Quantum LDPC codes and their hardware realization

3 problems

• Provable qLDPC decoders whose proven thresholds match observed ones

  Partially resolved

  Error correction needs a classical computer to read the check results and decide what went wrong before new errors pile up. For these codes, decoders with mathematical guarantees exist, but the noise levels they are proven to handle are far below what they handle in practice, and the decoders used in practice have no guarantees.

• Fault tolerance with constant space and constant time overhead

  Open

  Theorists can now run a quantum computation reliably with only a constant factor more qubits, but at the price of a slowdown that grows slowly with problem size. Whether both the qubit cost and the slowdown can be constant at once is unknown.

• Low-overhead universal logical gates on constant-rate qLDPC codes

  Partially resolved

  Storing quantum information in these codes is understood far better than computing with it. A way to apply every needed operation to the stored qubits without giving back the qubit savings is still missing in practice.