Formation of Robust Bound States of Interacting Photons on Quantum Processors

Formation of Robust Bound States of Interacting Photons

This post details a significant breakthrough in quantum computing, specifically concerning the use of superconducting qubits to simulate quantum phenomena. Researchers at Google Quantum AI have experimentally confirmed the existence of bound states of interacting photons and, more surprisingly, discovered their unexpected robustness to perturbations.

The Challenge of Quantum Simulation

Quantum computers were initially envisioned as powerful tools for understanding the quantum world, acting as "quantum simulators" to investigate complex quantum phenomena intractable for classical computers. However, a major hurdle has been utilizing superconducting qubits for discovery, as they have primarily been used to verify existing theories rather than uncover new insights. While trapped ions and cold atoms have shown promise in this regard, superconducting qubits, despite their potential for universal quantum computing, had yet to fulfill their discovery potential.

Key Findings: Bound States and Their Resilience

The research, published in Nature, presents two primary findings:

Confirmation of Bound States: The Google Sycamore quantum processor was used to experimentally confirm the theoretical prediction of bound states, or composite particles, formed by interacting photons.
Unexpected Robustness: The study revealed that these bound states are remarkably robust to perturbations that were expected to destroy them. This resilience was not anticipated, especially in systems that deviate from perfect integrability.

Understanding Photon Interactions

Photons, the quanta of electromagnetic radiation, typically do not interact with each other. This property is beneficial for applications like telecommunications but a limitation for light-based computing. Quantum processors, however, can induce interactions between photons using two-qubit operations within superconducting qubits. This allows for the simulation of models like the XXZ model, which describes interacting photons and is known for its high degree of symmetry and integrability.

Simulating the XXZ Model and Discovering Bound States

When the XXZ model was implemented on the Sycamore processor, researchers observed that the photon interactions led to the formation of bundles, or bound states. This provided a well-understood starting point for further investigation.

Breaking Integrability and the Surprise of Stability

The researchers then explored a less understood regime by breaking the high symmetries of the XXZ model. This was achieved by introducing additional sites that photons could occupy, making the system non-integrable and theoretically prone to chaotic behavior where bound states would typically dissolve. Contrary to expectations, the bound states persisted even under these conditions.

Experimental Setup and Methodology

The experiment involved a ring of superconducting qubits hosting microwave photons. The state of each qubit (occupied or unoccupied by a photon) was manipulated using the "fSim" quantum gate, which connects neighboring sites and allows photons to interact.

Qubit States: A qubit in state '1' indicates the presence of a photon, while '0' indicates its absence.
fSim Gate: This gate facilitates photon hopping and interaction between adjacent qubits.

The Physics of Bound States

Photon interactions affect their "phase," which tracks the oscillation of their wavefunction. In non-interacting systems, photons remain synchronized. However, when interactions occur, a photon hopping away from a neighbor changes its phase accumulation rate, leading to desynchronization. This results in destructive interference for paths where photons separate, allowing only configurations where photons remain clustered (bound states) to survive.

Observations and Data Analysis

Initialization: The experiment began by placing two to five photons on adjacent sites.
Behavior: In the theoretically predicted regime, photons remained bound. Larger bound states moved more slowly, consistent with their increased "mass."
Visualizations: Plots showed that the majority of photons remained bound together, with darker colors indicating higher occupation probability on sites closer to the initial photon cluster.

Measuring the Energy-Momentum Dispersion Relation

To rigorously confirm the behavior of bound states as single composite particles, the researchers measured their energy-momentum dispersion relation. This involved:

Phase Accumulation: Measuring the phase difference between a bound state and the vacuum (no photons) over time and space.
Fourier Transform: Applying a Fourier transform to convert the time-space data into momentum-energy information, revealing the characteristic dispersion relation of the quasiparticle.

The Impact of Breaking Integrability

Integrable systems, characterized by numerous conserved quantities, constrain dynamics to a limited phase space. Bound states in such systems, while predicted and observed previously, are typically fragile. Breaking integrability, by introducing new connections for photons to hop to, was expected to destabilize these bound states due to increased chaotic behavior and exploration of phase space.

However, the experiment showed that even with strong perturbations that made photons equally likely to hop to a new radial site as to their adjacent ring sites, the bound states remained intact. This resilience was observed up to the point where decoherence effects caused a slow decay.

Conclusion and Future Directions

The unexpected resilience of these bound states remains an area for further investigation. Researchers speculate that a phenomenon called "prethermalization," where differing energy scales prevent rapid thermal equilibrium, might be responsible. Future research aims to explore this interplay between prethermalization and integrability to gain deeper insights into many-body quantum physics.

Acknowledgements

The authors acknowledge Katherine McCormick, Quantum Science Communicator, for her assistance in writing the blog post.

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Formation of Robust Bound States of Interacting Photons on Quantum Processors