Post-processing method ‘SEMO’ corrects qubit errors in quantum annealers, dramatically accelerating the optimization of solutions to complex, real-world problems.

Optimization problems are everywhere. Whether scheduling deliveries, managing financial portfolios, or analyzing medical images, countless industries rely on the ability to find the best possible solution from an astronomically large number of options. Quantum annealers—a commercially available type of quantum computer made by D-Wave Systems—are purpose-built to tackle exactly these kinds of challenges. But a stubborn obstacle has stood in the way of their broad adoption: qubit errors.

When a quantum annealer runs a computation, a small fraction of its quantum bits, or qubits, can collapse into incorrect states. This might sound like a minor inconvenience, but the consequences compound rapidly. The probability of obtaining a correct answer decreases exponentially with the number of qubit errors, meaning that, as problems grow in size, the time required to reach the true optimal solution balloons just as quickly. For large, real-world problems, this makes unassisted quantum annealing—where the machine runs without any error correction or post-processing—impractical.

Researchers at CSIRO (Australia’s national science agency) have now developed a technique that cuts through this bottleneck. Their method, called SEMO (spin-error mitigation for optimization), is a post-processing algorithm that identifies and corrects the erroneous spin states left behind after quantum annealing. The work, published in Advanced Physics Research, demonstrates a million-fold improvement in the time required to reach the globally optimal solution for a combinatorial optimization problem.

Catching errors after the fact

Unlike quantum error correction (QEC), which attempts to protect qubits during computation by encoding each logical qubit across many physical qubits, SEMO operates after the quantum computation is complete. This distinction matters enormously in practice: QEC dramatically reduces the effective number of usable qubits in a system—a significant drawback when quantum hardware already has a limited qubit count. SEMO avoids this penalty entirely by working on the classical post-processing side.

The core insight behind SEMO is that qubit errors tend to be sparse. Only a small fraction of spins end up in the wrong state, and those erroneous spins form isolated clusters rather than being scattered uniformly. SEMO exploits this structure by systematically testing whether flipping individual spins or small groups of coupled spins would reduce the objective function (the mathematical quantity the annealer is trying to minimize). Where a reduction is found, SEMO makes the flip.

The algorithm proceeds iteratively: selecting a reference spin at random, generating nearby spin clusters, evaluating the effect of flipping them, and updating the solution when an improvement is found. This continues until each spin has been examined twice. The computational overhead is modest, running on a classical computer in milliseconds — far less than the time saved on the quantum side.

Million-fold improvement

To demonstrate SEMO’s effectiveness, the team applied it to a correlated 3D image segmentation problem drawn from materials science. Segmenting X-ray computed tomography (CT) images of material microstructures—distinguishing, say, a low-density phase from a high-density one across thousands of voxels—is a natural fit for quantum annealing because it can be formulated as a quadratic unconstrained binary optimization (QUBO) problem: the native language of quantum annealers.

Reproduced with permission from 10.1002/apxr.202500216. Average quantum annealing computing time per global optimal solution versus problem size, for different correction methods. Without error mitigation (black), compute time grows exponentially — over a million-fold from 1 to 512 spin variables. With SEMO applied (green), the curve is nearly flat, remaining around 0.1 ms regardless of problem size.

The practical value of getting this segmentation right is significant: SEMO-corrected quantum annealing transforms a noisy grey-scale sub-volume into a clean binary map of the material’s internal structure, faithfully separating its two compositional phases. Because the method accounts for correlations between neighboring voxels, the resulting segmentation is a more accurate 3D representation of the material distribution than classical gradient-descent methods, which can get stuck in suboptimal solutions. That accuracy matters — a reliable material map forms the essential foundation for subsequent modeling of how a material will behave under real-world conditions.

Without any error mitigation, the D-Wave Advantage quantum annealer required exponentially more computation time as problem size increased. Scaling from a 1-spin variable (equivalent to a single image voxel in this case study) to 512 spin variables pushed the average time per correct solution from 0.1 milliseconds to over 100 seconds — a million-fold slowdown. With SEMO applied, that curve flattened almost entirely: the time per optimal solution remained roughly constant, hovering around 0.1 milliseconds regardless of problem size.

Reproduced with permission from 10.1002/apxr.202500216. Average number of global optimum solutions per second for different correction methods. Quantum annealing paired with SEMO (dark green) produces roughly 1,000 optimal solutions per second—at least ten times more efficient than any competing approach. SEMO also significantly improves classical simulated annealing (blue), where methods like the Greedy Solver produced no measurable gain.

Comparisons with existing error mitigation methods—including D-Wave’s own Greedy Solver and the Single-Qubit Correction technique—showed that SEMO achieved success rates of up to 82–100% in finding the global optimum, far exceeding competing approaches, which topped out at a few percent.

Beyond image segmentation

Because SEMO operates at the level of the Ising spin-glass and QUBO formulations (mathematical frameworks that underpin a wide variety of combinatorial optimization problems), its applicability extends well beyond 3D imaging. Problems in logistics, finance, cryptography, and materials design can all be cast in QUBO form, making SEMO a broadly relevant tool.

Crucially, SEMO is not a quantum method. It runs entirely on classical hardware, meaning it can be used to refine results from simulated annealing and other classical optimization solvers as well as quantum ones. The researchers demonstrated that SEMO also significantly improved simulated annealing results, where comparable methods like the Greedy Solver and Single-Qubit Correction produced no measurable improvement at all.

“The quantitative demonstrations showcased the potential of error-mitigated quantum annealing in solving complex combinatorial optimization problems,” says YS Yang, first author of the study. “The method will be particularly impactful in time-critical applications such as real-time optimization in industry and defence scenarios.”

Scaling up: the case for more qubits

The main constraint on SEMO’s current impact is the hardware it relies on. Today’s quantum annealers cap out at around 5000 physical qubits, limiting the size of problems that can be embedded directly. The researchers note that D-Wave’s forthcoming Advantage III system, slated to feature 100,000 qubits, would substantially expand the range of problems amenable to this approach.

For now, SEMO represents a meaningful step toward making quantum annealing practically useful for complex real-world optimization, not by overhauling the hardware, but by being smarter about what happens after the quantum computation ends. Sometimes, the most powerful improvements come not from inside the quantum processor, but from the classical layer wrapped around it.

Reference: Yang et al., Toward Solution-Time Advantage with Error-Mitigated Quantum Annealing for Combinatorial Optimization. Advanced Physics Research (2026). DOI: 10.1002/apxr.202500216

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