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Can Noise on Qubits Be Learned in Quantum Neural Network? A Case Study on QuantumFlow

Zhiding Liang, Zhepeng Wang, Junhuan Yang, Lei Yang, Jinjun Xiong, Yiyu Shi, Weiwen Jiang

arXiv:2109.03430v2quant-phcs.LG

TL;DR

NISQ computers face high qubit noise and limited capacity, while quantum error correction requires many physical qubits. This paper uses QuantumFlow to combine application-specific mapping with error-aware QNN training; on ibmq_montreal, its QF-RobustNN and application-specific compiler achieved 80% accuracy versus 74% for the baseline model with the proposed compiling approach.

  • Problem

    NISQ computers have high noise and limited qubit counts, while quantum error correction may require over 1,000 physical qubits for one perfect qubit.

    Source: §I · p. 1

  • Method

    The paper combines a QuantumFlow-specific mapping algorithm with error-aware training to identify robust QNN models.

    Source: §I · pp. 1–2

  • Results

    On ibmq_montreal, QF-RobustNN with the application-specific compiler achieved 80% accuracy, versus 74% for the baseline model with the proposed compiling approach.

    Source: C. Accuracy, Efficiency, and Circuit… · p. 6

  • Takeaways & Limitations

    The approach targets QNN noise mitigation with no or only a small number of additional physical qubits.

    Source: §I · p. 1

    Training was performed on classical computing in this implementation; integration into quantum computing is described for when hardware is ready for QNNs.

    Source: §I · p. 2

Abstract

from arXiv · show

In the noisy intermediate-scale quantum (NISQ) era, one of the key questions is how to deal with the high noise level existing in physical quantum bits (qubits). Quantum error correction is promising but requires an extensive number (e.g., over 1,000) of physical qubits to create one "perfect" qubit, exceeding the capacity of the existing quantum computers. This paper aims to tackle the noise issue from another angle: instead of creating perfect qubits for general quantum algorithms, we investigate the potential to mitigate the noise issue for dedicate algorithms. Specifically, this paper targets quantum neural network (QNN), and proposes to learn the errors in the training phase, so that the identified QNN model can be resilient to noise. As a result, the implementation of QNN needs no or a small number of additional physical qubits, which is more realistic for the near-term quantum computers. To achieve this goal, an application-specific compiler is essential: on the one hand, the error cannot be learned if the mapping from logical qubits to physical qubits exists randomness; on the other hand, the compiler needs to be efficient so that the lengthy training procedure can be completed in a reasonable time. In this paper, we utilize the recent QNN framework, QuantumFlow, as a case study. Experimental results show that the proposed approach can optimize QNN models for different errors in qubits, achieving up to 28% accuracy improvement compared with the model obtained by the error-agnostic training.

I. INTRODUCTION

NISQ computers combine high noise with limited qubit counts, while quantum error correction requires over 1,000 physical qubits for a perfect qubit. The paper targets noise-resilient QNNs through application-specific mapping and error-aware training.

  • QEC may require more than 1,000 physical qubits to create one perfect qubit, beyond the limited capacity of NISQ computers.The paper therefore seeks a noise-mitigation approach requiring no or few additional qubits.Source: §I · p. 1
  • The paper targets application-specific noise mitigation for QNNs, aiming to learn errors during training without requiring many additional physical qubits.QNNs are proposed as candidates for noise resilience, rather than creating perfect qubits for general algorithms.Source: §I · p. 1
  • Mapping and training pose linked challenges: hardware implementations can vary, mapping must be integrated into lengthy training, and noisy weight updates can affect other weights.The paper identifies these challenges as reasons traditional training is not directly applicable.Source: §I · p. 1
  • The proposed QuantumFlow-specific mapping fixes logical-to-physical qubit mapping across quantum computers, minimizes physical gates, and uses a consistent procedure to reduce optimization time.The mapping is designed to support neural-network training.Source: §I · p. 1
  • The paper introduces an error-aware training framework for identifying robust QNNs, with training performed on classical computers in this implementation.The framework is described as extensible to quantum-computer training when hardware reaches a suitable scale for QNNs.Source: §I · p. 2
  • The authors present QF-RobustNN as a robust QNN obtained by learning quantum errors, alongside an application-specific mapping method for QuantumFlow.They describe the work as, to their best knowledge, the first to learn quantum error in QNNs.Source: §I · p. 2

