World news – Solving « barren plateaus » is the key to quantum machine learning

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March 19, 2021

from Los Alamos National Laboratory

Many algorithms for machine learning on quantum computers suffer from the dreaded « barren plateau » of unsolvability, where they run into dead ends when it comes to optimization problems. So far, this challenge has been researched relatively little. Rigorous theoretical work has created theorems that guarantee that a given machine learning algorithm will work when it scales on larger computers.

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« The work solves a key usability problem for quantum machine learning. We have rigorously proven the conditions under which certain architectures of variational quantum algorithms may or may not have barren plateaus when magnified, » said Marco Cerezo, lead author of the paper Published today in Nature Communications by a Los Alamos National Laboratory team. Cerezo is a post-doc researching quantum information theory in Los Alamos. « With our theorems, you can guarantee that the architecture is scalable to quantum computers with large numbers of qubits. »

« The usual approach has been to optimize and see if it works, which led to fatigue Researchers in the field, « said Patrick Coles, co-author of the study. Setting up mathematical theorems and deriving initial principles takes the guesswork out of developing algorithms.

The Los Alamos team used the common hybrid approach for quantum variation algorithms, trained and optimized the parameters on a classic computer and evaluated the cost function of the algorithm or the measure of the algorithm’s success on a quantum computer.

Machine learning algorithms translate an optimization task – such as finding the shortest route for a traveling salesperson through multiple cities – into a cost function, said co-author Lukasz Cincio. This is a mathematical description of a function that is being minimized. The function only reaches its minimum value if you solve the problem.

Most quantum variation algorithms initiate their search randomly and evaluate the cost function globally over each qubit, which often leads to a barren plateau.

« We were able to prove that by choosing a cost function that considers each individual qubit locally, we guarantee that the scaling does not lead to an incredibly steep time curve in relation to the system size and can therefore be trained.  » Said Coles.

A quantum variation algorithm creates a problem-solving landscape in which the peaks represent the high energy points of the system or problem and the valleys are the low energy values. The answer lies in the deepest valley. This is the basic state, represented by the function of minimized costs. To find the solution, the algorithm trains itself in the landscape and thus navigates to the bottom.

« People have proposed quantum neural networks and evaluated them through small simulations of 10s (or less) few qubits, » said Cerezo. « The problem is that you won’t see the barren plateau with a small number of qubits, but if you try to scale to more qubits it will appear. Then the algorithm needs to be reworked for a larger quantum computer. »

A barren plateau is a training problem that occurs in machine learning optimization algorithms when the problem-solving space becomes flat when the algorithm is executed. In this situation the algorithm cannot find the downward slope in a seemingly strange landscape and there is no clear path to the energy minimum. Without landscape features, machine learning cannot train itself to find the solution.

« When you have a barren plateau, all hope of quantum acceleration or quantum advantage is lost, » said Cerezo.

The breakthrough of the lot Alamos teams take an important step towards quantum advantage when a quantum computer performs a task that would take an infinite amount of time on a classic computer. Achieving a quantum advantage depends in the short term on the scaling of variation quantum algorithms. These algorithms have the potential to solve practical problems when quantum computers with 100 qubits or more become available – hopefully soon. Quantum computers currently have a maximum of 65 qubits. A qubit is the basic unit of information in a quantum computer, like bits in a classic digital computer. « The hottest topic in noisy medium-scale quantum computers is variation quantum algorithms, or quantum machine learning and quantum neural networks, » said Coles. « They have been proposed for applications ranging from solving the structure of a molecule in chemistry to simulating the dynamics of atoms and molecules and factoring numbers. »

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