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Dynamically Generated Logical Qubits

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arxiv 2107.02194 v2 pith:4ASKFXC7 submitted 2021-07-05 quant-ph

Matthew B. Hastings , Jeongwan Haah This is my paper · ORCID
classification quant-ph
keywords codelogicalqubitsmeasurementdynamicallygeneratedquantumallowing
verification ladder T0 review T1 audit T2 compute T3 formal

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We present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Our particular code gives a model very similar to the two-dimensional toric code, but each measurement is a two-qubit Pauli measurement.

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Planar fault-tolerant circuits for non-Clifford gates on the 2D color code

    quant-ph 2025-05 conditional novelty 8.0 of 10

    The paper constructs a family of planar fault-tolerant 'twisted color circuits' that implement logical T gates and magic-state measurements on the 2D color code via a path-integral and color-cohomology framework.

  2. Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry

    quant-ph 2024-11 conditional novelty 8.0 of 10

    Cohomology operations, including new higher Pontryagin powers, yield constant-depth logical R_k and multi-controlled R_k gates in homological quantum codes on projective spaces, extending the known color-code paradigm.

  3. A diagrammatic field theory of quantum error correction

    quant-ph 2026-07 conditional novelty 6.5 of 10

    Exact correctability of fusion-space codes is equivalent to fibrewise Knill–Laflamme conditions on syndrome-admissible footprint algebras, with a conditional Peierls threshold for growing families and explicit Ising e...

  4. A conditional no-go for resource-free magic-axis measurement on a static surface code

    eess.SY 2026-07 conditional novelty 6.0 of 10

    Under three stated assumptions, a resource-free static surface-code patch cannot sharply measure the magic axis at polynomial acceptance; it must pay with a resource, leave the dilute regime, or accept exponentially rarely.

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