Quantum Machine Learning and Optimisation: What Is Real and Why Everyone Is Racing

In short

A quantum computer works with an enormous space of possibilities at once, which sounds ideal for learning from data and for searching for the best option among billions.
The catch is getting data in and answers out. Reading a quantum computer gives only a few bits per run, so most of the theoretical power never reaches the user.
The clearest gains are for quantum data, such as molecules, materials and quantum sensors, and for a few problems with special structure. For everyday business data, classical methods still win today.
Governments and investors are racing because the same machines will also break today's encryption and reshape chemistry and materials science. Nobody wants to be the one who arrived late.

Why the interest

Two kinds of computing work dominate modern data centres. One is machine learning: training models on data so they can classify, predict or generate. The other is optimisation: finding the best route, schedule, portfolio or design from a very large number of options. Both are expensive, both keep growing, and both are limited by how fast computers can do linear algebra and search.

A quantum computer looks well suited to both on paper. A register of qubits describes its state with a list of numbers that doubles in length with every qubit added. Fifty qubits carry more than a million billion of them. Quantum gates act on that whole list at once, and the device can sample from probability distributions that classical computers struggle to reproduce. Machine learning is about vectors, matrices and distributions, so the overlap invites attention.

That is the promise. The rest of this post is about the fine print, which matters as much as the promise.

What quantum machine learning is

“Quantum machine learning” covers several different ideas. A useful way to sort them is by asking two questions: is the data classical or quantum, and is the computer doing the learning classical or quantum?

Classical data · classical computerOrdinary machine learning, plus quantum-inspired algorithms borrowed from quantum ideas

Classical data · quantum computerWhat most people mean by QML: images, text or prices fed into a quantum circuit

Quantum data · classical computerNeural networks that model molecules, control qubits or decode errors

Quantum data · quantum computerLearning directly from quantum states. The strongest proven advantages live here

The label “quantum machine learning” is used for all four. Most of the headlines are about the top right; most of the proven results are in the bottom right.

Within the quantum column, four approaches come up again and again:

Variational circuits. A parameterised quantum circuit plays the role of a neural network. A classical computer adjusts its settings in a loop until the output fits the data. This is the most common approach on today's noisy hardware.
Quantum kernels. The circuit maps each data point into the huge quantum state space, and the computer measures how similar two points look there. A classical support vector machine then does the learning. Havlíček and colleagues, and separately Schuld and Killoran, proposed this in 2019.
Quantum linear algebra. Algorithms such as HHL, from Harrow, Hassidim and Lloyd in 2009, solve certain systems of linear equations exponentially faster than classical methods, under strict conditions. Many early QML proposals were built on them.
Quantum generative models. A circuit's measurement results are themselves random samples, so the circuit can be trained to generate data that follows a target distribution. These are sometimes called Born machines.

What quantum optimisation is

Many hard optimisation problems, from vehicle routing to portfolio selection, can be rewritten as finding the lowest-energy arrangement of a set of interacting spins. This form is called an Ising problem, or QUBO. Quantum hardware is made of spins, so the match is natural. There are four main families of method:

Quantum annealing. Start with a simple problem whose answer is known, then slowly change it into the hard one, letting the system stay near its lowest energy. Kadowaki and Nishimori described it in 1998. Commercial annealers with thousands of qubits exist today.
QAOA. The quantum approximate optimisation algorithm, from Farhi, Goldstone and Gutmann in 2014, runs a short alternating circuit on a gate-based computer and tunes it classically. It is the gate-model cousin of annealing.
Search speedups. Grover's algorithm and its relatives find a marked item, or a minimum, in about the square root of the classical number of steps. The same idea speeds up Monte Carlo estimation, which is why finance has paid close attention.
New structured algorithms. Decoded quantum interferometry, from Jordan and colleagues and published in Nature in 2025, turns some optimisation problems into decoding problems and gives a large speedup for one class of polynomial-fitting problems.

How they differ from the classical versions

The difference is not just speed. Quantum computers handle information under rules that change how learning and search have to be designed.

	Classical ML and optimisation	Quantum ML and optimisation
Working space	Numbers held in memory, as many as you can afford	Amplitudes of a quantum state, 2ⁿ of them for n qubits
Getting data in	Load it from disk	Encode it into a circuit, which can cost as much as the computation it was meant to speed up
Getting answers out	Read any value directly	Each run returns n bits; estimating a number needs many repeated runs
Copying	Free and unlimited	Impossible for unknown quantum states, so every copy must be prepared again
Training	Backpropagation computes all gradients in one pass	Each gradient needs its own set of circuit runs
Noise	Hardware is effectively error-free	Errors build up with every gate until error correction matures
Typical speedup	Better hardware and better algorithms, steadily	Exponential for a few structured problems, quadratic for search, none known for many
Maturity	Runs the world's products	Research, pilots and small demonstrations

Most of the gap between the promise and the results comes from the second, third and fifth rows.

