IBM tests Hamiltonian-based quantum machine learning on 50 qubits

A team from IBM Research, with researchers from the universities of Leiden, Oxford and Chicago, proposes a new way of doing quantum machine learning (QML): encoding the whole training set in a single parameterised Hamiltonian and using its ground state, the one with the lowest energy, as the classifier. It is described in a preprint posted on 19 October, not yet peer reviewed, and has been tested on 50 qubits of an IBM Heron processor.

For years QML has been looking for models that train well, generalise and cannot be simulated on a classical computer, all three at once. According to the preprint, shallow circuits can often be simulated, and deep ones get stuck in barren plateaus, regions where training stops making progress.

How it works

Each training example contributes one term to the Hamiltonian, built from its label and from a circuit that encodes the input. Training means adjusting the parameters of that encoding to lower the energy of the ground state; to classify a new data point, an expectation value is computed on that state. The quantum computer is only used to approximate the ground state during training: with shallow encodings, the subsequent classification can be done on a classical computer.

• Theoretical guarantees. The authors prove that, for a fixed generalisation error, the number of examples needed grows linearly with the number of qubits and parameters, and that a subset of the parameters does not suffer from barren plateaus.
• Conditional advantage. They construct a classification problem that the model solves with a quantum computer and that no efficient classical algorithm can learn if computing cube roots modulo a product of two primes is hard, an assumption related to the one that protects RSA.
• Hardware test. 50 qubits of ibm_pittsburgh, a 156-qubit Heron r2, with no error mitigation other than dynamical decoupling and measurement twirling. The processor only generates samples: the rest of the computation runs on a laptop.

What the results show

The test is a classification of images of dresses and shirts from Fashion-MNIST, reduced to between 2 and 50 variables, with 448 training examples and 240 test examples. The best classical method, a support vector machine, reaches around 94.6% accuracy. Simulated with a classical method, the model reaches about 92.4% at intermediate sizes and drops to 88.6% with 50 qubits. It outperforms the quantum kernels it is compared with, which lose accuracy as they grow: one of them falls from 79.8% to 51.5%. On the Heron, the five 50-qubit runs improve on the classical simulation of the same data by between 0.4 and 5 points, and the authors describe them as competitive with the best classical method.

What changes for decision-makers

This is a QML proposal with training and generalisation guarantees that has already been run at a non-trivial scale on real hardware. But it is not yet a reason to invest in QML on classical data: the practical result is parity, and the proven advantage once again rests on the difficulty of factoring, as in the work we covered this month. What is worth watching is whether a useful problem appears, with no cryptographic basis, on which the model beats classical methods.