Demonstration of subspace-search variational quantum eigensolver using photonic orbital angular momentum qudits

To understand the material world, scientists often need to know not just how atoms sit still, but how they behave when they are excited. When a molecule absorbs energy, its electrons jump to higher levels, creating what are called excited states. These fleeting moments are responsible for the glow of a firefly, the color of a sunset, and the chemical reactions that power life. While computers have become very good at calculating the energy of atoms in their calm, resting state, figuring out the energy of these excited states has remained a stubborn problem. Classical computers struggle with the complexity of these higher energy levels, often producing unreliable results. This limitation has pushed researchers to look toward quantum computers, machines that use the strange rules of quantum physics to solve problems that are too hard for traditional supercomputers. However, the quantum computers available today are still small and prone to errors, making it difficult to run the complex calculations needed to find these excited states.

A team of researchers has now demonstrated a new way to tackle this problem using light. They successfully used a technique called the subspace-search variational quantum eigensolver to find the energy levels of excited states in a high-dimensional space. Instead of relying on the fragile, error-prone methods that usually require extra helper particles to compare states, they used a shared circuit to process multiple states at once. By encoding information into the swirling motion of light particles, they were able to estimate the energies of a simple molecule and a chain of magnetic atoms. This work shows that using photons to carry quantum information offers a practical and efficient path forward for simulating complex chemical processes that were previously out of reach.

The core challenge in this field is that finding the lowest energy state of a system is relatively straightforward for quantum algorithms, but finding the next few energy levels up is much harder. Traditional methods often require the computer to perform a series of delicate comparisons between different states, a process that becomes incredibly difficult as the system grows larger. To get around this, the researchers turned to a method known as the subspace-search variational quantum eigensolver. This approach allows the computer to hunt for several energy levels simultaneously by preparing a set of distinct, non-overlapping starting points and running them through the same optimization process. The key to making this work on today's imperfect machines was finding a way to prepare these distinct starting points without needing deep, complex sequences of operations that would introduce too many errors.

The team chose to use photons, or particles of light, as their quantum bits. Specifically, they utilized a property of light called orbital angular momentum, which can be thought of as the light twisting around its own axis like a corkscrew. By shaping the light with special holographic patterns, they could create different "twists" that acted as distinct, orthogonal states. In this context, orthogonal simply means that the states are completely independent of one another, like different channels on a radio that do not interfere with each other. This method allowed them to prepare multiple input states directly and efficiently, avoiding the need for the deep, error-prone gate sequences that plague other quantum computing platforms.

In their experiment, the researchers set up a system where a laser generated pairs of single photons. One photon served as a signal to confirm the other was ready, while the second photon was sent into the quantum processor. Inside the processor, the team displayed specific holographic patterns on a spatial light modulator, a device that can change the shape of a light beam. These patterns prepared the photon in one of several specific twisted states. The photon then passed through a second modulator that performed the necessary measurements to determine its energy properties. A classical computer monitored the results, adjusted the settings of the holograms, and repeated the cycle until the energy values stopped changing, indicating that the correct answers had been found.

The team tested this approach on two different systems. First, they modeled a simple molecule made of a helium atom and a hydrogen atom, known as HeH+. They successfully estimated the energies for four different levels of this molecule, including both its ground state and three excited states, and calculated the energy deviations between their experimental estimates and theoretical values. They then applied the method to a more complex system: a chain of eight magnetic atoms interacting with each other, estimating excited state energies for this eight-dimensional Heisenberg chain. In both instances, the experimental results provided estimates for the target energy levels, proving that the method works even as the size of the system increases.

This demonstration is significant because it shows that high-dimensional quantum systems can be explored without the heavy overhead of extra hardware or complex error-correction steps. By using the natural properties of light to encode information, the researchers created a scalable architecture that is well-suited for the current generation of quantum devices. The ability to accurately predict excited state energies opens the door to better understanding chemical reactions and material properties, potentially leading to the discovery of new drugs or more efficient solar cells. The work confirms that photonic systems, which use light rather than electricity to process information, are a viable and resource-efficient path toward solving some of the most difficult problems in chemistry and physics.