USC team runs Grover's search on three logical qubits by switching between codes

[Tia91]

Researchers at the University of Southern California and Quantum Elements have proposed a clever way around a fundamental limit in quantum error correction. Quantum Zeitgeist covered the paper by Shixin Wu, Dawei Zhong, Todd Brun and Daniel Lidar. They show how to get universal, weakly fault tolerant quantum computing by switching between two versions of a small code known as the [[8,3,2]] code

The limit they are working around is the Eastin-Knill theorem. It says no single error correcting code can perform a full universal set of gates in the simple, transversal way that keeps errors from spreading. Code switching gets around this by using different codes for different gates and moving the data between them

In this scheme, Version 1 of the code handles single qubit Clifford gates such as H and S. Version 2 handles a logical CCZ gate through transversal T gates, plus CZ, CNOT and SWAP. Both versions come from one subsystem code, depending on how its gauge qubits are fixed, which makes switching between them relatively simple

Because both versions have distance 2, they can detect errors but not correct them. The scheme works by spotting errors and discarding the failed runs. In simulations of state preparation, code switching and a three logical qubit Grover search, logical error rates fell quadratically in the runs that were kept. That is the hallmark of working error detection

These are numerical simulations rather than a hardware demonstration. The authors suggest neutral atom arrays or trapped ions with shuttling as good platforms to try it. Small codes like this are exactly what today's machines can run, so a real test could come quite soon

Is error detection with postselection a useful step towards full fault tolerance? And which hardware do you think will try this first?

Grover's Search Runs On Three Logical Qubits With This New Codequantumzeitgeist.com