Quantum machine learning, often branded “quantum AI”, sits at the overlap of quantum computing and classical machine learning.
Its central proposition is simple: use quantum processors to represent data distributions in ways that are hard for classical computers to do. In short, the use of quantum computing to take the place of at least some of the traditional computing resources used in running AI systems.
This, say its proponents, will improve key machine learning processes such as classification, optimisation or generative modelling. Those of a more cynical disposition may roll their eyes heavenwards at the conjoined buzzword, Quantum AI: just more hype to sustain corporate deep-tech valuations.
While it’s undeniable that breathless journalism does abound around quantum computing and AI, it’s also true that quantum computer processors are uncannily matched to the needs of machine learning. To see why this is, we need to take a deeper dive into the maths of both.
Feature Space meets Hilbert Space
Machine learning algorithms need to manipulate huge arrays of data as quickly as possible, and this means doing “matrix algebra”: manipulating these huge arrays of data. This job must be done as quickly as possible and, conventionally, the necessary matrix operations are outsourced to a specialised classical computer processor such as a graphics processing unit (GPU). However, quantum computers are particularly good at this job. In fact, quantum mechanics itself is, by happy coincidence, uniquely geared to handle this.
In machine learning, the input data points being processed by the algorithm live in an abstract world known “feature space”. This is the mathematical, multidimensional space. Each dimension corresponds to a specific attribute, or statistical feature, that describes your data. Raw data (like text or images) must be transformed into numbers before a computer can process it. A collection of these numbers for a single object is called a “feature vector”, and properties of this vector, such as where it “points” to, are used to classify objects in machine learning.
A helpful analogy might be with “RGB colour space”, an abstract 3-dimensional space in which each dimensions represents a respective one of red, green, and blue light. Any specific mixture (r, g, b) of these three primary colours produces a unique colour which we can visualise as an abstract vector: it points “r” amount in the red “direction” of colour space, “g” amount in the green direction and “b” amount in the blue. It ends on a point in colour space we’d classify as a particular hue, say, “purple”.
The same broad concept applies to “feature space” when we think in terms of abstract statistical “features” of data in place of the primary colours in colour space. A “feature vector” for machine learning is the vector that represents an object or data point in “feature space” and acts as a "numerical fingerprint" in that space where the data becomes easier to classify.
Quantum mechanics, which underpins quantum computing, shares this broad concept too. In analogy to “colour space”, we have “Hilbert space”. This is the abstract world where quantum states live, and it too represents quantum states as vectors within that space. The mathematical language of “feature space” and “Hilbert space”, known and linear algebra, is common to both.
Natural language
By speaking the same mathematical language, machine learning and quantum mechanics are well matched to work together. Using quantum states to represent feature vectors in machine learning accesses the special properties of quantum mechanics to make this match especially lucrative.
One such property is that quantum states are typically represented using complex numbers: two-dimensional numbers having a “real” component and an “imaginary” component. An immediate consequence of this is to vastly expand the dimensions of Hibert space thereby allowing a much richer palette with which to represent feature vectors.
Quantum properties such as superposition and entanglement of quantum states lead to a natural form of parallel processing, often referred to a “quantum parallelism”. This is a property of nature, at the quantum level, and it immediately makes the processing of the enormous data matrices typical of machine learning especially efficient. I this sense, quantum machine learning works with nature.
These factors have fuelled the ongoing interest in quantum machine learning and in 2026, the field is no longer purely speculative. Although it is fair to say this is not yet a mature commercial technology, it has certainly moved from being “interesting on paper” to prototypes showing early evidence of practical value.
The current state of the field
Most near-term quantum machine learning implementations are hybrid. Classical computers still perform data preparation, optimisation, model selection and much of the workflow, while a quantum processor is used for a specialised subroutine: estimating a quantum kernel, generating a feature map, sampling from a complex distribution, solving a high-dimensional optimisation problem, or evaluating a parameterised quantum circuit.
For commercial users, what matters is whether quantum machine learning improves a business or scientific workflow, even if only incrementally. This is why the most credible quantum machine learning use cases today are not general-purpose AI workloads, such as training large language models from scratch, but narrower tasks where efficient computation on feature spaces matters most.
Currently, specific implementations of quantum machine learning include variational quantum circuits, quantum neural networks, quantum support vector machines, quantum kernel methods and quantum generative models. These are attractive because they can run, at least in principle, on today’s noisy intermediate-scale quantum devices.
