Hybrid algorithms make 'noisy' quantum computers viable

Rather than waiting for fully mature quantum computers to emerge, researchers from Los Alamos National Laboratory and other institutions have developed hybrid classical–quantum algorithms to extract the most performance — and potentially quantum advantage — from today’s noisy, error-prone hardware.

As explained in the journal Nature Reviews Physics, the so-called variational quantum algorithms use the quantum boxes to manipulate quantum systems while shifting much of the workload to classical computers to let them do what they currently do best: solve optimisation problems.

“Quantum computers have the promise to outperform classical computers for certain tasks, but on currently available quantum hardware they can’t run long algorithms. They have too much noise as they interact with environment, which corrupts the information being processed,” said Los Alamos physicist Marco Cerezo, a lead author on the paper.

“With variational quantum algorithms, we get the best of both worlds. We can harness the power of quantum computers for tasks that classical computers can’t do easily, then use classical computers to complement the computational power of quantum devices.”

Current noisy, intermediate-scale quantum computers have between 50 and 100 qubits, lose their ‘quantumness’ quickly and lack error correction, which requires more qubits. Since the late 1990s, however, theoreticians have been developing algorithms designed to run on an idealised large, error-correcting, fault-tolerant quantum computer.

“We can’t implement these algorithms yet, because they give nonsense results or they require too many qubits,” said Patrick Coles, a theoretical physicist at Los Alamos and senior lead author on the paper. “So people realised we needed an approach that adapts to the constraints of the hardware we have — an optimisation problem.

“We found we could turn all the problems of interest into optimisation problems, potentially with quantum advantage, meaning the quantum computer beats a classical computer at the task,” Coles said. Those problems include simulations for material science and quantum chemistry, factoring numbers, big-data analysis and virtually every application that has been proposed for quantum computers.

The algorithms are called variational because the optimisation process varies the algorithm on the fly, as a kind of machine learning. It changes parameters and logic gates to minimise a cost function, which is a mathematical expression that measures how well the algorithm has performed the task. The problem is solved when the cost function reaches its lowest possible value.

In an iterative function in the variational quantum algorithm, the quantum computer estimates the cost function, then passes that result back to the classical computer. The classical computer then adjusts the input parameters and sends them to the quantum computer, which runs the optimisation again.

The review article is meant to be a comprehensive introduction and pedagogical reference for researches starting on this nascent field. In it, the authors discuss all the applications for algorithms and how they work, as well as covering challenges and pitfalls and how to address them. Finally, it looks into the future, considering the best opportunities for achieving quantum advantage on the computers that will be available in the next couple of years.

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