Reducing the Spatial Overhead for Quantum Error Correcting Codes

Abstract

Quantum computation is becoming increasingly mainstream; however, in order to adopt a fully fault-tolerant quantum computer, one must create robust procedures to correct inevitable errors that occur across a quantum channel. We adopt a mechanism to reduce the spatial overhead of quantum Low-Density Parity-Check (qLDPC) codes while maintaining the codes' useful parameters. Theoretically, the hypergraph product code offers theoretical guarantees of fault tolerance but can have some gaps in practical performance. We choose to study these codes in our work and aim to reduce the number of qubits used to correct errors.