Polylog-time- and constant-space-overhead fault-tolerant quantum computation with quantum low-density parity-check codes

Understand

A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate.

• We prove that a protocol using non-vanishing-rate quantum low-density parity-check (LDPC) codes, combined with concatenated Steane codes, achieves constant space overhead and polylogarithmic time overhead, even when accounting for non-zero classical computation time.
• This protocol offers an improvement over existing constant-space-overhead protocols, which have polynomial time overhead using quantum LDPC codes and quasi-polylogarithmic time overhead using concatenated quantum Hamming codes.
• To ensure the completeness of this proof, we develop a technique called partial circuit reduction, which enables error analysis for the entire fault-tolerant circuit by examining smaller parts composed of a few gadgets.