Implementing a topologically ordered time crystal on a quantum processor

Symmetry breaking in time transformation. Credit: Nature Communications (2024). DOI: 10.1038/s41467-024-53077-9
In a new study published in Nature Communications, scientists have implemented for the first time a topologically ordered time crystal on a quantum processor.
This heralds a new era in quantum technology, as it has traditionally been difficult to combine crystals with topological order. However, achieving this combination increases system stability and robustness, which is a requirement for quantum computing applications.
Time crystals are a recent introduction to science, an idea first proposed by Nobel Prize winner Frank Wilczek in 2012. This is a quantum system that can spontaneously oscillate between states without the need for a continuous external energy source.
Simply put, a time crystal is a type of material whose atoms are arranged periodically in time rather than space, similar to normal crystals (such as diamonds).
During vibration, the system always remains in its lowest energy state, i.e. at ground level. Time crystals were experimentally confirmed in 2017 and have potential applications in a variety of quantum technologies.
Due to the dynamic nature of crystals, achieving topological order, or global order, over time can be difficult. The research team aimed to fill this gap by demonstrating topologically ordered time crystals.
Phys.org spoke to researchers involved in the study, including Dr. Liang Xiang, Dr. Wenjie Jiang, Dr. Zehang Bao, Assistant Professor Qiijiang Guo, Professor Haohua Wang from Zhejiang University, and Associate Professor Dong-Ling Deng from Tsinghua University. Ta. .
Describing the process of bringing topologically ordered time crystals to life, the researchers say, “Theoretical physicists and experimental teams collaborated to realize this beautiful project. The goal is to advance understanding.”
The uniqueness of time crystals
Time crystals exhibit what is called time transformation symmetry breaking. Time transformation is a property of a system in which the state of the system does not change over time.
In the case of time crystals, this symmetry is broken because the time crystal oscillates periodically between different states. What is unique about time crystals is that they can exhibit periodic motion over time without dissipating energy.
However, it does not violate the Nature Conservation Act.
After the first push is applied, the system begins to vibrate at a lower frequency than the driving force. Vibrations become self-sustaining through multi-body interactions, producing collective synchronous vibrations.
Their lack of balance allows them to maintain movement indefinitely, even in their ground state. This symmetry breaking is a form of non-equilibrium matter that brings out the uniqueness of time crystals.
topological order
Systems can be characterized by two types of properties: local and global.
Local properties are properties that depend on a particular environment or location within a system, such as the spin or magnetic moment of an atom.
Global properties, on the other hand, depend on the entire system. These properties have long range compared to local properties which have short range. An example of a global property is superconductivity.
Topological order is a type of global property of a system that is not described by local disturbances or noise. This occurs as a result of long-range entanglements within the system. This means that changes in one part of the system can affect other parts of the system.
Quantum computers are highly susceptible to errors and noise from the environment. These interact with the system and can lead to inconsistencies. This means that the system is no longer able to maintain superposition and entanglement, which are the core features of quantum systems.
Topological order is interesting for topological quantum computing because it is stable against local disturbances.
The challenge in introducing topological order into time crystals is their dynamic nature. Topological order requires a state of stability and equilibrium, but in this state no crystals appear.
Programmable superconducting qubit
The researchers set up the processor using 18 programmable superconducting transmon qubits arranged in a two-dimensional square lattice. These qubits are more stable than other qubits.
The square lattice facilitates qubit interaction and helps generate entanglement needed for quantum algorithms and error correction (noise reduction).
The researchers highlighted the surface cord as a key feature of the setup.
“Surface codes are not only one of the most successful models for quantum error correction, but also support exotic topologically ordered phases. The quantum processor developed by the experimental team at Zhejiang University naturally Adapted to the surface code model.
“This makes it an ideal test bed for exploring these elusive topologically ordered states and potentially extending their boundaries from equilibrium to non-equilibrium systems,” the researchers said. explained.
The company’s processor has a depth of 700 circuit layers and can run 2,300 single-qubit gates and 1,400 two-qubit gates. This shows that it can handle large and complex calculations.
The platform can also simulate four-body interactions needed for modeling complex systems. Additionally, we used neuroevolutionary algorithms to find optimal configurations of quantum circuits that can improve computational efficiency and effectiveness.
The researchers went on to say that they have made “significant efforts to improve the performance of processors with state-of-the-art gate fidelity and qubits to meet the demanding requirements of observing long-lived topological time-crystal dynamics. I’m here,” he added. Now it’s coherence time. ”
Robust and stable topological time crystal order
The researchers demonstrated the stability of this system by finding that it can maintain stable operation at fractional frequencies of the driving force, even when dealing with noise. The system stabilized without any unwanted oscillations after being disturbed.
The system also remained stable even with small fluctuations, allowing it to function in noisy environments. When faced with stronger disturbances, the system loses its time crystal-like behavior.
The researchers found that the system’s topological entanglement is consistent with theoretical predictions, suggesting that its properties are robust and well-defined.
In the case of four-body qubit interactions, the system was able to successfully measure interactions with high precision. The system can also create and verify periodically driven quantum states to support their time-periodic behavior.
Commenting on the potential of their system, the researchers said, “By expanding the system’s size, control precision, and coherence time, superconducting processors will allow scientists to explore more exotic non-equilibrium phases of inaccessible materials.” I believe it will happen,” he said. Made of natural materials. ”
They also state that their experiments demonstrate all the building blocks needed to implement a Floquet-rich topological order that hosts dynamic anyon substitutions and emergent non-abelian anyons.
“Observation of such an unconventional phenomenon will be an important step toward improving our understanding of exotic non-equilibrium phases,” the researchers said.
Further information: Liang Xiang et al., Long-lived topological time-crystal order on quantum processors, Nature Communications (2024). DOI: 10.1038/s41467-024-53077-9
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