Achim Kempf and Einar Gabbassov are researchers at the University of Waterloo and the nearby Perimeter Institute. To do that they have most recently released a pioneering research effort published in the journal Quantum Science and Technology. Their work shows that the intrinsic hardness of a problem determines the efficiency of a quantum computer. This fascinating insight greatly enriches our understanding of underlying quantum computing dynamics. Their focus is mainly on the role of entanglement in quantum computing computational complexity. Their insights have the potential to make quantum computing far more viable for applications including medicine and supply chain optimization.
This works, doi 10.1088/2058-9565/ae0364, sheds light on an important and often overlooked relationship between problem complexity and computational speed. The authors argue that the manipulation of entangled particles is key to understanding how quickly quantum computers can solve complex problems. Their findings show how important entanglement is to quantum computation. Moreover, they create a useful template that can inform more research going forward.
Understanding Intrinsic Difficulty
Central to understanding Kempf and Gabbassov’s study is the idea of intrinsic difficulty in computational problems. They compare this extensive complexity to crossing a rocky landscape, where the greatest solutions are often difficult to find.
In this analogy, easy problems are like flat fields, and hard problems are like rocky mountains, filled with boulders and crevasses. Kempf warns that when faced with difficult problems, one may find themselves stuck in local minima, far from the actual optimal solution:
“Imagine you are parachuted down onto a landscape with hills and valleys and cliffs, and you want to find the lowest possible point, where you’ve been told you’ll find a treasure chest.”
This new understanding helps make sense of why some mathematical problems are very easy to solve, and other problems are well-known to be difficult.
“But for a hard problem, the corresponding landscape is rugged, and you might easily find yourself at the bottom of a valley with no treasure in sight, because the actual lowest point is in a deeper chasm 20 kilometers away.”
From all of this, entanglement paintings emerge as an important player in establishing how fast you can compute. As Kempf and Gabbassov explain, difficult problems require large-scale intervention on deeply nested tangled solutions. Each entangled particle acts as part of a unified system, influencing one another even over vast distances—a phenomenon Albert Einstein famously referred to as “spooky action at a distance.”
The Role of Entanglement
Achim Kempf asserts that once particles are entangled, they cannot be viewed as separate entities:
This ability to be inter-connected is what enables quantum computers to solve complicated problems more quickly than classical computers. Einar Gabbassov adds:
“You can have two separate objects, two particles or two qubits, and once they get entangled, they kind of become one entity.”
The authors first suggest that a precise understanding of this relationship between entanglement and computational complexity will unlock a wealth of further research and application.
“It is not possible to view them separately: They become one thing in the same state.”
The impacts of this research reach farther than the borders of theoretical physics. They hold great promise for real-world application. Quantum computers have the potential to tackle complex issues that extend far beyond the federal sector, including improving supply chain logistics and accelerating drug discovery.
Implications for Quantum Computing
Kempf emphasizes that their findings could accelerate the economic viability of quantum computing:
Additionally, by connecting mathematics and physics, Kempf hopes that their work sets the stage for future developments. He states:
“I think this research will speed up the economic viability of quantum computing. We now better understand how to turn a mathematical problem into a physical problem.”
The research represents an important advance toward making quantum computers more powerful. With clearer insights into how entanglement affects computational speed, researchers may develop more effective algorithms and systems that leverage these principles.
“We’ve basically provided a new bridge between mathematics and physics, and we think that a lot of traffic can be put on that bridge.”
The study serves as a critical step towards enhancing the capabilities of quantum computers. With clearer insights into how entanglement affects computational speed, researchers may develop more effective algorithms and systems that leverage these principles.