Automated Quantum Algorithm Discovery for Quantum Chemistry
Quantinuum, the world's leading quantum computing company, and Hiverge, a Cambridge-based startup developing an engine for automated algorithm discovery, have initiated a collaboration on quantum algorithm discovery.
Authors:
Quantinuum (alphabetical order): Eric Brunner, Steve Clark, Fabian Finger, Gabriel Greene-Diniz, Pranav Kalidindi, Alexander Koziell-Pipe, David Zsolt Manrique, Konstantinos Meichanetzidis, Frederic Rapp
Hiverge (alphabetical order): Alhussein Fawzi, Hamza Fawzi, Kerry He, Bernardino Romera Paredes, Kante Yin
What if every quantum computing researcher had an army of students to help them write efficient quantum algorithms? Large Language Models are starting to serve as such a resource.
Quantinuum’s processors offer world-leading fidelity, and recent experiments show that they have surpassed the limits of classical simulation for certain computational tasks, such as simulating materials. However, access to quantum processors is limited and can be costly. It is therefore of paramount importance to optimise quantum resources and write efficient quantum software. Designing efficient algorithms is a challenging task, especially for quantum algorithms: dealing with superpositions, entanglement, and interference can be counterintuitive.
To this end, our joint team used Hiverge’s AI platform for automated algorithm discovery, the Hive, to probe the limits of what can be done in quantum chemistry. The Hive generates optimised algorithms tailored to a given problem, expressed in a familiar programming language, like Python. Thus, the Hive’s outputs allow for increased interpretability, enabling domain experts to potentially learn novel techniques from the AI-discovered solutions. Such AI-assisted workflows lower the barrier of entry for non-domain experts, as an initial sketch of an algorithmic idea suffices to achieve state-of-the-art solutions.
In this initial proof-of-concept study, we demonstrate the advantage of AI-driven algorithmic discovery of efficient quantum heuristics in the context of quantum chemistry, in particular the electronic structure problem. Our early explorations show that the Hive can start from a naïve and simple problem statement and evolve a highly optimised quantum algorithm that solves the problem, reaching chemical precision for a collection of molecules. Our high-level workflow is shown in Figure 1. Specifically, the quantum algorithm generated by the Hive achieves a reduction in the quantum resources required by orders of magnitude compared to current state-of-the-art quantum algorithms. This promising result may enable the implementation of quantum algorithms on near-term hardware that was previously thought impossible due to current resource constraints.
The Electronic Structure Problem in Quantum Chemistry
The electronic structure problem is central to quantum chemistry. The goal is to prepare the ground state (the lowest energy state) of a molecule and compute the corresponding energy of that state to chemical precision or beyond. Classically, this is an exponentially hard problem. In particular, classical treatments tend to fall short when there are strong quantum effects in the molecule, and this is where quantum computers may be advantageous.
The paradigm of variational quantum algorithms is motivated by near-term quantum hardware. One starts with a relatively easy-to-prepare initial state. Then, the main part of the algorithm consists of a sequence of parameterised operators representing chemically meaningful actions, such as manipulating electron occupations in the molecular orbitals. These are implemented in terms of parameterised quantum gates. Finally, the energy of the state is measured via the molecule’s energy operator, the “Hamiltonian”, by executing the circuit on a quantum computer and measuring all the qubits on which the circuit is implemented. Taking many measurements, or “shots”, the energy is estimated to the desired precision. The ground state energy is found by iteratively optimising the parameters of the quantum circuit until the energy converges to a minimum value. The general form of such a variational quantum algorithm is illustrated in Figure 2.
The main challenge in these frameworks is to design an appropriate quantum circuit architecture, i.e. find an efficient sequence of operators, and an efficient optimisation strategy for its parameters. It is important to minimise the number of quantum operations in any given circuit, as each operation is inherently noisy and the algorithm’s output degrades exponentially. Another important quantum resource to be minimised is the total number of circuits that need to be evaluated to compute the energy values during the optimisation of the circuit parameters, which is time-consuming.
To meet these challenges, we task the Hive with designing a variational quantum algorithm to solve the ground state problem, following the workflow shown in Figure 1. The Hive is a distributed evolutionary process that evolves programs. It uses Large Language Models to generate mutations in the form of edits to an entire codebase. This genetic process selects the fittest programs according to how well they solve a given problem. In our case, the role of the quantum computer is to compute the fitness, i.e., the ground state energy. Importantly, the Hive operates at the level of a programming language; it readily imports and uses all known libraries that a human researcher would use, including Quantinuum’s quantum chemistry platform, InQuanto. In addition, the Hive can accept instructions and requests in natural language, increasing its flexibility. For example, we encouraged it to seek parameter optimisation strategies that avoid estimating gradients, as this incurs significant overhead in terms of circuit evaluations. Intuitively, the interaction between a human scientist and the Hive is analogous to a supervisor and a group of eager and capable students: the supervisor provides guidance at a high level, and the students collaborate and flesh out the general idea to produce a working solution that the supervisor can then inspect.