The read-out limit is the one people miss most often. A 50-qubit state holds about a million billion amplitudes, but measuring it gives you 50 bits and destroys the state. Training a variational circuit means estimating many expectation values, each from thousands of shots, and computing gradients with methods such as the parameter-shift rule that need extra runs for every parameter. A classical network with a billion parameters gets all its gradients from one backward pass. A quantum model with a thousand parameters needs thousands of separate estimates.

What the last decade taught

The field has been through a useful correction. Several early claims did not hold up, and the reasons explain where quantum advantage can and cannot come from.

1998 Kadowaki and Nishimori propose quantum annealing.
2009 The HHL algorithm promises exponential speedups for linear systems, under strict conditions.
2014 QAOA is introduced for gate-based optimisation.
2015 Aaronson's “Read the fine print” sets out the conditions HHL-style speedups depend on.
2018 McClean and colleagues identify barren plateaus in variational training.
2019 Tang gives a classical algorithm matching a celebrated quantum recommendation algorithm. Quantum kernels are proposed.
2021 Liu, Arunachalam and Temme prove a quantum speedup for a learning task built on discrete logarithms.
2022 Huang and colleagues show an exponential advantage in learning from quantum experiments, on real hardware.
2024 Simulations of QAOA show better scaling than leading exact solvers on one hard problem class.
2025 Error correction runs below threshold on superconducting hardware; decoded quantum interferometry appears in Nature; a scaling advantage is reported for approximate optimisation with annealing.

Four lessons stand out.

Many speedups disappear when classical algorithms are given the same help

Quantum linear-algebra algorithms usually assume the data is already loaded into a quantum state through QRAM. In 2019 Ewin Tang showed that if a classical computer gets a comparable way to sample from the data, the quantum recommendation algorithm loses its exponential edge. The work started a line of dequantisation results that removed several claimed advantages.

Training can get stuck on flat ground

McClean and colleagues showed in 2018 that randomly initialised variational circuits suffer from barren plateaus. As circuits grow, the gradient becomes exponentially small, and no realistic number of shots can find a direction to move in. Fixes exist, but a 2025 perspective by Cerezo and colleagues argued that many of the models that avoid barren plateaus do so by working in a small space that a classical computer can also simulate. Trainable and quantum-hard may be difficult to get at the same time.

Quadratic speedups are not enough on early hardware

Grover-style speedups are real, but error-corrected quantum operations are slow and expensive compared with classical ones. Babbush and colleagues estimated in 2021 that, with current error-correction overheads, a quantum computer would need very long runs before a quadratic speedup overtook a classical machine, so the gain is unlikely to pay off on early fault-tolerant computers. Larger speedups are needed. A study of quantum derivative pricing the same year put the threshold for advantage at about 7,500 error-corrected qubits running at clock rates well beyond today's.

Benchmarks need strong classical baselines

Bowles, Ahmed and Schuld tested popular quantum models against simple classical ones in 2024 and found that the classical models generally did as well or better on the small datasets typically used. Removing the entanglement from some quantum models did not hurt them either. Small, carefully chosen examples can make almost anything look promising.

Where they can help

The correction did not end the field. It made the claims more precise. These are the places where the case is strongest, from the most solid to the most speculative.

Learning from quantum systems. When the data is itself quantum, from a molecule, a material or a quantum sensor, a quantum computer can work with it directly instead of measuring it first. Huang and colleagues proved, and showed on hardware in 2022, that some properties can be learned with exponentially fewer experiments this way. This is the clearest form of quantum advantage in learning.
Problems with hidden structure. Some learning and optimisation problems have algebraic structure that quantum algorithms exploit, as in the 2021 discrete-logarithm result and the polynomial-fitting problems in decoded quantum interferometry. The open question is how many real problems have that structure.
Hard optimisation where good is good enough. Many business problems need a very good answer, not a perfect one. The 2024 QAOA study on the LABS problem and the 2025 annealing study by Munoz-Bauza and Lidar both report better scaling than strong classical solvers on approximate solutions. Neither yet solves a commercial problem faster than a classical machine.
Sampling and simulation inside larger pipelines. A quantum computer may produce samples, energies or training data that a classical model then uses. For chemistry and materials, the quantum part is usually simulation rather than learning, with classical machine learning around it.
Ideas that run on classical hardware. Tensor networks and quantum-inspired sampling methods grew out of this research and already run on GPUs today.

