### Parity quantum computers facilitate the implementation of complex algorithms.

In a quantum computer, quantum bits (qubits) simultaneously act as a computing unit and a memory. Quantum information cannot be stored in a memory like in a classical computer since it cannot be copied. Because of this restriction, qubits in a quantum computer must all be able to interact with each other. This continues to be a significant obstacle to the development of powerful quantum computers. In order to overcome this problem, theoretical physicist Wolfgang Lechner, in collaboration with Philipp Hauke and Peter Zoller, proposed a new architecture for a quantum computer in 2015. This architecture is now known as the LHZ architecture after the authors.

“This architecture was originally designed for optimization problems,” recalls Wolfgang Lechner from the Department of Theoretical Physics at the University of Innsbruck, Austria. “In the process, we reduced the architecture to a minimum in order to solve these optimization problems as efficiently as possible.”

The physical qubits in this architecture encode the relative coordination between bits rather than representing individual bits.

“This means that all qubits no longer have to interact with each other,” explains Wolfgang Lechner. With his team, he has just shown that this concept of parity is also suitable for a universal quantum computer.

#### Complex operations are simplified

Parity computers can perform operations between two or more qubits on a single qubit. “Existing quantum computers already perform such small-scale operations very well,” says Michael Fellner of Wolfgang Lechner’s team.

“However, as the number of qubits increases, it becomes increasingly complex to implement these gate operations.”

In two publications in *Physical examination letters* and *Physical examination A*the Innsbruck scientists now show that parity computers can, for example, perform quantum Fourier transforms – a fundamental element of many quantum algorithms – with far fewer computational steps and therefore faster.

“The high parallelism of our architecture means that, for example, Shor’s well-known algorithm for factoring numbers can be executed very efficiently,” says Fellner.

#### Two-step error correction

The new concept also offers hardware-efficient error correction. Since quantum systems are very sensitive to disturbances, quantum computers must constantly correct errors. Significant resources must be devoted to protecting quantum information, which greatly increases the number of qubits needed.

“Our model works with two-step error correction, one type of error (bit flip error or phase error) is avoided by the hardware used,” explain Anette Messinger and Kilian Ender, also members of the Innsbruck research team. There are already first experimental approaches for this on different platforms.

“The other type of error can be detected and corrected through software,” Messinger and Ender explain. This would make it possible to achieve a next generation of universal quantum computers with manageable effort. Spin-off company ParityQC, co-founded by Wolfgang Lechner and Magdalena Hauser, is already working in Innsbruck with scientific and industrial partners on possible implementations of the new model.

References: “Universal Parity Quantum Computing” by Michael Fellner, Anette Messinger, Kilian Ender and Wolfgang Lechner, October 27, 2022, *Physical examination letters*.

DOI: 10.1103/PhysRevLett.129.180503

“Applications of Universal Parity Quantum Computing” by Michael Fellner, Anette Messinger, Kilian Ender and Wolfgang Lechner, October 27, 2022, *Physical examination A*.

DOI: 10.1103/PhysRevA.106.042442

The research was funded by the Austrian Science Fund and the Austrian Research Promotion Agency.

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