We find that from an extremely basic starting point, consisting of a skeleton for a variational quantum algorithm, the Hive can autonomously assemble a bespoke variational quantum algorithm, which we call Hive-ADAPT. Specifically, the Hive evolves heuristic functions that construct a circuit as a sequence of quantum operators and optimise its parameters. Remarkably, the Hive converged on a structure resembling the current state-of-the-art, ADAPT-VQE. Crucially, however, Hive-ADAPT substantially outperforms this baseline, delivering significant improvements in chemical precision while reducing quantum resource requirements.
A molecule’s ground state energy varies with the distances between its atoms, called the “bond length”. For example, for the molecule H2O, the bond length refers to the length of the O-H bond. The Hive was tasked with developing an algorithm for a small set of bond lengths and reaching chemical precision, defined as within 1.6e-3 Hartree (Ha) of the ground state energy computed with the exact Full Configuration Interaction (FCI) algorithm. As we show in Figure 3, remarkably, Hive-ADAPT achieves chemical precision for more bond lengths than ADAPT-VQE. Furthermore, Hive-ADAPT also reaches chemical precision for other “unseen” bond lengths, showcasing the generalisation ability of the evolved quantum algorithm. Our results were obtained from classical simulations of the quantum algorithms, where we used NVIDIA CUDA-Q to leverage the parallelism enabled by GPUs. Further, relative to ADAPT-VQE, Hive-ADAPT exhibits one to two orders of magnitude reduction in quantum resources, such as the number of circuit evaluations and the number of operators used to construct circuits, which is crucial for practical implementations on actual near-term processors.
For molecules such as BeH2 at large Be-H bond lengths, a complex initial state is required for the algorithm to be able to reach the ground state using the available operators. Even in these cases, by leveraging an efficient state preparation scheme implemented in InQuanto, the Hive evolved a dedicated strategy for the preparation of such a complex initial state, given a set of basic operators to achieve the desired chemical precision.
To validate Hive-ADAPT under realistic conditions, we employed Quantinuum’s H2 Emulator, which provides a faithful classical simulator of the H2 quantum computer, characterised by a 1.05e-3 two-qubit gate error rate. Leveraging the Hive's inherent flexibility, we adapted the optimisation strategy to explicitly penalise the number of two-qubit gates—the dominant noise source on near-term hardware—by redefining the fitness function. This constraint guided the Hive to discover a noise-aware algorithm capable of constructing hardware-efficient circuits. We subsequently executed the specific circuit generated by this algorithm for the LiH molecule at a bond length of 1.5 Å with the Partition Measurement Symmetry Verification (PMSV) error mitigation procedure. The resulting energy of -7.8767 ± 0.0031 Ha, obtained using 10,000 shots per circuit with a discard rate below 10% in the PMSV error mitigation procedure, is close to the target FCI energy of -7.8824 Ha and demonstrates the Hive's ability to successfully tailor algorithms that balance theoretical accuracy with the rigorous constraints of hardware noise and approach chemical precision as much as possible with current quantum technology.
For illustration purposes, we show an example of an elaborate code snippet evolved by the Hive starting from a trivial version:
Quantinuum’s in-house quantum chemistry expert, Dr. David Zsolt Manrique, commented,
“I found it amazing that the Hive converged to a domain-expert level idea. By inspecting the code, we see it has identified the well-known perturbative method, ‘MP2’, as a useful guide; not only for setting the initial circuit parameters, but also for ordering excitations efficiently. Further, it systematically and laboriously fine-tuned those MP2-inspired heuristics over many iterations in a way that would be difficult for a human expert to do by hand. It demonstrated an impressive combination of domain expertise and automated machinery that would be useful in exploring novel quantum chemistry methods.”
Looking to the Future
In this initial proof-of-concept collaborative study between Quantinuum and Hiverge, we demonstrate that AI-driven algorithm discovery can generate efficient quantum heuristics. Specifically, we found a great reduction in quantum resources, which is impactful for quantum algorithmic primitives that are frequently reused. Importantly, this approach is highly flexible; it can accommodate the optimisation of any desired quantum resource, from circuit evaluations to the number of operations in a given circuit. This work opens a path toward fully automated pipelines capable of developing problem-specific quantum algorithms optimised for NISQ as well as future hardware.
An important question for further investigation regards transferability and generalisation of a discovered quantum solution to other molecules, going beyond the generalisation over bond lengths of the same molecule that we have already observed. Evidently, this approach can be applied to improving any other near-term quantum algorithm for a range of applications from optimisation to quantum simulation.
