Quantum computers promise to solve certain problems that overwhelm classical machines, but tapping that power in practice has been an uphill climb. One grand challenge is finding the ground state of complex molecular systems, essentially the lowest-energy arrangement of electrons, akin to finding the deepest valley in a vast mountainous landscape.
Traditional quantum algorithms often wander this landscape inefficiently or get stuck on plateaus, especially given today’s imperfect hardware. Now, researchers have unveiled a “greedy” gradient-free quantum algorithm that acts like a savvy mountain guide: at each step it picks the quickest path downwards, quickly homing in on the low-energy valley.
This new approach not only uses far fewer quantum operations to reach accurate results, but it has also proven surprisingly robust to noise, even demonstrating its prowess on a real 25-qubit quantum computer. The development moves us closer to practical quantum advantage in chemistry and materials science, where quantum computers could soon tackle problems beyond the reach of classical computation.
Identifying the ground state of a molecule or material is a fundamental task in quantum chemistry and physics. It’s key to predicting chemical reactions, material properties, and drug interactions. However, solving for a many-particle ground state exactly on a classical computer is notoriously difficult, as the complexity grows exponentially with system size. Quantum computing offers a principle advantage here by encoding quantum states directly into qubits, but today’s devices (often called NISQ devices, for “noisy, intermediate-scale quantum”) are limited by noise and short coherence times. This means algorithms have to be especially efficient, using shallow circuits with as few operations as possible so that noise doesn’t wash out the result.
One popular approach for near-term hardware is the Variational Quantum Eigensolver (VQE). VQE is a hybrid algorithm that uses a quantum processor to evaluate the energy of a parameterized wavefunction (or ansatz) while a classical optimizer tunes those parameters to lower the energy. It’s like adjusting knobs on a machine (the angles of quantum gates) to minimize a measured output (the energy). VQE’s flexibility makes it promising for chemistry, but in practice it faces two big obstacles: barren plateaus (flat regions in the energy landscape where the optimizer gets no guidance) and a deluge of measurements needed to guide the optimization.
A clever variant called ADAPT-VQE tackled the first issue by building the ansatz iteratively, adding one new quantum gate at a time, chosen based on where the gradient is largest. This adaptive, gradient-driven strategy can bypass barren plateaus and find better solutions with a more compact circuit.
The catch?
ADAPT-VQE’s method of selecting each new gate and then re-optimizing all parameters at every step is hugely measurement-intensive and doesn’t play well with real hardware.
In fact, full implementations of ADAPT-VQE had never been demonstrated on quantum hardware because the requirements were impractical under realistic noise and shot (sampling) limits. When simulated with noise, even a simple molecule’s ADAPT-VQE solution lost accuracy and stalled out above the chemical accuracy threshold.
Enter the new approach, termed Greedy Gradient-Free Adaptive VQE (GGA-VQE). In essence, the researchers found a way to simplify ADAPT-VQE’s two-step loop (choose an operator, then globally re-optimize) into a single step that chooses an operator and its optimal parameter in one go. They describe it as giving ADAPT-VQE “a practical makeover by using a simple trick”.
The trick leverages a bit of math insight: when you add a single parameterized gate to the quantum circuit, the resulting energy as a function of that gate’s angle isn’t arbitrary, it forms a simple curve (in fact, a cosine or sine-like curve). That means with only a handful of energy measurements at different angles, one can fit this curve and find its minimum exactly
In plainer terms, it’s like knowing that a valley’s cross-section is a smooth U-shape – a few soundings can tell you where the bottom is. Armed with this knowledge, GGA-VQE makes its moves as follows:
This greedy one-step-at-a-time construction yields a somewhat less flexible final circuit than if one re-optimized everything repeatedly, but it dramatically cuts down the required quantum evaluations and is far more NISQ-friendly. By building the ansatz “one local update at a time,” GGA-VQE sidesteps the costly, noise-sensitive and shot-intensive optimization loops that plagued ADAPT-VQE.
In fact, the new algorithm needs only a fixed, small number of measurements for each iteration – the authors report just two-to-five circuit measurements per iteration, regardless of the number of qubits or operators considered. This represents a huge improvement in resource efficiency. It’s like reducing a thorough survey of an entire mountain range to a quick check of a few key trails when searching for the lowest point.
Crucially, this greedy strategy also turns out to be more robust against noise. By avoiding a high-dimensional parameter search, GGA-VQE minimizes the accumulation of error from repeated measurements. The team found that in simulations of small molecules (like H₂O and LiH), GGA-VQE maintained much better accuracy under realistic noise than ADAPT-VQE. For instance, after ~30 iterations on a water molecule, the greedy algorithm was nearly twice as accurate as the traditional adaptive method when shot noise was present. In a lithium hydride case, it was about five times more accurate under the same conditions. In other words, by “being greedy” and sacrificing the global re-optimization, the algorithm gains a resilience to measurement noise that the fully flexible approach lacked. This noise-resistant quality is a big deal for near-term quantum computing – it suggests a way to get useful results from devices that otherwise would drown in noise before finishing a calculation.
It’s one thing to test a new quantum algorithm in classical simulations or on a small number of qubits, but the ultimate goal is to run it on actual quantum hardware. The researchers behind GGA-VQE have done exactly that. They implemented their algorithm on a 25-qubit trapped-ion quantum computer (IonQ’s Aria system) via Amazon Braket, pushing the envelope of what’s been achieved with adaptive VQE methods on real devices. The task chosen for this demonstration was to find the ground state of a 25-spin transverse-field Ising model, a well-known physics problem that, serving as a proving ground prior to tackling molecular systems, still represents a highly non-trivial computation for quantum hardware.
