Quantum error correction reduces measurements and qudits needed for recovery
Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery
Information Theory
Summary
Quantum computers need to fix mistakes caused by noise, and this requires measuring certain parts of their data and using specific qudits (quantum bits). The authors found a way to identify the smallest number of measurements and qudits necessary to recover the data after some are lost or erased. Their approach uses linear algebra and works efficiently for large sets of qudits. They also provide special formulas for certain types of quantum codes and relate their findings to ideas from classical data recovery.
What this means in practice
- •For quantum hardware engineers: Design quantum hardware with fewer qudits and simpler measurements to recover from errors during computation.
- •For quantum communication developers: Construct protocols that minimize the measurement and qudit resources needed to fix erasures in quantum networks.
Authors
Ryutaroh Matsumoto
Abstract
For a general entanglement-assisted or unassisted quantum error-correcting code, a set of erasures, and an associated repair group, we propose a linear algebraic procedure to compute a reduced set of observables and a reduced repair group of codeword qudits for correcting the given erasures. The procedure has cubic complexity in the repair group size and the computed set of observables has the smallest possible size for correcting the given erasures. We specialize the general procedure to quantum codes constructed from Euclidean and Hermitian orthogonality, and provide closed-form upper bounds on the size of reduced repair groups for those special cases. Based on these closed-form bounds, we propose quantum counterparts of the information locality of classical local recovery.