# Error-Free Quantum Computing Becomes Reality

### Demonstration of the fundamentals of fault-tolerant quantum computing

Due to the high-quality workmanship, errors when processing and storing information have become rare in modern computers. However, for critical applications, where even simple errors can have serious effects, error correction mechanisms based on the redundancy of processed data are always used.

Quantum computers are inherently much more sensitive to disturbances and therefore error correction mechanisms will almost always be required. Otherwise, errors will propagate uncontrollably through the system and information will be lost. Since the fundamental laws of quantum mechanics prohibit copying quantum information, redundancy can be achieved by distributing logical quantum information in an entangled state of multiple physical systems, for example, multiple individual atoms.

The research team, led by Thomas Monz from the Department of Experimental Physics at the University of Innsbruck and Markus Müller from RWTH University of Aachen and Forschungszentrum Jülich in Germany, has now succeeded for the first times to perform a set of computational operations on two quantum logical bits that can be used to implement any possible operation. “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 performed

The research team implemented this set of universal gates on an ion trap quantum computer with 16 trapped atoms. Quantum information was stored in two logical quantum bits, each spread over seven atoms.

Now, for the first time, it has been possible to implement two computational gates on these fault-tolerant quantum bits, which are necessary for a universal set of gates: 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 theoretical physicist Markus Müller. “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.” Physicists demonstrated the T-gate by preparing a special state in a logical quantum bit and teleporting it to another quantum bit via an entangled gate operation.

#### Complexity increases, but so does precision

In the encoded logical quantum bits, the stored quantum information is protected against errors. But this is useless without calculation operations, and these operations are themselves error-prone.

The researchers implemented operations on the logical qubits in such a way that errors caused by the underlying physical operations could also be detected and corrected. Thus, they implemented the first fault-tolerant implementation of a universal set of gates on encoded logic quantum bits.

“Fault-tolerant implementation requires more operations than non-fault-tolerant operations. This will introduce more errors at the scale of single atoms, but nevertheless experimental operations on logical qubits are better than non-fault-tolerant logical operations,” says Thomas Monz. “The effort and complexity increase, but the resulting quality is better.” The researchers also verified and confirmed their experimental results using numerical simulations on conventional computers.

Physicists have now demonstrated all the building blocks of fault-tolerant computing on a quantum computer. The task now is to implement these methods on larger and therefore more useful quantum computers. The methods demonstrated in Innsbruck on an ion trap quantum computer can also be used on other quantum computer architectures.

Reference: “Demonstration of operations of fault-tolerant universal quantum gates” by Lukas Postler, Sascha Heuβen, Ivan Pogorelov, Manuel Rispler, Thomas Feldker, Michael Meth, Christian D. Marciniak, Roman Stricker, Martin Ringbauer, Rainer Blatt, Philipp Schindler , Markus Müller and Thomas Monz, May 25, 2022, *Nature*.

DOI: 10.1038/s41586-022-04721-1

Financial support for the research has been provided, among others, by the European Union under the flagship initiative Quantum as well as the Austrian Research Promotion Agency FFG, the Austrian Science Fund FWF and the Federation of Austrian industries in the Tyrol.