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Symmetric quantum codes tie deletion correction to insertion

A peer-reviewed mathematical paper finds that a particular family of symmetric quantum codes can correct the insertion of qubits whenever it can correct the same number of deletions. The authors also derive stricter conditions for errors that combine additions and losses. This is a proof about code properties, with no new hardware test or measured communication speed.

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One paper proves an error-correction equivalence

At Sheffield University, Lewis Bulled and Yingkai Ouyang established an equivalence between insertion and deletion correction for symmetric quantum codes.[1], [2]

A peer-reviewed mathematical study in npj Quantum Information examines errors that change the number of qubits, the basic units of quantum information, in a coded system. In this code family, correcting a given number of unknown-position deletions also permits correction of the same number of insertions, and the reverse holds.[1]

Known and unknown losses are different

The proof distinguishes a deletion at an unknown position from an erasure whose position is known. Insertion means one or more unwanted qubits appear in the sequence. The authors derived necessary and sufficient algebraic conditions for insertion correction and matched them to established deletion conditions. They explicitly limit this equivalence to the symmetric code class, so the result cannot be applied to every quantum code used in computing or communication.[1]

Combined errors demand stricter conditions

The analysis also covers a channel where qubits are both inserted and deleted. If insertion occurs first, some of the newly added qubits may then be lost; that order differs from deleting original qubits before an insertion. The paper expresses the more complex sequence through probability-weighted simpler processes and derives stronger correction conditions. It reports no correcting circuit built on hardware, experimental success rate or transmission-speed measurement; the advance is a property established by proof.[1]

References

  1. News sourcenpj Quantum InformationInsertion and deletion correction proved equivalent for symmetric quantum codes↩1↩2↩3↩4
  2. News sourceQuantum ZeitgeistSymmetric quantum codes can correct qubit losses and additions↩
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