Example 1: quantum kernels and scientific classification
A leading example is quantum kernel machine learning, especially in scientific classification problems. Quantum kernel methods encode classical data into quantum states and estimate similarities between data points by measuring overlaps or related quantities on a quantum device. The appeal is that the quantum feature space can be extremely large, and in some constructed cases hard to reproduce classically. Recent work has extended this idea beyond simple binary classification, including multiclass classification studies reporting that quantum algorithms can outperform classical counterparts across several real-world datasets in simulation.1,2
Experimental progress has also been made on photonic quantum processors. A 2025 Nature Photonics paper reported experimental quantum-enhanced kernel-based machine learning on a photonic integrated processor, using two-boson Fock-state evolution to estimate a quantum kernel and reporting enhanced accuracy relative to comparison approaches. This matters because photonic processors are natural platforms for high-dimensional linear-optical transformations, which can be useful in kernel estimation, sampling and pattern recognition.3,4
Similar ideas are being explored in high-energy physics, neuroscience and biomedical data analysis. CERN’s Quantum Technology Initiative has explicitly identified quantum computing and quantum machine learning as possible tools for future high-energy physics workflows, including pattern recognition, simulation and anomaly detection in very large detector datasets. A 2025 Nature Scientific Reports study applied quantum machine learning models to predictive analysis of CERN-related data, reflecting the wider push to test whether quantum models can improve regression and classification tasks in scientific environments. 5,6
These examples show credible routes toward quantum advantage in real applications, particularly where the data or model structure aligns naturally with quantum feature spaces. They do not yet establish that quantum machine learning will beat classical AI across ordinary enterprise datasets. The best current evidence is domain-specific: quantum machine learning looks most promising where classical feature engineering is expensive, where the relevant correlations are high-dimensional, or where the underlying system is itself quantum mechanical.
Example 2: quantum-enhanced algorithmic bond trading
One of the strongest recent examples comes from HSBC and IBM. In September 2025, HSBC announced a trial using IBM quantum hardware for algorithmic bond trading, specifically predicting the probability that a customer inquiry in the European corporate bond market would be filled at a quoted price. The work used a hybrid quantum-classical approach on real, production-scale trading data and reported up to a 34% improvement over common classical techniques for predicting trade-fill probability.7,8
This is significant because finance is one of the clearest commercial targets for quantum machine learning: market data are high-dimensional, noisy, non-stationary and rich in correlations. A quantum feature map may, in favourable circumstances, expose structure that is difficult for conventional models to capture.
The lesson is that early quantum machine learning advantage may arrive as a “workflow advantage” rather than a headline “exponential speed-up”. A bank does not need a quantum computer to replace all classical trading infrastructure. It needs a quantum processor that improves prediction, ranking or risk estimate enough to justify integration.
Where commercial quantum machine learning is heading
The quantum computing sector hopes quantum machine learning will provide one of the first commercially valuable uses of near-term quantum hardware. Quantum machine learning is appealing because hybrid quantum-classical computing can tolerate some imperfection and can be embedded in existing AI workflows.
Cloud quantum providers, banks, pharmaceutical companies, materials companies and research labs are therefore looking for “quantum utility” cases: not necessarily universal “quantum advantage”, but measurable improvement in prediction, optimisation or simulation for a valuable problem.
Quantum machine learning’s commercial future will likely be incremental before it is revolutionary. The near-term uses are likely to be highly specific applications in finance, chemistry, materials and scientific data analysis where a quantum subroutine can be validated against a business or scientific metric.
For now, quantum machine learning is perhaps best described as a serious emerging engineering discipline, overhyped in some marketing, but increasingly credible where the problem, data and quantum hardware are well matched.
[3] https://www.nature.com/articles/s41566-025-01682-5
[4] https://www.nature.com/collections/iheeaggidj
[5] https://physicsworld.com/a/cern-qti-harnessing-big-science-to-accelerate-quantum-innovation/
[6] https://www.nature.com/articles/s41598-025-30305-w
[8] https://www.ibm.com/quantum/blog/hsbc-algorithmic-bond-trading
Andrew is a Senior Associate and Patent Attorney at Mewburn Ellis. He works primarily in the fields of telecoms, electronics and engineering, and specialises in quantum technologies, photonics and ion optics. Andrew has extensive experience of drafting and prosecution, global portfolio management and invention capture to secure a commercially valuable IP portfolio. He also conducts freedom to operate analyses and performs due diligence.
Email: andrew.fearnside@mewburn.com