II. PRELIMINARIES

The section introduces qubits, gates, circuits, and processors, then describes how connectivity limits and noise shape quantum compilation. QuantumFlow is an important target because training it can require compiling many weight-specific circuits.

Quantum Gates and Circuits

  • Quantum circuits combine quantum gates; circuit depth reflects algorithm time complexity, while circuit width indicates the number of qubits used.Clifford gates together with the T gate form a universal gate set.Source: §II · p. 2

Quantum Processor

  • A quantum processor has physical qubits that may be incompletely connected and subject to operating noise.BRIDGE and SWAP operations can enable communication between separated qubits, but require additional CNOT gates.Source: §II · p. 2

Noisy Qubits

  • Qubit errors include state flips, phase shifts, readout assignment errors, and depolarization.Readout errors are represented by probabilities P(n|m) relating noisy measurement n to ideal measurement m.Source: §II · pp. 2–3

Target Quantum Application

  • QuantumFlow and other QNNs may require compiling many distinct circuits as their weights change, creating a high demand for compiler efficiency.A quantum compiler maps logical circuits to physical qubits and may optimize gate count, circuit depth, or fidelity.Source: §II · p. 3

III. MOTIVATION

The motivation is to learn QNN weights that account for qubit noise, while addressing unpredictable error exposure and costly compilation. A fixed, efficient mapping is needed to make error-aware training practical.

Noise effects

  • 45.10% accuracy is reported for QuantumFlow with both bit-flip and phase errors at rate 0.1, versus 98.04% on perfect qubits.At rate 0.01, the combined-error accuracy is 77.78%; bit-flip and phase errors separately also reduce accuracy from the perfect-qubit result.Source: §III · p. 3

Motivation

  • The paper proposes learning errors during QNN training so the resulting model can be more robust to noise.This aim is framed as addressing noise effects in a dedicated algorithm rather than relying only on general quantum error correction.Source: §III · pp. 3–4

Error unpredictability

  • Different weights can change the logical-to-physical qubit mapping, so the same weight may encounter different errors across QNN models.The L1 and L2 example maps q0 and q1 to different physical qubits after weight-dependent circuit changes.Source: §III · p. 3

Compiler efficiency

  • More than 400 seconds are needed to compile a six-gate circuit with the tested general-purpose compiler configuration.The passage notes that QuantumFlow circuits are more complicated and compilation would be repeated for each newly identified training weight.Source: §III · p. 3

A. Problem Statement

The paper frames error-aware QNN training as a search for weights that maximize accuracy while accounting for physical-qubit errors. It also defines the compiler mapping needed to support that training.

A. Problem Statement

  • Quantum-error-aware training searches for neural-network weights that maximize model accuracy while considering errors on physical qubits.The problem assumes a given network and its implementation on physical qubits.Source: A. Problem Statement · p. 4
  • The implementation of each quantum circuit requires compilation, motivating an application-specific compiler for the training procedure.The paper treats compiler design as a supporting problem for error-aware training.Source: A. Problem Statement · p. 4
  • The application-specific compiler maps a logical circuit to a processor so each qubit has a fixed physical mapping while circuit length is minimized.Its stated inputs are a dataset, quantum algorithm, and quantum processor.Source: A. Problem Statement · p. 4

B. Quantum-error-aware training framework

The framework iteratively maps QuantumFlow circuits, builds mapping-dependent error models, evaluates accuracy, and updates weights. Its mapping procedure uses fixed logical-to-physical correspondence and routing operations to handle gate connectivity.

