The Unexpected Demise of Entanglement: When Quantum Advantage Disappears
The world of quantum computing is filled with promises of solving problems that are intractable for classical computers. But not every question about quantum systems demands a quantum solution. Some problems are equally accessible to both classical algorithms, which run on ordinary computers, and their quantum counterparts. Others remain stubbornly challenging for both.
A key puzzle in this field involves understanding when and where quantum algorithms truly shine. Researchers often study spin systems – mathematical models that capture the behaviour of interacting atoms – to unravel this mystery. By analyzing these systems, researchers can investigate questions like: what happens to a spin system when it is left to equilibrate at a given temperature?
This equilibrium state, known as thermal equilibrium, is crucial as it determines many of a system’s properties. Finding these equilibrium states has therefore been a long-standing goal for physicists and computer scientists.
The quantum advantage in tackling this goal, however, is not a clear-cut case. At high temperatures, classical algorithms readily solve the problem. As temperatures drop and quantum phenomena become more pronounced, the problem grows increasingly difficult. For some systems, it even becomes too complex for even quantum computers to handle within a reasonable timeframe. Yet, the specific details of this transition remain shrouded in uncertainty.
"When do you go to the space where you need quantum, and when do you go to the space where quantum doesn’t even help you?" asks Ewin Tang, a researcher at the University of California, Berkeley, highlighting the key challenge facing the field. "Not that much is known.”
In an exciting development, Tang, along with researchers Ankur Moitra, Ainesh Bakshi, and Allen Liu from MIT, delved into this puzzle, focusing on the relatively high-temperature regime. The team, with backgrounds in learning theory – a field focused on algorithms for statistical analysis – approached the problem from a fresh perspective. Moitra, reflecting on their unique angle, explains, “One of our strengths is that we don’t know much quantum. The only quantum we know is the quantum that Ewin taught us.”
Their initial goal was to develop fast, efficient quantum algorithms for the high-temperature regime, a region where some believed such algorithms existed but had not yet been mathematically proven. Their efforts quickly led them to a breakthrough – they managed to adapt an established technique from learning theory to create a new, fast algorithm. However, their work was overshadowed by another team independently arriving at similar results. Another group had already proven the effectiveness of a promising algorithm developed a year prior for high-temperature scenarios. Their research had been scooped.
Undeterred, Tang and her collaborators went on to collaborate with Álvaro Alhambra, a physicist at the Institute for Theoretical Physics in Madrid, who had co-authored the rival paper. Their aim was to uncover the differences between their independent results. But the review of their findings yielded a stunning surprise.
During an intermediate step in their research, Tang and her colleagues had discovered a remarkable phenomenon: Entanglement, a fundamental concept in quantum mechanics that describes the interconnectedness of quantum systems, vanishes entirely in thermal equilibrium above a specific temperature. "I told them, ‘Oh, this is very, very important,’” remarked Alhambra upon realizing the significance of their discovery.
This unexpected finding represents a significant turning point in our understanding of quantum systems and their interactions. It challenges the commonly held perception that quantum phenomena are always present and dominant in complex systems. The realization that entanglement, a hallmark of quantum behaviour, vanishes entirely under certain conditions calls for a reevaluation of how we conceptualize the quantum world.
This research has profound implications for the development of quantum computing. Understanding the limitations of quantum algorithms and identifying where classical approaches offer alternatives is crucial for designing efficient and effective computational systems. The vanishing of entanglement at high temperatures reveals a previously unknown boundary, highlighting the temperature-dependent nature of quantum advantage.
As Tang herself emphasizes: “We are trying to understand the boundary of when it’s useful, when it’s not useful, and what the conditions are for finding that boundary. It’s really just an open question.” This discovery underscores the ongoing journey of unraveling the mysteries of quantum systems and their potential applications. Exploring this boundary and delving into the intricate dance between classical and quantum worlds is a necessary step towards realizing the full potential of quantum computing.
