Erasure Conversion Protocols

• Erasure conversion protocols are techniques that transform undetected errors into flagged erasures by leveraging computational and ancillary detection methods.
• They are implemented across various quantum platforms such as semiconductor spin qubits, trapped ions, and superconducting circuits, achieving detection efficiencies often above 90%.
• These protocols significantly enhance fault tolerance by increasing error correction thresholds and reducing resource overhead for robust quantum information processing and sensing.

Erasure conversion protocols transform arbitrary or platform-specific errors into detectable erasures—errors at known locations—which enables significant improvements in error correction, quantum information processing, and thermodynamics of information erasure. Modern research across disparate platforms has unified and extended the principles underpinning erasure conversion, revealing its generality, practical impact, and role as a maximal resource for fault tolerance and error-corrected sensing.

1. Principles of Erasure Conversion

A physical or logical system encodes information in a computational subspace, while undesired evolutions, leakage, or noise can transfer population out of this subspace. Erasure conversion is the process by which these irrecoverable or unpredictable errors are detected and flagged, either through active measurement, ancillary subspaces, or engineered transitions, thereby signaling to the classical or quantum processor that a particular site or qubit is erroneous but at a known location. This converts “invisible” errors, which are difficult to correct, into “located” errors, which are straightforwardly flagged for correction or discard.

Key features:

• Computational vs. erasure subspaces: The encoded information resides in a protected computational subspace (e.g., |0⟩, |1⟩ for a qubit or dual-spin codes), with leakage proceeding to auxiliary levels (ancilla, loss, or noncomputational modes).
• Detection mechanisms: These include fluorescence or parity measurements, composite detection circuits, ancilla-coupled circuits, dispersive readout, or dynamical syndrome checks.
• Mathematical formalism: The process is described using Kraus operators, POVMs, or channel twirling, resulting in an explicit erasure channel:

$$\mathcal{E}(\rho) = (1-p_\mathrm{era}) P_C \rho P_C + p_\mathrm{era} P_L \rho P_L$$

where $p_\mathrm{era}$ is the erasure probability, $P_C$ the projector onto the computational subspace, and $P_L$ onto erasure/leakage.

• Error conversion efficiency: Defined as the fraction of physical or gate errors mapped to detectable erasures, with high-performing systems often $R_e \gtrsim 0.9$.

2. Physical Implementations Across Quantum Platforms

Erasure conversion protocols have been realized and analyzed in a variety of platforms, each leveraging specific Hamiltonian structure, dissipation pathways, and detection methods.

• Semiconductor Spin Qubits: Singlet-triplet encoding in double quantum dots allows single-spin bit flips (local $X$) to map to leakage, which is efficiently projected and detected via leakage-detection gadgets. This hardware-efficient, feedback-free protocol automatically returns leaked pairs to the computational subspace, with strong synergies to biased surface codes (XZZX) (Siegel et al., 15 Jan 2026).
• Molecular Tweezer Arrays: Mid-circuit composite detection uses hyperfine shelving, trap-depth control, and fluorescence imaging to resolve population outside the qubit manifold, thereby flagging blackbody- or state-prep-induced leakage events as erasures with >96% fidelity (Holland et al., 2024).
• Trapped Ions (Metastable Qubits): Encoding in metastable D$_{5/2}$ levels of $^{40}$Ca$^+$ ions, together with rapid fluorescence checks, allows nearly all spontaneous Raman scattering errors (and essentially all natural decays) to be flagged as erasures. Integration with high-fidelity gates yields fault tolerance at code thresholds surpassing 5% for pure erasure errors (Quinn et al., 2024).
• Alkaline-Earth Rydberg Atom Arrays: By encoding qubits in $^3$P$p_\mathrm{era}$0 manifolds and monitoring population transfer to $p_\mathrm{era}$1S$p_\mathrm{era}$2 or other Rydberg levels, spontaneous decay is mapped to detectable states via rapid fluorescence or ion-loss detection. An erasure conversion efficiency $p_\mathrm{era}$3 is achieved, consistent with a fourfold increase in surface-code threshold (Wu et al., 2022).
• Neutral Atom Arrays and LDUs: Circuit-based leakage detection units (LDUs) realize ancilla-coupled, non-destructive erasure conversion. Gate-based protocols (e.g., Rydberg dressing gates) preserve the quantum information for non-leaked atoms and swap out leaked or lost atoms with ancillas, attaining >93% erasure detection probability (Chow et al., 2024).
• Majorana Qubits: Local measurement of the quasiparticle position operator allows detection of Wannier quasiparticles (WQPs) near Majorana-zero modes, converting fermion-parity-changing Poisoning errors into erasures with an exponentially small Pauli escape probability in the size of the measured region (Alase et al., 2023).
• Integer Fluxonium and Superconducting Circuits: Parity-protection mechanisms and dispersive readout in multi-level fluxonium or dual-rail qubits convert $p_\mathrm{era}$4 relaxation outside the code space into heralded erasures, achieving >20x enhancement of effective coherence and dramatically lowering logical error rates (Wang et al., 22 Mar 2026, Gu et al., 2023).

3. Protocol Design, Circuit Integration, and Mathematical Modeling

Erasure conversion protocols are integrated into computational or memory circuits using both hardware and software primitives.

