Co-Designing Error Mitigation and Error Detection for Logical Qubits

2026-04-21

AI Summary

This work addresses the limitations of quantum error detection (QED) and probabilistic error cancellation (PEC) in near-term quantum computing, where each approach is constrained by either resource overhead or accuracy and lacks synergistic design. The paper introduces the first joint optimization framework that integrates QED and PEC through a tunable QED measurement interval, a steady-state error extraction protocol, and a high-rate Iceberg logical encoding scheme, enabling efficient hardware-software co-designed error mitigation. When applied to the [[6,4,2]] Iceberg code in QAOA executions, the proposed method reduces absolute error by 2–11× and mean squared error by up to 31× compared to PEC on physical qubits, achieving substantially lower resource costs without compromising accuracy.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Near-term quantum workloads demand error management, yet the two lightest-weight techniques, Quantum Error Detection (QED) and Probabilistic Error Cancellation (PEC), have complementary cost profiles whose joint architectural design space remains unexplored. QED encodes logical qubits and discards error-flagged runs, filtering noise with low qubit overhead but leaving residual errors; PEC can correct these in software, but at exponential cost in noise strength. If QED efficiently reduces per-gate noise, PEC's cost savings can outweigh QED's discard overhead; realizing this, however, requires solving two system-level design challenges. First, the \textit{QED interval} -- how often detection cycles are inserted -- is a tunable architectural parameter governing the cost-accuracy tradeoff. We derive an efficiency condition and show that the canonical one-cycle-per-gate frequency does not achieve break-even in any code we evaluate, while optimized intervals on high-rate Iceberg codes do. Second, we discover that naive PEC+QED integration \textit{degrades} accuracy below the QED-only baseline. The root cause is a transient error profile in the first detection cycle that corrupts PEC's noise model. We develop \textit{steady-state extraction}, a co-designed characterization protocol that isolates steady-state error behavior, reducing estimation bias by up to $10.2\times$. On a $[[6,4,2]]$ Iceberg code running QAOA ($p{=}4$--$8$) with a fixed shot budget, PEC+QED achieves $2$--$11\times$ lower absolute error and up to $31\times$ lower MSE versus PEC on physical qubits, with per-interval savings compounding over interval depth.

Problem

• Quantum Error Detection
• Probabilistic Error Cancellation
• Logical Qubits
• Error Mitigation
• Error Management

Innovation

• Quantum Error Detection
• Probabilistic Error Cancellation
• Co-Design
• Steady-State Extraction
• Iceberg Code