B. Quantum-error-aware training framework

  • Each training iteration obtains a QuantumFlow circuit, maps it to physical qubits, builds its error model, evaluates accuracy, and updates the weights.The framework starts from trained weights and outputs QF-RobustNN when training converges.Source: B. Quantum-error-aware training… · p. 4
  • A controller can use accuracy to update its parameters and generate new QNN weights, selecting the highest-accuracy result as Searched_Weight.The framework allows different optimization approaches, with an RNN-based controller given as an example.Source: B. Quantum-error-aware training… · p. 4
  • The mapping description uses CCCZ and decomposed CCX gates alongside a physical-qubit coupling graph to specify connectivity and routing.Qn denotes the physical qubit corresponding to logical qn, and AUXn denotes the physical qubit corresponding to auxiliary qubit auxn.Source: B. Quantum-error-aware training… · pp. 4–5, Figure 4 · p. 5
  • The mapping design aims to restore the same logical-to-physical mapping at the procedure’s end while avoiding additional SWAP gates to minimize circuit length.Computing and auxiliary qubits are interleaved in a chain, and CCX processing is divided into forward and backward phases.Source: B. Quantum-error-aware training… · p. 5
  • Forward routing inserts a SWAP to connect required qubits, while backward routing uses a BRIDGE to connect Q2 and AUX0 with fewer basic CNOT gates than two SWAPs.The example states that BRIDGE uses three basic gates where two SWAPs would cost eight.Source: B. Quantum-error-aware training… · p. 5

V. RESULTS AND DISCUSSIONS

The evaluation uses a synthetic-dataset baseline for accuracy comparisons and existing compilers for efficiency comparisons.

  • The baseline for accuracy comparison is an initial weight that performs best on a synthetic dataset in the perfect model.Source: §V · p. 5
  • Existing compilers serve as the baselines for efficiency comparison.Source: §V · p. 5
  • The setup distinguishes accuracy and efficiency comparisons by using different baselines.Source: §V · p. 5

A. Accuracy Comparison

QF-RobustNN is evaluated in simulation under bit-flip and phase-shift errors and on an IBM quantum processor; under larger simulated errors, it outperforms the perfect-setting baseline.

A. Accuracy Comparison

B. Efficiency Comparison

The application-specific compiler maps circuits in under 0.1 seconds, exceeding 200× speedup over HA, while general-purpose compiler runtimes vary sharply with circuit complexity.

B. Efficiency Comparison

  • QUEKO takes 484.775 seconds for simple circuits and 5332.903 seconds for middle circuits, and cannot optimize complex circuits within 10 hours.Source: B. Efficiency Comparison · p. 6
  • The efficiency comparison uses three circuits with simple, middle, and complex levels; HA completes all three within 5 seconds.Source: B. Efficiency Comparison · p. 6
  • Over 200× speedup over HA is achieved by the application-specific compiler, which completes mapping within 0.1 seconds.The authors report that this efficiency allows the compiler to be integrated into the training framework.Source: B. Efficiency Comparison · p. 6

C. Accuracy, Efficiency, and Circuit Depth

On ibmq_montreal, the application-specific compiler and QF-RobustNN achieve higher accuracy than the baseline model, while using fewer extra SWAP gates than HA.

C. Accuracy, Efficiency, and Circuit Depth

VI. CONCLUSION

The proposed error-aware optimization framework targets qubit noise in QNNs by learning errors during training and using an application-specific compiler. Results on simulated and actual quantum computers demonstrate improved performance.

VI. CONCLUSION

  • Results on both simulation and actual quantum computers demonstrate that error-aware optimization can improve performance.Source: §VI · p. 6
  • The framework targets QNNs by learning qubit errors during training to mitigate noise.Source: §VI · p. 6
  • An application-specific compiler is proposed to provide efficient mapping for the lengthy training procedure.Source: §VI · p. 6
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