• Segmentation and erasure checks: Circuits are partitioned into segments by the insertion of erasure checks. Each segment’s outcome determines where and with what probability Pauli errors are injected, with independence (approximate) or full joint correlation (exact) preserved according to decoding requirements (Bhave et al., 7 Feb 2026).
• Error propagation and mapping to stabilizer circuits: Erasure-annotated circuits are efficiently mapped to standard stabilizer-based decoding architectures. Mathematical tools include hypergraph matching, minimum-weight perfect matching, and syndrome tracking. Engineered schedules (e.g., 2EC, 4EC) balance overhead, detection timeliness, and throughput (Bhave et al., 7 Feb 2026).
• Noise models: Erasure-prone systems are characterized by parameters: site erasure rate $p_\mathrm{era}$5, depolarizing rate $p_\mathrm{era}$6, and flag bit-flip rate $p_\mathrm{era}$7. Conversion maps complex error processes into erasure-dominated stochastic processes whose logical error scaling is governed by code distance $p_\mathrm{era}$8: $p_\mathrm{era}$9, with exponent $P_C$0 set by the erasure rate (Gu et al., 2023).

4. Impact on Quantum Error Correction, Resource Scaling, and Fault-Tolerance

The central advantage of erasure conversion is improved correctability—erasure errors, being located, are much easier to correct than arbitrary Pauli errors. This is quantified by dramatic increases in code thresholds and reductions in logical error rates and required code distances.

• Threshold enhancement: Erasure conversion commonly increases code thresholds by factors of 2–5; e.g., $P_C$1 (Pauli) rises to $P_C$2 (erasure-dominated) for surface codes, and up to $P_C$3 for XZZX codes with singlet-triplet encoding (Wu et al., 2022, Siegel et al., 15 Jan 2026).
• Logical error suppression: For erasure codes, logical failure probabilities scale exponentially in $P_C$4 instead of $P_C$5, effectively doubling the error distance for a given code size and achieving order-of-magnitude reductions at fixed $P_C$6.
• Resource overheads: Conversion reduces total ancillary resource and cycle counts for a target logical error rate by up to an order of magnitude, translating to more practical, smaller-scale, or faster QEC implementations.
• Syndrome decoding: Erasure-aware decoding (assigning zero edge-weight to flagged locations) enables efficient use of classical algorithms such as MWPM or Union-Find, and is robust to erasure-detection infidelity (Gu et al., 2023, Bhave et al., 7 Feb 2026).

5. Extensions Beyond Quantum Computing: Sensing, Classical Channels, and Thermodynamics

Erasure conversion transcends quantum computation, improving performance in metrology, communication, and classical information erasure.

• Quantum metrology under thermal noise: Encoding a logical qubit into two physical qubits and monitoring the code-parity converts amplitude-damping into heralded erasures. This restores Heisenberg scaling for parameter estimation and attains the ultimate quantum Fisher information per unit time, saturating the optimal bounds for erasure-detected channels (Arieli et al., 12 Mar 2026).
• Classical erasure queue channels and memory: In communication systems with time-correlated erasures (e.g., queueing-induced decoherence), interleaving-based “wrappers” convert arbitrary erasure patterns into memoryless equivalents, allowing capacity-achieving codes to be used with minimal adaptation (Mandalapu et al., 2023).
• Thermodynamics of majority-logic erasure: Erasure conversion at the hardware level, such as majority-logic decoding of many two-level units, can improve the speed-precision-efficiency trade-off in finite-time erasure, reducing minimal achievable error and operation time, and in some regimes even increasing erasure efficiency (Sheng et al., 2019).

6. Performance Metrics, Experimental Benchmarks, and Prospects

The efficacy of erasure conversion protocols is now established across multiple physical implementations, each characterized by experimental and simulated performance benchmarks.

Platform	Erasure Conversion Efficiency	Gain in Threshold	Key Detection Mechanism
$P_C$7Ca$P_C$8 Metastable Ions	$P_C$994%	%%%%30$X$31%%%%	Fluorescence check
Alkaline-Earth Rydberg ($P_L$2Yb)	$P_L$398%	$P_L$44.4$P_L$5	Fluorescence + autoionization
Optical Tweezer Molecules	$P_L$695%	Order-of-magnitude	Composite imaging + repumping
Singlet-Triplet Spin (ST)	$P_L$7	%%%%38$P_L$39%%%%	Hardware-efficient exchange gadget
Neutral Atom Arrays (LDUs)	$R_e \gtrsim 0.9$093–96%	Code goes from 0 to $R_e \gtrsim 0.9$1	Ancilla-based circuit
Majorana Qubits	$R_e \gtrsim 0.9$2 escape	Double threshold	WQP parity measurements

Limitations and open directions include optimizing detection overhead, improving false-positive/negative rates, exploiting non-Markovian or higher-dimensional leakage structures, and extending design criteria across platforms (including superconducting qubits, molecular arrays, and hybrid architectures).

Erasure conversion is now a cornerstone for the next generation of scalable, resource-frugal, and robust quantum technologies. It is a cross-cutting principle linking hardware engineering, control theory, error correction, and metrology (Siegel et al., 15 Jan 2026, Holland et al., 2024, Quinn et al., 2024, Wu et al., 2022, Gu et al., 2023, Bhave et al., 7 Feb 2026, Arieli et al., 12 Mar 2026).