**The computing power of quantum computers is currently still very low. Increasing it is currently still proving to be a major challenge. Physicists at the University of Innsbruck now present a new architecture for a universal quantum computer that overcomes such limitations and could be the basis for building the next generation of quantum computers in the near future. **

In a quantum computer, quantum bits (qubits) serve as a computing unit and memory at the same time. Because quantum information cannot be copied, it cannot be stored in a memory as in a classical computer. Because of this limitation, all qubits in a quantum computer must be able to interact with each other. This is currently still a major challenge for building powerful quantum computers. In 2015, theoretical physicist Wolfgang Lechner, together with Philipp Hauke and Peter Zoller, addressed this difficulty and proposed a new architecture for a quantum computer, now named the LHZ architecture after the authors. "This architecture was originally designed for optimization problems," recalls Wolfgang Lechner of the Institute of Theoretical Physics at the University of Innsbruck. "In the process, we reduced the architecture to a minimum in order to solve these optimization problems as efficiently as possible." In this architecture, the physical qubits do not represent individual bits, but represent the relative coordination between the bits. "This means that all qubits no longer have to interact with each other," explains Wolfgang Lechner. With his team, he has now shown that this parity concept is also suitable for a universal quantum computer.

## Complex arithmetic operations are simplified

Parity computers can perform interacting gate operations - computing operations between two or more qubits - on a single qubit. ÜExisting quantum computers already implement such operations very well on a small scale," explains Michael Fellner from Wolfgang Lechner’s team. "However, with the number of qubits, it becomes more and more complex to implement these interacting gate operations." In two publications in *Physical Review Letters* and *Physical Review A*, the Innsbruck scientists now show that parity computers can, for example, perform quantum Fourier transformations - a fundamental building block of very many quantum algorithms - with significantly fewer computational steps and thus more quickly. "Due to the high parallelism of our architecture, the well-known Shor algorithm for factoring numbers, for example, can be executed very efficiently," Fellner explains.

## Two-stage error correction

The new concept also offers hardware-efficient error correction. Because quantum systems are very sensitive to interference, quantum computers must correct errors continuously. Significant resources must be devoted to protecting quantum information, which greatly increases the number of qubits required. "Our model works with a two-stage error correction, one type of error (bit flip error or phase error) is prevented by the hardware used," say Anette Messinger and Kilian Ender, also members of the Innsbruck research team. There are already initial experimental approaches for this on different platforms. "The other type of error can be detected and corrected via the software," Messinger and Ender say. This would allow a next generation of universal quantum computers to be realized with manageable effort. The spin-off company ParityQC, co-founded by Wolfgang Lechner and Magdalena Hauser, is already working in Innsbruck with partners from science and industry on possible implementations of the new model.

The research at the University of Innsbruck was financially supported by the Austrian Science Fund FWF and Forschungsförderungsgesellschaft FFG.

**Publications:**

Universal Parity Quantum Computing. Michael Fellner, Anette Messinger, Kilian Ender, and Wolfgang Lechner. Phys. Rev. Lett. 129, 180503 (2022) doi: 10.1103/PhysRevLett.129.180503

Applications of Universal Parity Quantum Computation. Michael Fellner, Anette Messinger, Kilian Ender, and Wolfgang Lechner, Phys. Rev. A 106, 042442 (2022) doi: 10.1103/PhysRevA.106.042442