Remarkably, the greedy algorithm was able to build a good approximation of the Ising model’s ground state on the 25-qubit machine. Each iteration required only five observables to be measured, keeping the hardware run efficient.
After building up an ansatz step by step, the team hit more than 98% fidelity when compared to the true ground state, despite the hardware noise and imperfections. The trick was that after the quantum processor was finished, the resulting circuit, which is the list of chosen gates and angles, was taken and evaluated with a high-precision classical emulation to confirm its energy.
Put simply, the quantum computer provided the blueprint of the solution, and a classical computer then verified the quality of that solution. The ansatz structure was good enough to yield a low energy when errors were removed, despite the noise that affected the raw energy measurements on the QPU. This approach, which uses the quantum device to build the answer and verified by a classical post-processing, is a smart way to deal with noise until there’s access to better hardware in the future.
It highlights the algorithm's surprising noise-resilience: despite noisy energy readings, it can still zero in on the correct ground-state form.
This experiment is more than just another data point; it represents a milestone. It’s the first time an adaptive variational algorithm of this kind has been fully run to convergence on real quantum hardware. Previous attempts at running ADAPT-VQE-like methods on actual devices were stymied by noise and resource demands. By successfully computing a 25-qubit ground state, the GGA-VQE demonstration shows that today’s quantum machines, with the right algorithmic boosts, are on the cusp of tackling problems at a scale that challenges classical brute-force simulation (a 25-qubit space has over 33 million basis states).
The authors put it best. “This research brings key progress towards the full implementation of variational methods for quantum chemistry and proposes a first – real life – converged computation on an actual NISQ quantum computer”. In short, it’s a proof-of-concept that real-world quantum advantage – using quantum hardware to solve useful chemistry problems better than classical methods – is getting closer.
The greedy gradient-free algorithm isn’t just a one-off trick for the Ising model or a physics curiosity. Its core ideas carry broad significance for quantum computing’s future in chemistry, materials, and beyond. By drastically reducing the number of quantum gates and measurements needed, the approach makes better use of scarce quantum resources. Shorter, more efficient circuits suffer less from decoherence and hardware errors, which means more reliable outcomes without needing fully error-corrected quantum computers.
This is exactly the kind of innovation needed in the NISQ era: tailor the algorithm to work with the noise constraints instead of against them. As seen in the molecular simulations the team ran, GGA-VQE’s noise tolerance can put previously unreachable accuracy within reach on current devices. That could open the door to tackling small but chemically relevant molecules on hardware in the near term – for example, accurate energies for reaction intermediates or novel materials, computed by a quantum processor where traditional methods struggle.
Equally exciting is how this development can integrate with advances in classical and hybrid computing, including the realm of AI. In recent months, there’s been a surge in interest around foundation models in chemistry (such as the FeNNix-Bio1 model) that use machine learning trained on quantum chemistry data to predict molecular properties.
One of the bottlenecks for these AI models is obtaining high-quality quantum data for training. That’s where algorithms like GGA-VQE could play a pivotal role. Jean-Philip Piquemal, a lead researcher on this study and also a co-developer of FeNNix-Bio1, highlighted the convergence of quantum computing, high-performance computing (HPC), and AI as a path to what he calls “quantum AI”.
“We’re already starting to use quantum-computing algorithms to generate data to enhance our models,” Piquemal says. In this vision, a quantum algorithm running on a real device (like the 25-qubit experiment here) might calculate energies or optimize molecular states that are fed into a machine learning model. The AI model, in turn, can generalize and scale up those insights to bigger systems or longer timescales than the quantum hardware could handle alone.
It’s a symbiotic strategy: the precision of quantum physics combined with the power of AI. The success of GGA-VQE on hardware strengthens confidence that near-term quantum processors can contribute meaningfully to such pipelines, effectively acting as specialized“co-processors” for tasks like ground-state prep that greatly benefit from quantum mechanics.
Finally, this work serves as a guiding benchmark for quantum hardware development. Running a non-trivial algorithm on 25 qubits with error mitigation and seeing it through to a verified result provides invaluable data. It helps pinpoint what improvements in noise rates or qubit counts will yield the biggest gains. These experiments “are essential for benchmarking actual hardware and guiding algorithm development toward ever more efficient use of quantum resources,” the authors note. In other words, each time researchers push the limit of what’s doable on current quantum chips, we learn how to better design both the algorithms and the machines themselves. GGA-VQE’s success suggests that we should continue to explore greedy, adaptive, and noise-aware algorithms as we march toward the era of fault-tolerant quantum computing.
Bottom line: A once purely theoretical algorithm has been reimagined into a practical form and put to the test on cutting-edge hardware. The greedy gradient-free approach achieved accurate ground-state results with a leaner circuit and greater noise resilience than its predecessors. It’s a vivid demonstration of how ingenuity in algorithm design can unlock more from today’s quantum technology.
Like a skilled mountaineer taking sure-footed steps down a treacherous slope during an earthquake, GGA-VQE finds the low-energy solution where others stumble. This not only marks a step forward in quantum computing experiments (solving a 25-body problem on real qubits), but also lights the way toward practical quantum advantage in solving chemical and materials problems. The hike toward quantum advantage is far from over, but with this new strategy, the summit – or rather, the lowest valley – is in sight.
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