In a captivating interview at CERN, renowned theoretical physicist John Preskill delved into a range of topics, from his beginnings in physics and quantum computing to the profound implications of quantum information science on our understanding of space-time. Today, we'll focus on two key areas where Preskill's insights illuminate the significance of Quantum Error Correction (QEC): its surprising connection to the phases of matter and its transformative role in quantum gravity.

About John Preskill

John Preskill, Richard P. Feynman Professor of Theoretical Physics at Caltech and 2024 Bell Prize laureate, is a leading figure in the field of quantum information science. His groundbreaking research has not only advanced our understanding of quantum computing but also revealed unexpected connections between quantum information, condensed matter physics, and the mysteries of quantum gravity.

QEC and Phases of Matter

Physicists discovered that the same principles underlying Quantum error correction (QEC) also appear in the behavior of certain phases of matter. The relationship between quantum error correction and phases of matter is a beautiful example of how seemingly unrelated fields can intersect and enrich each other. It highlights the deep connections between quantum information, topology, and condensed matter physics, and promises to unlock new discoveries in both fields.

Topological Order and Non-Local Information

One example is systems with topological order. These are exotic phases of matter where information is encoded in a highly non-local way. Unlike in ordinary materials, where you can learn about the system by examining a small part of it, in topologically ordered systems, the information is spread out across the entire system. You can only retrieve it by measuring a global property, much like in QEC.

Different Codes, Different Phases

It turns out that different types of quantum error correcting codes (the mathematical recipes for encoding quantum information) correspond to different phases of matter. This connection is a goldmine for physicists. It allows them to use the tools of quantum information theory to study and classify phases of matter, and vice-versa.

Key Ideas and Implications

  • Understanding Exotic Matter: This connection helps us understand exotic phases of matter that were previously difficult to grasp.
  • New Quantum Technologies: It opens up the possibility of designing new quantum technologies based on these exotic phases.
  • Robust Quantum Computing: The insights gained from this connection could lead to more robust quantum computers.

QEC and Quantum Gravity

Quantum error correction (QEC), initially designed for quantum computers, is surprisingly insightful in the realm of quantum gravity. The holographic principle, suggesting that gravity emerges from a non-gravitational theory, mirrors QEC's redundancy for protecting information. This connection has led to breakthroughs in understanding Anti-de Sitter space and the black hole information paradox, but challenges remain in applying it to our universe's model, de Sitter space. Nevertheless, QEC remains a vital tool for unraveling the complexities of quantum gravity.

Quantum Gravity and the Holographic Principle

Quantum gravity is the elusive theory that aims to unify Einstein's theory of general relativity (gravity) with the principles of quantum mechanics. One of the most promising approaches to quantum gravity is the holographic principle, which suggests a remarkable duality.

The holographic principle states that the information contained within a volume of space can be encoded entirely on the boundary of that space, much like a hologram encodes a 3D image on a 2D surface. This duality has profound implications, suggesting that gravity in the bulk (the interior of space) is somehow emergent from a non-gravitational theory on the boundary.

QEC and the Holographic Duality

The connection between QEC and holography lies in how information is encoded and protected in both cases.

In holography, the bulk geometry is thought to be encoded in the degrees of freedom (the information carriers) of the boundary theory. Just as QEC protects quantum information by encoding it redundantly, the holographic duality seems to protect the bulk geometry from errors or damage at the boundary.

Think of it like this: if you remove a few qubits from a quantum error-correcting code, you can still recover the original information because it's spread out across many qubits. Similarly, removing or disturbing a portion of the boundary theory doesn't completely destroy the bulk geometry, as the information about the geometry is not localized to a single point.

Key Ideas and Implications

  • The holographic principle suggests that gravity is emergent from a non-gravitational theory on the boundary of space.
  • QEC principles appear to protect the bulk geometry in the same way they protect quantum information.
  • This connection is well-established in anti-de Sitter (AdS) space and offers insights into the black hole information paradox.
  • Quantum computers may become a crucial tool for investigating and testing ideas about quantum gravity.

Original Interview

https://ep-news.web.cern.ch/content/depth-conversation-john-preskill