Quantum advantage in learning from experiments

Short answer: A 2022 Science paper proves that for certain learning tasks, a quantum machine that processes quantum data can learn from exponentially fewer experiments than a conventional setup that measures one quantum state at a time. The authors back this with proof-of-principle experiments on up to 40 superconducting qubits. The advantage is about the number of experiments for specific tasks on quantum systems, not a general speedup for machine learning.

The setting

The paper, "Quantum advantage in learning from experiments", compares two ways to learn about a physical system. In a conventional experiment, the system is measured and the outcomes are processed on a classical computer. In the quantum alternative, an experimental setup transduces data from the physical system into a stable quantum memory and processes it with a quantum computer. The authors say the second approach could have significant advantages.

What they prove

The arXiv abstract says the authors prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than conventional experiments require. The exponential advantage holds for predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. The text says earlier mathematical analyses by some of the authors showed properties of an n-qubit system that a quantum machine can learn efficiently, while the number of conventional experiments needed is exponential in n. It contrasts this with the quadratic advantage achieved in many earlier proposals for improving sensing with quantum technology.

The paper also says the quantum processing needed can be modest in some tasks. For example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system at a time.

The experiments

The authors report experiments with up to 40 superconducting qubits and 1,300 quantum gates on a Google Sycamore processor. The Science summary says that in these proof-of-principle experiments the authors achieved almost four orders of magnitude of reduction in the required number of experiments compared with the best-known classical lower bounds. The authors conclude that a substantial quantum advantage can be realized with today's relatively noisy quantum processors, even when the quantum memory and processor are both noisy. These are the authors' claims, from a single research group and platform.

What kind of advantage this is

The advantage is in sample complexity: how many experiments are needed. The quantum machine in the proof is assumed to have access to a stable quantum memory that receives the data from the physical system. That is a different setting from machine learning on classical datasets, which this paper does not address.

What this does not tell you

The abstracts do not say that quantum computers speed up machine learning on classical data, such as images or text. They do not describe a deployed use, and the experiments are proof-of-principle demonstrations of specific tasks. Whether classical methods could close the gap for other settings is outside what these summaries say.

FAQ

What did the paper prove?

That for certain tasks, quantum machines can learn from exponentially fewer experiments than conventional experiments require.

Which tasks?

Predicting properties of physical systems, quantum principal component analysis on noisy states, and learning approximate models of physical dynamics.

Was it demonstrated on hardware?

The authors report experiments with up to 40 superconducting qubits and 1,300 gates on a Google Sycamore processor.

Does this speed up machine learning in general?

No. The advantage concerns learning about quantum systems from experiments, not learning from classical datasets.

Does it need error correction?

The authors say the advantage can be realized with today's relatively noisy processors, in their experiments.