### Fundamental Building Blocks for Fault-Tolerant Quantum Computing Demonstrated

Errors in information processing and storage have become rare in modern computers due to high-quality manufacture. However, error correcting systems based on the redundancy of the processed data are still utilized in important applications where even single mistakes might have catastrophic consequences.

Quantum computers are intrinsically more prone to errors, hence error correcting systems will almost probably be necessary in the future. Otherwise, faults would spread uncontrollably across the system, resulting in data loss. Because replicating quantum information is forbidden by quantum mechanics' fundamental constraints, redundancy can be obtained by dispersing logical quantum information into an entangled state of different physical systems, such as several individual atoms.

The research team, led by Thomas Monz of the University of Innsbruck's Department of Experimental Physics and Markus MÃ¼ller of RWTH Aachen University and Forschungszentrum JÃ¼lich in Germany, has now realized a set of computational operations on two logical quantum bits that can be used to implement any possible operation for the first time. “For a real-world quantum computer, we need a universal set of gates with which we can program all algorithms,” says Lukas Postler, an experimental physicist from Innsbruck.

### Fundamental quantum operation realized

The researchers used an ion trap quantum computer with 16 trapped atoms to create this universal gate set. Two logical quantum bits, each dispersed across seven atoms, were used to store the quantum information.

For the first time, two computational gates that are required for a universal set of gates can now be implemented on fault-tolerant quantum bits: a computational operation on two quantum bits (a CNOT gate) and a logical T gate, which is particularly difficult to implement on fault-tolerant quantum bits.

“T gates are very fundamental operations,” says Markus MÃ¼ller, a theoretical physicist. “They are particularly interesting because quantum algorithms without T gates can be simulated relatively easily on classical computers, negating any possible speed-up. This is no longer possible for algorithms with T gates.” The T-gate was shown by establishing a particular state in a logical quantum bit and then teleporting it to another quantum bit via an entangled gate operation.

### Complexity increases, but accuracy also

The quantum information is shielded against mistakes in encoded logical quantum bits. However, without computational activities, which are inherently error-prone, this is meaningless.

The researchers designed logical qubit operations in such a way that faults produced by the underlying physical processes may be recognized and fixed as well. As a result, they've created the world's first fault-tolerant implementation of a universal set of gates on encoded logical quantum bits.

“The fault-tolerant implementation requires more operations than non-fault-tolerant operations. This will introduce more errors on the scale of single atoms, but nevertheless the experimental operations on the logical qubits are better than non-fault-tolerant logical operations,” Thomas Monz reports.“The effort and complexity increase, but the resulting quality is better.”

The researchers also used numerical simulations using traditional computers to examine and corroborate their experimental results.

On a quantum computer, the researchers have now proved all of the building elements for fault-tolerant computing. The next step is to put these approaches into practice on larger, more usable quantum computers. The techniques developed at Innsbruck on an ion trap quantum computer can also be applied to other quantum computer designs.