With all the ongoing research into error correction for fault tolerant computers, one thing that hasn’t be achieved yet is to demonstrate error correction that works with a universal gate set. If one can implement a universal gate set, then, at least theoretically, a quantum computer can process any quantum algorithm that is available. Much of the research so far has only worked with a limited set of quantum gates, such as ones from the Clifford group (such as H, S, and CNOT). However, if you are only limited to these gates, not only will you not be able to implement many important algorithms such as Shor’s algorithm, and because of the Gottesman-Knill theorem a classical computer would be able to efficiently simulate your algorithms. This would make a quantum computer unnecessary.
To create a universal gate set, one needs to be able to implement non-Clifford gates such as the T gate or the Toffoli gate that you can use with gates from the Clifford group. However, these gates are not as straightforward to implement in a fault tolerant way. To implement them, one uses a multi-stage process called Magic State Distillation which will generate a purified version of a non-Clifford state from an originating noisy qubit. Then this purified qubit in the magic state can be combined with Clifford gates to implement full fault tolerance. However, many of the techniques to do this take a large number of gates to create this magic state.
Now, IBM has released a new paper published on Nature titled Encoding a magic state with beyond break-even fidelity that describes how they were able to produce high quality magic states on one of their 27 qubit superconducting quantum processor. A key point of their technique is that they use a relatively new feature in their processors call dynamic circuits. An important point is that in their demonstration they were able to obtain beyond break-even fidelity. In other words, the fidelity of the magic states were better than the fidelity that could be achieve with raw qubits without the magic state distillation.
To learn more about IBM’s work in this area, you can read the full paper posted on the Nature website here and also a blog post on the IBM Research website here.
January 11, 2024