# New Benchmark Solves The Toughest Quantum Problems

|**Eddie Gonzales Jr****. – MessageToEagle.com – **Predicting the behavior of interacting quantum particles is complex but crucial for real-world quantum computing. EPF (École Polytechnique Fédérale de Lausanne ) -led researchers have developed a method to compare quantum algorithms and identify the hardest problems to solve.

Quantum systems, from subatomic particles to complex molecules, are key to understanding the universe.

*Image credit: geralt – Pixabay*

However, there’s a catch: modeling these systems quickly becomes uncontrollable, like predicting the behavior of a massive crowd where everyone influences each other. Replace the people with quantum particles, and you face a “quantum many-body problem.”

Quantum many-body problems are efforts to predict the behavior of a large number of interacting quantum particles. Solving them can unlock huge advances in fields like chemistry and materials science, and even push the development of new tech like quantum computers.

But the more particles you throw into the mix, the harder it gets to model their behavior, especially when you’re looking for the ground state, or lowest energy state, of the system. This matters because the ground state tells scientists which materials will be stable and could even reveal exotic phases like superconductivity.

**For every problem, a solution: but which one?**

Scientists have used quantum Monte Carlo simulations and tensor networks to approximate solutions, each with strengths and weaknesses. However, it’s been unclear which method suits specific problems best, lacking a universal way to compare their accuracy.

A large collaboration of scientists, led by Giuseppe Carleo at EPFL has now developed a new benchmark called the “V-score” to tackle this issue. The V-score (“V” for “Variational Accuracy”) offers a consistent way to compare how well different quantum methods perform on the same problem. The V-score can be used to identify the hardest-to-solve quantum systems, where current computational methods struggle, and where future methods —such as quantum computing — might offer an advantage.

The breakthrough method is published in Science.

**How the V-score works**

The V-score is calculated using two key pieces of information: the energy of a quantum system and how much that energy fluctuates. Ideally, the lower the energy and the smaller the fluctuations, the more accurate the solution. The V-score combines these two factors into a single number, making it easier to rank different methods based on how close they come to the exact solution.

To create the V-score, the team compiled the most extensive dataset of quantum many-body problems to date. They ran simulations on a range of quantum systems, from simple chains of particles to complex, frustrated systems, which are notorious for their difficulty. The benchmark not only showed which methods worked best for specific problems, but also highlighted areas where quantum computing might make the biggest impact.

**Solving the hardest quantum problems**

Testing the V-score, scientists found that some quantum systems are easier to solve than others. One-dimensional systems, like chains of particles, are relatively easy to tackle using methods like tensor networks. However, complex high-dimensional systems, such as frustrated quantum lattices, have higher V-scores and are much harder to solve with current classical computing methods.

The researchers also found that methods relying on neural networks and quantum circuits — two promising techniques for the future — performed quite well even when compared to established techniques. What this means is that, as quantum computing technology improves, we may be able to solve some of the hardest quantum problems out there.

The V-score is a powerful tool for measuring progress in solving quantum problems as quantum computing develops. By identifying the toughest problems and classical method limitations, it can guide future research. Industries like pharmaceuticals or energy could use these insights to focus on areas where quantum computing offers a competitive edge.

**Written by Eddie Gonzales Jr. – MessageToEagle.com Staff Writer**