We have already demonstrated an error-corrected implementation of quantum phase estimation on quantum hardware, and an AI-driven approach promises further hardware-tailored improvements and optimal use of quantum resources. Beyond NISQ, we envision that AI-assisted algorithm discovery will be a fruitful endeavour in the fault-tolerant regime, as well, where high-level quantum algorithmic primitives (quantum fourier transform, amplitude amplification, quantum signal processing, etc.) are to be combined optimally to achieve computational advantage for certain problems.
Notably, we’ve entered an era where quantum algorithms can be written in high-level programming languages, like Quantinuum’s Guppy, and approaches that integrate Large Language Models directly benefit. Automated algorithm discovery is promising for improving routines relevant to the full quantum stack, for example, in low-level quantum control or in quantum error correction.
About Quantinuum
Quantinuum, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Quantinuum’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Quantinuum leads the quantum computing revolution across continents.
Quantinuum is pleased to announce that applications are now open for the Quantinuum SG Grand Challenge 2026, a global innovation challenge designed to bring together researchers, developers, scientists and innovators to explore practical applications of quantum computing.
Organized by Quantinuum and supported by Singapore's National Quantum Office and Aqora, the three-month program aims to foster collaboration across academia, industry and the quantum developer community while supporting the continued growth of Singapore's quantum ecosystem.
A Platform for Quantum Computing Innovation
Participants will work in teams to develop solutions across a range of challenge areas, including chemistry and molecular simulation, optimization, AI for quantum systems, quantum error correction, condensed matter and materials science, and open innovation. Throughout the program, participants will have access to mentoring, technical enablement and Quantinuum quantum computing resources.
Singapore Grand Finale
Selected finalist teams will be invited to present their work at the Grand Finale hosted in Singapore before representatives from academia, and industry. The event will celebrate innovative applications of quantum computing while providing an opportunity for participants to engage with Singapore's growing quantum community.
Join the Challenge
The Quantinuum SG Grand Challenge welcomes participants from around the world. Whether you are an experienced quantum researcher or beginning your quantum computing journey, the program offers an opportunity to collaborate, learn and contribute to the development of practical quantum applications.
Applications are now open. Spaces are limited and subject to review and approval.
- Researchers from Quantinuum, Caltech, the University of Chicago, and Harvard created a rare topologically ordered state of matter on Quantinuum's System Model H2 and used it to perform protected universal quantum gates with non-Abelian anyons.
- The work explores an alternative approach to fault tolerance by using topological properties to protect quantum information. This could reduce the need for magic state distillation, which can (in some circumstances) be resource-intensive.
- Quantinuum continues to show leadership in fault tolerance, with successful demonstrations spanning world record error rates to exotic approaches like topological computing
Quantum computing is all about putting the exotic properties of physics to work. Qubits can exist in two states at once, like the famous cat that is both alive and dead. Qubits can also be entangled, where the state of one will instantaneously affect the state of another - even when they have no way to “talk” to each other. Qubits can even be teleported, moving a quantum state from one place to another without physically moving it through space.
These features give quantum computing its power. But the ‘spooky’ nature of quantum computing doesn’t stop there: our quantum computers are potent enough to make exotic states of matter out of our qubits, and to perform calculations that would warp the mind of more traditional thinkers.
A new approach
In a recent paper published in Nature, researchers at Quantinuum teamed up with Caltech, the University of Chicago, and Harvard to create a rare ‘topologically ordered’ state of matter from our qubits.
When the qubits become ‘topologically ordered’, they become more than individual particles, now ‘related’ to each other in a specific way. This is like how hydrogen and oxygen act as individual gas particles alone, but you can put them together in a certain way so that they become water, a liquid, and an entirely different creature.
When the qubits become topologically ordered, the quantum information that they carried individually gets spread out over the whole system, which acts as a sort of protection from noise. This is like how a net makes a stronger barrier than a bunch of un-knotted ropes.
Once the researchers had topologically ordered qubits, they used the exotic particles that resulted (called non-Abelian anyons) to compute, performing error-protected gates and measurements.
To perform gates, the researchers 'braided' the anyons, which is like changing the shape of the “net”. This is something like the children’s game ‘cats cradle’. Through a sequence of changes to the “net”, the quantum computer can perform full calculations, one day helping scientists to understand the secrets hidden in the world around us.
Why go to such trouble? Well, for the love of discovery of course - but the team had an additional, specific motivation. One of the biggest challenges in building practical quantum computers is protecting them from errors while still being able to perform every operation needed for computation (this is referred to as universality).
This work takes a fresh approach to this challenge. Unlike traditional quantum error correction, the special properties of topological matter enable a universal set of fault tolerant gates without relying on expensive magic state distillation.
