Pseudomagical Quantum States: A Path to Quantum Supremacy

A new study in Physical Examination Letters (PRL) introduces the concept of pseudomagical quantum states, which appear to have high stability (or complexity) and can bring us closer to quantum supremacy.

Quantum supremacy or quantum advantage is the ability of quantum computers to simulate or perform calculations that classical computers cannot (due to their limited computational capabilities).

The realization of universal quantum computing is the ability of quantum computers to perform any arbitrary quantum calculation, and quantum supremacy is at its heart.

New PRL the study explores non-stabilizing states or magical states. These are quantum states that enable quantum calculations that cannot be efficiently simulated on classical computers. It is this complexity that gives quantum computers their potential power.

Phys.org spoke with paper co-authors Andi Gu, a Ph.D. student at Harvard University and Dr. Lorenzo Leone, postdoctoral researcher at Freie Universität Berlin.

“The starting point for understanding our research is that quantum computing is more powerful than classical computing. In quantum computing, the term non-stabilization or magic refers to a measure of the non-classical resources possessed by a quantum state,” he said. Gu explained.

Stabilizing and non-stabilizing quantum states

Every quantum system can be represented as a quantum state, a mathematical equation containing all the information about the system.

A stabilizing state is a type of quantum state that can be efficiently simulated (or executed) on a classical computer.

“These states, together with a restricted set of quantum operations called stabilization operations, form a classically simulable framework. However, states and stabilization operations alone are not sufficient to achieve universal quantum computing,” explained Dr. Leone.

To perform truly quantum calculations and beyond classical capabilities, non-stabilizing states are necessary. These states can allow quantum computers to perform tasks that are impossible for classical computers. However, one of the main challenges is building these magical states.

Non-stabilizing states are inherently difficult to construct because they require more complex quantum operations.

“In this context, non-stabilization is best viewed as a resource because it is essential for gaining quantum advantage. The more non-stabilization a quantum state has, the more powerful it is as a resource for quantum computing,” he said. Gu explained.

Pseudomagic States

The researchers found a way around this challenge by introducing the concept of pseudomagical quantum states.

Pseudomagical quantum states appear to have the properties of non-stabilizing states (complexity and non-classical operations), but are computationally indistinguishable from random quantum states, at least to an observer with limited computational resources.

In simple terms, this means that pseudomagic quantum states resemble magical states but are much less complex to construct. Especially for someone with a not-so-powerful computer, pseudomagical quantum states are indistinguishable from random quantum states.

“This indistinguishability comes from the fact that effectively distinguishing pseudo-magical states from truly magical states would require an exponential amount of computational resources, making it impossible for any realistic observer,” Dr. Leone said.

Gu added: “Just as pseudo-random number generators produce sequences that appear random to computationally limited classical observers, pseudomagic states are designed to appear highly non-stabilizing to computationally limited quantum observers.”

Lay the foundations

Over the course of six theorems, the researchers laid the theoretical foundations of pseudomagic states as well as their implications for applications of quantum computing.

They constructed the pseudomagic states in such a way that the gap between their real and apparent non-stabilization was adjustable.

“This means that we can create states that can appear to be powerful resources for quantum computing, even if they are not as resource-intensive as they seem,” Dr. Leone explained.

The core of this framework revolved around the concept of stabilizing entropy. It is a measure of the non-stabilizing character (or complexity) of a quantum system.

What is unique about stabilizer entropy is that, unlike other measures of non-stabilization, it is less computationally intensive.

Implications for quantum computing applications

The researchers focused on three areas where pseudomagic states could have implications, starting with quantum cryptography.

According to the study, pseudomagic states introduce a new quantum cryptography protocol based on EFI (or efficiently prepareable, statistically distant, but computationally indistinguishable) pairs.

These pairs can improve the security of data communication and can be constructed using pseudomagic states.

The researchers also show that pseudomagic states can provide new insights into quantum chaos and scrambling, which are important for understanding the behavior of complex quantum systems and the diffusion of quantum information.

“By demonstrating that the apparent magic of a quantum state can differ from its actual magic, our work highlights the need to consider the limitations of realistic, computationally limited observers when studying quantum systems and their applications,” Gu explained.

Finally, they also demonstrate that pseudomagic states can be used to build more efficient fault-tolerant quantum computers using a process called magic state distillation.

Magic state distillation is essentially a purification process that improves the fidelity of magic states, making them more suitable for use in quantum algorithms and error correction systems.

The researchers want to explore the relationship between pseudomagic states and concepts from quantum information theory in the future. Additionally, they want to explore the experimental realization of pseudomagical states with existing and near-term quantum devices.

“This could lead to the development of practical applications exploiting the unique properties of these states,” concluded Dr. Leone.