What remains open before deployment

Error-corrected qubits at scale

Most algorithms with proven speedups need logical qubits and millions of reliable operations. In results published in 2025, Google showed a surface-code memory whose errors fell as the code grew, the threshold behaviour the field had waited decades for. Getting from a handful of logical qubits to thousands, with fast logical gates, is the main engineering task of the next decade.

Loading data

Big classical datasets have to be turned into quantum states. Without fast QRAM, loading can erase the speedup, and building QRAM that is large, fast and error-tolerant is unsolved. This is the main reason the strongest results involve quantum data, which needs no loading.

Trainability without simulability

The field needs model families that can be trained without barren plateaus and that a classical computer still cannot simulate. Good initialisations, problem-inspired circuits and new cost functions are all being tried. A clear answer would decide whether variational QML has a future at scale.

Finding the right problems

Speedups are proven for problems with special structure. Matching that structure to problems a company actually has, in logistics, finance or drug design, is mostly undone. Much current work is the slow job of checking, one application at a time, whether any advantage survives end-to-end costs.

Honest benchmarks

Results need to be compared against the best classical method run on modern hardware, at problem sizes that matter, counting every cost, including data loading, repeated shots and error correction. Shared benchmark suites and standard reporting rules are only starting to appear.

Noise on today's machines

Before full error correction, results depend on error mitigation, whose cost grows quickly with circuit size. Mitigation stretches what noisy machines can do, but it cannot scale indefinitely.

Fitting into classical computing

Useful systems will be hybrid. Quantum processors will sit next to CPUs and GPUs, often in the same data centre, with tight loops between them. Scheduling, software, latency between the two, and the skills to use both are all still being built.

Verifying the answer

For optimisation a good answer can usually be checked. For learning and sampling it is harder to confirm that a quantum model did what was claimed, especially when no classical computer can reproduce it. Verification methods for quantum learning are an active research area.

The impact if it works

If error-corrected machines arrive and the right problems are matched to them, the largest gains are expected where nature itself is quantum. Better simulation of molecules and materials would help with catalysts, battery chemistry, fertiliser production and drug candidates. In finance, faster risk estimation would change how often portfolios can be re-evaluated. In logistics and energy, better approximate optimisation on very large instances could save fuel and balance power grids with more renewable supply. In science, quantum computers linked to quantum sensors could learn from experiments in ways classical computers cannot.

The economic estimates are large and should be read with care. They depend on hardware timelines that have slipped before. A safer statement is that the potential is big enough that waiting until it is certain is itself a risk.

Why the global race

If the near-term results are mixed, why is the money moving so fast? Several reasons reinforce each other.

It is one race, not several. The machines that would run QML and optimisation are the same machines that, at scale, run Shor's algorithm and break today's public-key encryption. A lead in one is a lead in all, which makes quantum computing a security question as much as a commercial one.
Governments are treating it as strategic. The OECD counted 18 of its members, plus the European Union, with national quantum strategies by November 2025, and around 250 quantum policies across about 40 countries.
Private money has arrived. McKinsey's 2026 Quantum Technology Monitor puts investment in quantum start-ups at 12.6 billion dollars in 2025, 6.3 times the 2024 figure, with almost all of it from private investors.
Talent and supply chains are scarce. There are few people who understand both quantum hardware and machine learning, and few suppliers of specialist parts such as dilution refrigerators, lasers and control electronics. Early movers hire first and lock in suppliers.
Standards and platforms are being set now. The software frameworks, programming interfaces and benchmarks chosen in the next few years will shape who builds on whom later.
Fear of arriving late. Companies remember being slow to adopt the cloud and deep learning. Small bets now are cheaper than catching up later, even if the payoff is uncertain.

The race has a downside. Money that arrives faster than results invites overstated claims, and the history above shows how often bold early claims have been revised. The healthiest projects are the ones that publish careful benchmarks against strong classical baselines.

What to do now

For most organisations, the useful work today is preparation rather than deployment. Identify which of your hardest problems are optimisation, sampling or simulation, and write them down precisely. Measure how well the best classical methods do on them, because that is the bar any quantum method must clear. Try quantum-inspired and tensor-network methods, which can pay off on current hardware. Build a small team that can read the research critically.

One item cannot wait for the hardware: encryption. Data captured today can be decrypted later by the same machines this post describes, so moving to post-quantum cryptography is the quantum preparation with a deadline.

Quantum machine learning and optimisation: what is real, what is hype, and why everyone is racing.