🧬 biology

Quantum approximate optimization of population-level acetabular screw parameters on gate-based hardware

This study demonstrates that while the Quantum Approximate Optimization Algorithm (QAOA) can outperform random sampling in selecting acetabular screw parameters on current IBM quantum hardware, its practical utility for patient-specific planning is currently limited by noise, seed dependence, and the difficulty of handling cardinality constraints compared to classical methods.

Original authors: Günbay Noyan Dirlik¹

Published 2026-09-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Günbay Noyan Dirlik¹

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

In the world of modern medicine, surgeons often rely on precise measurements to guide their tools through the complex landscape of the human body. When a bone in the hip socket, known as the acetabulum, breaks, doctors may need to insert a metal screw to hold the pieces together. Finding the perfect path for this screw is a delicate task; the route must be wide enough to fit the metal without cracking the bone, yet long enough to provide strong support. Because every person's anatomy is slightly different, and because these measurements can vary across different populations, surgeons traditionally use computer models based on large groups of people to determine the safest and most effective screw size and angle. For decades, these calculations have been done by standard computers, which are incredibly fast at sorting through lists of options to find the best one. However, a new type of computing technology, called quantum computing, has emerged with the promise of solving complex problems in entirely different ways. This technology uses the strange rules of physics at the smallest scales to explore many possibilities at once, leading some to wonder if it could one day outperform the machines we use today, even for medical planning.

A recent study set out to test this idea in a very specific, real-world scenario: choosing the right parameters for a hip screw. The researchers took a simplified version of the problem, based on published measurements from Turkish men, and tried to solve it using a quantum computer. They did not attempt to plan a surgery for a specific patient, but rather asked a broader question: can a quantum machine successfully identify the best screw size and length from a list of options, and how does it compare to the standard computers we already trust? To do this, they translated the medical decision into a language the quantum computer could understand, turning the choice of screw length, diameter, and angle into a series of binary switches. They then ran this problem on two different quantum processors available to the public, testing the machine's ability to find the correct answer among many possibilities.

The results of this experiment were revealing, though perhaps not in the way one might hope for a technological revolution. The quantum computer was able to find the best solution more often than random chance would allow. In the most successful run, the machine picked the correct screw configuration about 41 percent of the time, which is significantly better than the roughly 3 percent chance of guessing correctly at random. However, when the researchers compared this to a standard computer, the difference was stark. A conventional computer solved the exact same problem in less than a millisecond, finding the perfect answer every single time. The quantum computer, by contrast, took several seconds of actual processing time and still failed to find the right answer more than half the time. The study showed that while the quantum machine could indeed find the solution, it was not faster, nor was it more reliable, than the tools surgeons already use.

The researchers also discovered that the difficulty did not come from the medical problem itself, which is actually quite straightforward, but from the way the problem was translated for the quantum machine. The quantum computer struggled with a specific type of rule that forced it to pick exactly one option from a list, a constraint that made the path to the solution unstable and prone to errors. When the researchers tried to run a more complete version of the problem, which included more variables and a larger list of options, the quantum machine's performance dropped significantly, even in a perfect, noise-free simulation. This suggested that the challenge was not the hardware's current limitations alone, but rather the method used to encode the medical decision into the quantum system. The study concluded that for this type of task, the quantum approach was not yet ready to offer any advantage over classical methods.

Despite the lack of a speed advantage, the experiment was a significant step forward for the field. It was the first time an orthopedic parameter-selection problem had been run on a real quantum computer, moving the conversation from theoretical speculation to actual hardware testing. The researchers demonstrated that while quantum computers can handle these medical calculations, they currently face hurdles in stability and efficiency that prevent them from being useful for patient-specific planning. The study highlighted that for quantum computing to become a true tool for surgeons, future work needs to focus on finding better ways to translate complex anatomical problems into quantum language, rather than simply trying to make the current machines bigger or faster. Until those hurdles are cleared, the most reliable way to plan a hip screw remains the standard computer, which continues to provide exact answers in the blink of an eye.

Technical Summary: Quantum Approximate Optimization of Population-Level Acetabular Screw Parameters

Problem Definition
The study addresses the selection of optimal parameters for percutaneous retrograde intramedullary screw fixation in acetabular fractures. While clinical feasibility depends on individual osseous corridor dimensions, the author formulated a simplified, population-level decision problem rather than a patient-specific planning system. The objective was to determine if a combinatorial optimization task involving screw entry point, trajectory angles, length, and diameter could be encoded as a Quadratic Unconstrained Binary Optimization (QUBO) problem, executed on current gate-based quantum hardware, and compared against classical ground truth. The specific instance focused on a Turkish male population subgroup, selecting from 162 possible configurations based on published CT morphometry.

