In high school, we learn about a random walk or a drunkard's walk, a mathematical concept describing a path consisting of a sequence of random steps on some mathematical space. It can be used to explain phenomena like Brownian motion, which is the random motion of particles in air or liquid. In quantum mechanics, which describes the behaviour of quantum particles like electrons and photons, we get quantum walks, which are like the quantum version of a random walk describing the motion of a quantum particle through space. Quantum walks are essential for developing new quantum technologies, from super-fast computers to secure communication systems.
Although similar, quantum particles behave very differently from classical objects, like humans and chairs. Quantum objects can be in a superposition of multiple states at the same time, meaning they can be in multiple places and multiple states at the same time. These quantum properties, however, can disappear when the quantum object is observed or interacts with the environment - a phenomenon known as wave function collapse or decoherence. Quantum walks, which depend on the quantum behaviour, can be easily disrupted by decoherence. Researchers are trying to understand how to keep these quantum walks stable and coherent, long enough to be used in applications like quantum computers.
A new study from the Indian Institute of Science Education and Research (IISER) Pune, Indian Institute of Science Education and Research (IISER) Thiruvananthapuram, and the University of Turku,Finland, sheds light on how the very structure of the networks these particles travel through plays a crucial role.
The research looked into how different types of networks and different ways decoherence can happen affect the stability of these quantum walks. They looked at various network structures, from simple ones like cycles and stars to more complex ones like scale-free networks, which are common in social networks and the internet. They also examined three specific ways decoherence can occur: intrinsic decoherence (the particle losing its quantumness on its own), Haken-Strobl noise (decoherence caused by interactions with the environment in a specific way), and quantum stochastic walks (a model that bridges the gap between purely quantum and classical behaviour).
To determine the stability of the quantum walks, the researchers used a variety of tools. They measured factors, like how likely the particle was to be found at different points in the network over time, how much coherence (a key quantum property) the particle retained, how similar the quantum path was to its starting point, and how much the quantum walk behaved like a classical one.
They discovered that the stability of the quantum walk depends on a complex interplay between the network's design and the type of noise or decoherence it encounters. They found that intrinsic decoherence was the gentlest, allowing the quantum properties to last the longest. Haken-Strobl noise was a bit more disruptive, and quantum stochastic walks caused the quickest loss of coherence.
Interestingly, the structure of the network itself made a big difference. Heterogeneous networks, like star networks where one central point is connected to many others, or scale-free networks with a few highly connected hubs, tended to be more stable. This is because these structures can help keep the quantum particle localised, meaning it stays in a particular area of the network, which helps preserve its quantumness. Homogeneous networks, like a simple cycle where each point is only connected to its immediate neighbours, were more vulnerable to decoherence. However, a complete graph, where every point is connected to every other point, was surprisingly stable despite being homogeneous, likely due to its dense connections.
The researchers also noted that where the quantum particle started its journey within a network, especially in these heterogeneous ones, had a significant impact. Starting at a highly connected hub node often led to better stability. This is because the centrality of a node, meaning its importance in the network's structure, can influence how the quantum walk behaves.
The study provides a comprehensive look at the stability of the quantum walk. It highlights the importance that the best network or decoherence model can depend on what you're trying to achieve. For instance, sometimes a bit of decoherence can even help with certain tasks, like quantum search algorithms. The study also highlights that different ways of measuring stability can give slightly different answers, meaning scientists need to use a combination of these tools to get a full picture.
By understanding how network structure affects quantum stability, engineers can design better quantum computers and communication systems. Knowing which network designs are more robust against environmental noise is crucial for ensuring the information stays quantum and doesn't get corrupted. This work provides valuable insights into how to engineer these delicate quantum systems to be more resilient and reliable, paving the way for more advanced quantum technologies.
This article was written with the help of generative AI and edited by an editor at Research Matters.