Pseudomagic quantum states: a path to quantum supremacy

A new study in Physical Assessment Letters (PRL) introduces the concept of pseudomagic quantum states, which appear to have high stabilizer (or complexity) and could bring us closer to achieving 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 computing capabilities).

Achieving universal quantum computation is the ability of quantum computers to perform arbitrary quantum computations, and quantum supremacy is at the core of this.

The new PRL study examines non-stabilizing states or magical states. These are quantum states that enable quantum computations that cannot be efficiently simulated on classical computers. This complexity is what 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, a postdoctoral researcher at Freie Universität, Berlin.

“The premise for understanding our research is that quantum computation is more powerful than classical computation. In quantum computing, the term non-stabilizing power or magic refers to a measure of the non-classical resources available to a quantum state,” Gu explains.

Stabilizer versus non-stabilizer quantum states

Any quantum system can be represented as a quantum state, a mathematical equation that contains all the information about the system.

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

“These states – together with a limited set of quantum operations called stabilizer operations – form a classical simulatable framework. However, stabilizer states and operations alone are not sufficient to realize universal quantum computation,” explains Dr. Leone.

To perform calculations that are truly quantum and beyond classical capabilities, non-stabilizer states are required. These states can enable quantum computers to perform tasks that are infeasible for classical computers. One of the biggest challenges, however, is constructing these magical states.

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

“In this context, non-stabilization is best thought of as a resource, because it is essential for achieving quantum advantage. The more non-stabilization a quantum state possesses, the more powerful it is as a resource for quantum computation,” Gu explains.

Pseudomagic states

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

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

Simply put, this means that pseudomagical quantum states are similar to magical states, but are much less complex to construct. Especially for someone with a not so powerful computer, pseudomagic quantum states are indistinguishable from random quantum states.

“This indistinguishability arises from the fact that efficiently distinguishing between pseudomagical states and truly magical states would require an exponential amount of computing power, making it infeasible for any realistic observer,” said Dr. Leone.

Gu added, “Just as pseudorandom 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.”

Laying the foundations

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

They constructed the pseudomagical states in such a way that the gap between their real and apparent non-stabilizing nature was tunable.

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

The core of this framework revolved around the concept of stabilizer entropy. This is a measure of the non-stabilization (or complexity) of a quantum system.

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

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 protocol for quantum cryptography based on EFI pairs (or Efficiently preparable, statistically Far, but computationally Indistinguishable).

These pairs can improve the security of data communications 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 propagation of quantum information.

“By showing 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,” explains Gu out.

Finally, they also show 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 reliability of the magic states, making them more suitable for use in quantum algorithms and error correction schemes.

In the future, the researchers want to investigate the relationship between pseudomagic states and concepts in quantum information theory. In addition, they want to investigate the experimental realization of pseudomagical states with existing and future quantum devices.

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