Methodology
The research employed the Quantum Approximate Optimization Algorithm (QAOA) on IBM Heron r2 processors (ibm_fez and ibm_marrakesh). The methodology involved two distinct encoding strategies:

Reduced 5-Qubit Benchmark: The five lowest-cost configurations (based on a cost function minimizing deviation from population means and maximizing screw size/length within safety constraints) were encoded using a "one-hot" representation (one qubit per candidate). A cardinality constraint (exactly one candidate selected) was enforced via a penalty term ( $A=2.0$ ) in the QUBO Hamiltonian. This instance was run at depths $p=1$ to $4$ with 1,000 shots per run.
Complete 14-Qubit Encoding: To avoid classical pre-selection, the full discretized instance was encoded using variable-wise one-hot groups (3 qubits for entry point, 3 for craniocaudal angle, 3 for mediolateral angle, 3 for length, and 2 for diameter). This 14-qubit QUBO was assessed in noiseless simulation at $p=3$ .

The study utilized classical baselines (exhaustive enumeration, tabu-style steepest descent, and simulated annealing) to establish ground truth and performance benchmarks. Variational parameters were optimized on a noiseless statevector simulator using COBYLA before execution on hardware. Measurement error mitigation and internal controls (e.g., bit-order checks) were employed to assess noise and stability.

Key Results

Hardware Performance (5-Qubit): On the reduced 5-qubit instance, the best hardware run (on ibm_fez at $p=2$ ) sampled the model optimum with a probability of $0.409 \pm 0.008$ . This is approximately 13 times higher than the $1/32$ ($0.031 $) unconditional random baseline, though it remained below 50% success. Performance was non-monotonic with circuit depth; on `ibm_fez`, success probability decreased as depth increased from$ p=1$ to $p=4$ , while ibm_marrakesh showed different trends, indicating device- and time-dependent variability.
Complete Encoding (14-Qubit): In noiseless simulation, the 14-qubit model sampled the optimum with a probability of $0.019$ at $p=3$ . While this is roughly 300 times the probability of uniform sampling over all $2^{14}$ bitstrings, it is only about three times the baseline of uniform sampling over the 162 admissible configurations. The simulation showed marked seed dependence (probabilities ranging from 0.005 to 0.027), suggesting the one-hot penalty structure creates a difficult variational landscape even without hardware noise.
Classical Comparison: Classical methods solved the same instance exactly in milliseconds (e.g., exhaustive enumeration in 0.146 ms). No quantum advantage in terms of speed or solution quality was observed.
Population Profiles: Across eight population-sex profiles, hardware success probabilities ranged from 0.223 to 0.334. The model successfully reproduced population-specific recommendations (e.g., selecting 4.5 mm screws for profiles with narrow corridors where 6.5 mm screws violated safety margins), though this was a direct consequence of the imposed constraints rather than a novel clinical finding.
Stability and Reproducibility: The study highlighted significant session dependence. An earlier experimental session produced lower success probabilities and anomalous results that were not replicated in a later controlled run, underscoring the sensitivity of NISQ experiments to temporal device variations.

Significance and Claims
The paper positions itself as a proof-of-concept and a transparent benchmark rather than a demonstration of clinical utility or quantum advantage. Its primary contributions are:

First Hardware Execution: To the author's knowledge, this is the first reported execution of an orthopaedic parameter-selection QUBO on gate-based quantum hardware.
Representation-Induced Difficulty: The study identifies that the difficulty in optimization arises not from the clinical objective (which is separable and classically simple) but from the "one-hot" cardinality constraints. These constraints create a challenging variational landscape, particularly when penalty coefficients must exceed the range of normalized candidate costs.
Methodological Rigor: The work emphasizes the necessity of repeated circuits, session controls, and comparison with noiseless ground truth for clinically motivated NISQ studies. It demonstrates that plausible single-session patterns (such as depth trends) can be misleading without replication.
Limitations: The author explicitly states that the model does not establish patient-specific planning or clinical safety, as it treats anatomically coupled variables (entry point, trajectory, length) as separable. The discretization was coarse, and hard exclusions reflected a single surgeon's judgment.

In conclusion, the paper asserts that while population-level orthopaedic parameter selection can be formulated as a QUBO and executed on current hardware, the current limitations of the formulation (specifically one-hot encodings) and hardware noise prevent any demonstration of quantum advantage. Future work should prioritize patient-specific 3D coupling and more efficient, feasibility-preserving encodings.

Technical Summary: Quantum Approximate Optimization of Population-Level Acetabular Screw Parameters

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