involved, most notably: their ground state energy. This is the lowest possible energy a molecule can have. We need to calculate this ground state energy very accurately, and classical methods quickly struggle as the system gets larger.
Molecules are made up of many electrons and their behavior is described by quantum mechanics. Achieving an accurate simulation of these systems on classical computers would require an exponential amount of information, something beyond the limits of classical computers. Orbitals describe the possible places electrons can be, which helps define the energy of the system. To give an idea, we are limited to around 25 orbitals, while we would need 76 for FeMoco and at least 58 for P450.
To study larger or more complex molecules with the tools available today, we rely on approximations, like DFT, that simplify the problem. For instance, DFT looks at the overall electron density, rather than tracking each electron one by one. And while these methods work well in many industrial applications, they break down in cases where the correlations between electrons are particularly strong. FeMoco and P450 are well-known examples of this: strongly correlated systems where classical approximations fail.
Unlike classical computers, however, quantum computers don’t suffer from exponential memory requirements when simulating quantum systems. Instead, the computational cost should grow only polynomially with the system size. Thus, using the QPE algorithm, we can go beyond classical approximations and accurately calculate a molecule’s ground state energy, even for complex systems.
Our Resource Estimate Methodology
The Algorithm
In this article, we present our own resource estimation for FeMoco and P450 using the algorithm described by a 2020 study from Google researchers, enabling a fair, head-to-head comparison. Even though newer and more efficient versions of this algorithm exist, we chose it because it gives a detailed specification to be run on superconducting quantum computers. This allowed us to adopt the same parameters, like the standard active space, important for capturing key chemical features, and targeting the same run time of respectively 78h for FeMoco and 99h for P450.
The Tool
In fault-tolerant approaches, there is always a tradeoff between reliability and qubit count for any given algorithm, and this is determined by the code distance. The code distance determines how well logical qubits are protected against noise; a higher code distance improves protection, but it requires us to add more physical qubits. To compute the code distance and the necessary number of qubits, we used our own open-source resource estimator, tuned to cat qubit noise models.
The Magic
On fault-tolerant quantum computers, any operation can be decomposed into transversal gates and non-transversal gates such as the essential Toffoli gate. Transversal gates are relatively easy to implement while non-transversal ones require a magic state factory, which makes their execution significantly slower, dive deeper in this blogpost. That is why, to accurately estimate execution time, we modified our standard open-source model to implement the autocorrected Toffoli gate. For the implementation of magic state factories, we use the approach outlined in our 2023 paper.
27× Fewer Qubits with Cats
Our results show that we could simulate FeMoco and P450 using cat qubits with 27× fewer physical qubits than the equivalent approach using transmons with the same runtime: 78 hours for FeMoco and 99 hours for P450. This advantage comes from cat qubits’ intrinsic error correction at the hardware level, with which we could run useful algorithms with significantly fewer qubits.
And this is just the beginning. We’re already working on further reducing the resources needed to simulate FeMoco and P450. We plan to do this in two main ways: first, by replacing the repetition code with an even more efficient LDPC-cat code (paper), and second, by the state-of-the-art magic state factories we recently designed (paper).
It’s not just about doing more with fewer resources. By reducing the number of qubits needed to scale quantum computers, we may well be able to build and run large-scale quantum computers sooner, bringing powerful tools that could benefit humanity closer.
Look out for our next papers to see what we can do next with cats!
In the meantime, check our infographic for a visual explainer.
