We have reported in the QCR recently on several research projects to create quantum error correction codes (see here, here, here, and here), but one of the most significant challenges for implementing a full fault tolerant quantum computer is being able to robustly support a complete, universal gate set that could conceivably implement any quantum algorithm. It is one thing to create logical qubits using a specific error correction code, but it is another thing to be able to perform gate operations on those qubits to do something useful. When one examines the types of gates that need to be implemented, they can be divided into two categories, Clifford gates and Non-Clifford gates. A set of Clifford gates would include the Hadamard, CNOT, and S (Phase gate). From these many of the other common gates can be synthesized. However, the Clifford set is not sufficient or running any quantum algorithm nor is it able to provide a quantum advantage over a classical algorithm, per the Gottesman-Knill theorem. In order to achieve full advantage, one needs to implement non-Clifford gates such as the T-gate, the Toffoli gate or other non-Clifford gates. When both the gates from the Clifford group as well as a non-Clifford gate are available, the quantum computer will have a universal gate set that can conceivably process any quantum algorithm and provide a speedup over a classical implementation.

Full report : Quantinuum Demonstrates Two Techniques for Generating High-fidelity Logical Non-Clifford Gates.

For more see the OODA Company Profile on Quantinuum.