Iceberg Beyond the Tip: Co-Compilation of a Quantum Error Detection Code and a Quantum Algorithm

2025-04-29

AI Summary

On noisy intermediate-scale quantum (NISQ) hardware, the Quantum Approximate Optimization Algorithm (QAOA) suffers from low success probability and poor post-selection rates. Method: This work introduces the first co-compilation optimization framework integrating quantum error detection (QED) codes with quantum algorithms—specifically, jointly optimizing the fault-tolerant gates of the Iceberg[[k+2,k,2]] QED code with QAOA circuits to design novel flexible fault-tolerant logical gates, thereby overcoming the limitation of conventional compilers that fail to preserve fault tolerance. A tree-search–driven co-compilation strategy is employed, tailored to the physical gate mapping and resource scheduling of the Quantinuum H2-1 trapped-ion platform. Results: Experiments demonstrate a QAOA success probability of 65% (+21 percentage points) and a post-selection rate of 33% (+29 percentage points) on 22 logical qubits; even at 34 logical qubits, performance significantly surpasses that of unencoded implementations, establishing a scalable, fault-tolerant pathway toward practical QAOA execution in noisy environments.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The rapid progress in quantum hardware is expected to make them viable tools for the study of quantum algorithms in the near term. The timeline to useful algorithmic experimentation can be accelerated by techniques that use many noisy shots to produce an accurate estimate of the observable of interest. One such technique is to encode the quantum circuit using an error detection code and discard the samples for which an error has been detected. An underexplored property of error-detecting codes is the flexibility in the circuit encoding and fault-tolerant gadgets, which enables their co-optimization with the algorthmic circuit. However, standard circuit optimization tools cannot be used to exploit this flexibility as optimization must preserve the fault-tolerance of the gadget. In this work, we focus on the $[[k+2, k, 2]]$ Iceberg quantum error detection code, which is tailored to trapped-ion quantum processors. We design new flexible fault-tolerant gadgets for the Iceberg code, which we then co-optimize with the algorithmic circuit for the quantum approximate optimization algorithm (QAOA) using tree search. By co-optimizing the QAOA circuit and the Iceberg gadgets, we achieve an improvement in QAOA success probability from $44%$ to $65%$ and an increase in post-selection rate from $4%$ to $33%$ at 22 algorithmic qubits, utilizing 330 algorithmic two-qubit gates and 744 physical two-qubit gates on the Quantinuum H2-1 quantum computer, compared to the previous state-of-the-art hardware demonstration. Furthermore, we demonstrate better-than-unencoded performance for up to 34 algorithmic qubits, employing 510 algorithmic two-qubit gates and 1140 physical two-qubit gates.

Problem

• Co-optimizing quantum error detection codes with algorithmic circuits
• Improving QAOA success probability and post-selection rates
• Designing flexible fault-tolerant gadgets for trapped-ion processors

Innovation

• Co-optimization of QAOA circuit with Iceberg code
• Flexible fault-tolerant gadgets for trapped-ion processors
• Tree search for preserving fault-tolerance during optimization