Toward error-free quantum computing

Errors must be recognized and fixed for quantum computers to be useful in practice. A team of experimental physicists at the University of Innsbruck, Austria, has now implemented a universal set of computational operations on fault-tolerant quantum bits for the first time, demonstrating how an algorithm may be written on a quantum computer so that mistakes do not ruin the outcome.

Because of high-quality production, mistakes in information processing and storage have become rare in modern computers. However, in important applications where even little mistakes can have major consequences, error correcting systems based on data redundancy are still utilized.

Quantum computers are naturally more vulnerable to disturbances and will almost certainly always require error correcting systems, as faults will spread uncontrollably throughout the system and information will be lost. Because quantum mechanics' fundamental constraints prohibit copying quantum information, redundancy can be obtained by dispersing logical quantum information into an entangled state of different physical systems, such as several individual atoms.

The team led by Thomas Monz of the University of Innsbruck's Department of Experimental Physics and Markus Müller of RWTH Aachen University and Forschungszentrum Jülich in Germany has now realized for the first time a set of computational operations on two logical quantum 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," argues 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. The quantum data was encoded in two logical quantum bits, each spread across seven atoms.

For the first time, two computational gates required for a universal set of gates may 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 challenging to execute on fault-tolerant quantum bits.

"T gates are very fundamental operations," theoretical physicist Markus Müller says. "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 transporting it to another quantum bit via an entangled gate operation.

Complexity increases, but accuracy also

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

The researchers built logical qubit operations in such a way that faults produced by the underlying physical processes may also be recognized and fixed. As a result, they created the first fault-tolerant implementation of a universal set of gates based 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 is pleased to report. "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.

The physicists have now proved all of the building pieces for fault-tolerant computing on a quantum computer. The issue now is to apply these approaches on bigger and thereby more usable quantum computers. The methods developed at Innsbruck on an ion trap quantum computer can be applied to different quantum computer designs.