Why this matters
Quantum error correction is essential for large-scale quantum computing. While it protects fragile quantum information from noise by turning delicate physical qubits into robust logical qubits, it also introduces a significant constraint: not every quantum gate can be performed directly on logical qubits.
For decades, the standard solution has been to supplement error-corrected operations with magic states. These specially prepared quantum resources enable universal computation but can come at a steep cost - in many estimates of future fault-tolerant quantum computers, magic state preparation dominates both the physical qubit count and the runtime of useful algorithms.
Reducing this overhead has therefore become an important goal in quantum computing. This new approach may significantly reduce the cost by enabling the ‘topological preparation’ of magic states, eliding expensive protocols like distillation. If universal computation can be performed without large-scale magic state distillation, quantum computers could require significantly fewer physical qubits and spend much less time generating computational resources before running useful algorithms.
We will never stop exploring
While there is still considerable work ahead to understand the practical implementation and scalability of these ideas, this result expands the landscape of what's possible in quantum fault tolerance.
Of course, this impressive demonstration describes just one approach we are taking to fault tolerance at scale. We will continue to push forward with topological computing alongside more traditional approaches to quantum error correction, as well as exploring everything we can imagine in between. We are looking at a number of ways to reduce the resource cost of magic states in particular, and are making strides in multiple dimensions. With machines that are both flexible and accurate enough to do it all, who can resist?
- Quantinuum continues its progress toward fault-tolerant quantum computing, with a series of peer-reviewed breakthroughs in fault-tolerant operations.
- Our progress is not only scientific; it is commercial. By improving logical-qubit reliability and encoding efficiency, Quantinuum is reducing the resource overhead required to scale its quantum computers toward commercially useful workloads.
- These results were achieved on commercial Quantinuum hardware, reinforcing that our architecture is not just setting new standards, but building a practical foundation for customers, partners, and researchers preparing for the fault-tolerant era.
Fault-tolerant quantum computing is the threshold the industry must cross before quantum computers can solve the hardest, highest-value problems with confidence. To be commercially useful at scale, the question is not simply who can build more qubits. It is who can build reliable, efficient, scalable systems that reduce technical risk and accelerate the path to commercial usefulness.
Quantinuum is progressing on that path.
Last year, in partnership with Microsoft, we published a breakthrough in logical computing, demonstrating logical qubits that outperformed their physical counterparts by a factor of 800. We are proud to announce that this work is now being published in Nature, one of the most highly regarded scientific journals in the world.
This work highlights our leading fidelities, as shown in Table 1:
Since then, we’ve accelerated our efforts to reach large-scale fault tolerance and advanced what we believe to be the core building blocks of fault-tolerant quantum computing, from logical-qubit teleportation and multiple error-correction breakthroughs to one of the first meaningful computations using logical qubits. Importantly, these results were achieved on commercial Quantinuum hardware, demonstrating not just scientific progress, but a practical and efficient path toward scalable, customer-ready fault tolerance.
A Recap of Our Recent Technical Progress
Since the work with Microsoft, we achieved a milestone years ahead of schedule, demonstrating high-fidelity teleportation of a logical qubit, which was published in Science, one of the world’s most prestigious journals. Later, we beat our own record in this crucial fault tolerance milestone, thanks to continued improvements to our System Model H2’s fidelity.
Then, a series of results demonstrating more error-correcting milestones (and codes):
- Better than physical results in a high-rate non-local code,
- First-ever demonstration of a single-shot error correcting code (which significantly reduces resource requirements) in 4 dimensions
- Extending qubit lifetimes by 10x with a concatenated code
- Observed fault-tolerance thresholds with concatenated codes
- High fidelity magic states and a fully fault tolerant universal gate set in two different papers
Recently, we topped ourselves yet again by performing one of the first meaningful computations with logical qubits – exploring key questions in materials and magnetism, using logical qubits with better error rates than their physical counterparts. This result also includes a leading “encoding rate” squeezing 48 logical qubits out of just 98 physical qubits, emphasizing how our architecture helps to support large scale fault tolerance without enormous resource costs.
It is worth noting that all these results were achieved on our commercial hardware, not on one-off laboratory test-stands – reflecting the performance that we are able to deliver to our customers.
We also did crucial theoretical work, exploring new options for error correction that can reduce resource requirements, time to solution, and shorten the timeline to large scale fault tolerance.
Commercial Implications and the Road Ahead
We believe the commercial implication is clear: Quantinuum is reducing the uncertainty around the path to fault-tolerant quantum computing. Our architecture, hardware fidelity, full-stack control, and error-correction progress are converging into a practical roadmap for systems that can support valuable scientific and commercial workloads.
For those evaluating when quantum computing will become strategically relevant, we believe the signal is also increasingly clear: the fault-tolerant era is no longer a distant concept. It is becoming an engineering reality, and Quantinuum is leading the way.