Technical perspective: Deciphering errors to reduce the cost of quantum computation

Abstract

quantum LDPC codes exhibit a uniquely quantum phenomenon known as “degeneracy:” Multiple different errors can act the same way on the codewords, which confuses the classical algorithms. A new approach is needed, and in the following paper, the authors, building on earlier work by themselves and others, produce an algorithm that can rapidly deduce the error in a quantum expander code, even when the syndrome is partially incorrect. The key to making the algorithm work is to consider multiple qubits at a time. Rather than treating each individual qubit separately, the algorithm looks for small groups of qubits that are part of the error; considering sets of qubits as a unit resolves the ambiguity introduced by degeneracy. The authors then use a result about percolation to show that errors appear in only small clusters, meaning many local decisions about errors can be performed independently and even simultaneously. Consequently, not only does the algorithm work but it is highly parallelizable, making it potentially even faster than the algorithms used for syndrome decoding of surface codes. To see if expander codes are genuinely useful, much more work is needed, however. We need good codes of reasonable size and better ways of performing fault-tolerant algorithms on encoded qubits. We need to better understand how much error expander codes can tolerate and to deal with the requirement for long-range interactions. If these problems can be solved, expander codes will offer an exciting alternative to surface codes for fault tolerance in a large quantum computer.