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GSQAS: Graph Self-supervised Quantum Architecture Search

Zhimin He, Maijie Deng, Shenggen Zheng, Lvzhou Li, Haozhen Situ

TL;DR

Quantum architecture search is limited by the need to evaluate a vast number of candidate circuits. GSQAS introduces graph-based circuit encoding combined with graph-based self-supervised learning to pretrain a circuit encoder on unlabeled data and then fine-tune with a small set of labeled circuits, significantly reducing ground-truth evaluations. The method leverages a VGAE with a GIN-based encoder to learn informative latent representations and uses a downstream predictor to estimate circuit performance with minimal labeled data. Across VQE for TFIM and a quantum state classifier, GSQAS with unsupervised representation learning (URL) and pre-training/fine-tuning (PF) consistently outperforms the traditional predictor-based QAS using image encodings, achieving higher accuracy or better energy estimates while requiring fewer labeled circuits and fewer total ground-truth evaluations.

Abstract

Quantum Architecture Search (QAS) is a promising approach to designing quantum circuits for variational quantum algorithms (VQAs). However, existing QAS algorithms require to evaluate a large number of quantum circuits during the search process, which makes them computationally demanding and limits their applications to large-scale quantum circuits. Recently, predictor-based QAS has been proposed to alleviate this problem by directly estimating the performances of circuits according to their structures with a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is very time-consuming to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS, which trains a predictor based on self-supervised learning. Specifically, we first pre-train a graph encoder on a large number of unlabeled quantum circuits using a well-designed pretext task in order to generate meaningful representations of circuits. Then the downstream predictor is trained on a small number of quantum circuits' representations and their labels. Once the encoder is trained, it can apply to different downstream tasks. In order to better encode the spatial topology information and avoid the huge dimension of feature vectors for large-scale quantum circuits, we design a scheme to encode quantum circuits as graphs. Simulation results on searching circuit structures for variational quantum eigensolver and quantum state classification show that GSQAS outperforms the state-of-the-art predictor-based QAS, achieving better performance with fewer labeled circuits.

GSQAS: Graph Self-supervised Quantum Architecture Search

TL;DR

Quantum architecture search is limited by the need to evaluate a vast number of candidate circuits. GSQAS introduces graph-based circuit encoding combined with graph-based self-supervised learning to pretrain a circuit encoder on unlabeled data and then fine-tune with a small set of labeled circuits, significantly reducing ground-truth evaluations. The method leverages a VGAE with a GIN-based encoder to learn informative latent representations and uses a downstream predictor to estimate circuit performance with minimal labeled data. Across VQE for TFIM and a quantum state classifier, GSQAS with unsupervised representation learning (URL) and pre-training/fine-tuning (PF) consistently outperforms the traditional predictor-based QAS using image encodings, achieving higher accuracy or better energy estimates while requiring fewer labeled circuits and fewer total ground-truth evaluations.

Abstract

Quantum Architecture Search (QAS) is a promising approach to designing quantum circuits for variational quantum algorithms (VQAs). However, existing QAS algorithms require to evaluate a large number of quantum circuits during the search process, which makes them computationally demanding and limits their applications to large-scale quantum circuits. Recently, predictor-based QAS has been proposed to alleviate this problem by directly estimating the performances of circuits according to their structures with a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is very time-consuming to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS, which trains a predictor based on self-supervised learning. Specifically, we first pre-train a graph encoder on a large number of unlabeled quantum circuits using a well-designed pretext task in order to generate meaningful representations of circuits. Then the downstream predictor is trained on a small number of quantum circuits' representations and their labels. Once the encoder is trained, it can apply to different downstream tasks. In order to better encode the spatial topology information and avoid the huge dimension of feature vectors for large-scale quantum circuits, we design a scheme to encode quantum circuits as graphs. Simulation results on searching circuit structures for variational quantum eigensolver and quantum state classification show that GSQAS outperforms the state-of-the-art predictor-based QAS, achieving better performance with fewer labeled circuits.
Paper Structure (19 sections, 12 equations, 11 figures, 2 tables)

This paper contains 19 sections, 12 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Terminologies and notations
  3. Related works
  4. Quantum architecture search
  5. Self-supervised learning
  6. Graph self-supervised quantum architecture search (GSQAS)
  7. Circuit encoding scheme
  8. Pretext task learning
  9. Encoder
  10. Decoder
  11. Pretext training
  12. Downstream predictor learning
  13. Results
  14. Variational quantum eigensolver for TFIM
  15. 2D visualization of the proposed circuit encoding
  16. ...and 4 more sections

Figures (11)

  • Figure 1: The workflow of predictor-based QAS. (1)Predictor training: train a predictor using a small set of circuits as well as their ground-truth performances. The ground-truth performances are obtained by circuit training. (2)Large-scale screening: sample a large number of quantum circuits from the search space and estimate their performances by the trained predictor. (3)Final selection: select the top-K best circuits according to the predicted performances as candidate circuits, calculate their ground-truth performances, and output the top-1 best circuit according to the ground-truth performances.
  • Figure 2: The predictor training part of GSQAS. Stage 1: unsupervised learning of a pretext task using a large number of unlabeled circuits. Stage 2: fine-tuning the encoder and the predictor using a small number of labeled circuits. The blue lines indicate the workflow of Stage 1 while the red lines denote the workflow of Stage 2.
  • Figure 3: An example of the graph encoding scheme.
  • Figure 4: The architecture of the predictor.
  • Figure 5: Energy distribution of the TFIM model with 50,000 randomly generated quantum circuits. The energy of a quantum circuit is calculated by optimizing the gate parameters of this circuit until convergence. The inset shows the distribution between -7.8 and -7.4.
  • ...and 6 more figures