Source-linked AI summary
Transfer learning in hybrid classical-quantum neural networks
Andrea Mari, Thomas R. Bromley, Josh Izaac, Maria Schuld, Nathan Killoran
TL;DR
The paper addresses the limited development of transfer learning for hybrid neural networks containing classical and quantum components. It proposes transfer-learning variants centered on augmenting pre-trained classical networks with variational quantum circuits, and demonstrates proof-of-concept classification on simulated and physical quantum systems. The reported experiments include successful high-resolution image classification using IBM and Rigetti processors.
Problem
The paper investigates how transfer learning can be extended to hybrid neural networks combining classical neural networks and variational quantum circuits.
Method
The paper proposes hybrid transfer-learning variants, focusing on classical networks that preprocess data and connect to variational quantum circuits through classical embedding and readout layers.
Results
Theoretical proposals receive proof-of-concept demonstrations, including successful high-resolution image classification on IBM and Rigetti quantum processors.
Takeaways & Limitations
Transfer learning is presented as a promising approach that can be particularly convenient for near-term quantum devices.
Takeaways & Limitations
Real NISQ devices impose technical constraints because quantum-network feature counts are often linked to physical system size.
Abstract
from arXiv · showhide
We extend the concept of transfer learning, widely applied in modern machine learning algorithms, to the emerging context of hybrid neural networks composed of classical and quantum elements. We propose different implementations of hybrid transfer learning, but we focus mainly on the paradigm in which a pre-trained classical network is modified and augmented by a final variational quantum circuit. This approach is particularly attractive in the current era of intermediate-scale quantum technology since it allows to optimally pre-process high dimensional data (e.g., images) with any state-of-the-art classical network and to embed a select set of highly informative features into a quantum processor. We present several proof-of-concept examples of the convenient application of quantum transfer learning for image recognition and quantum state classification. We use the cross-platform software library PennyLane to experimentally test a high-resolution image classifier with two different quantum computers, respectively provided by IBM and Rigetti.
1 Introduction
The paper extends transfer learning to hybrid classical-quantum neural networks and focuses on demonstrating its feasibility rather than comparing quantum and classical performance. It develops several transfer variants and experimentally applies classical-to-quantum transfer to high-resolution image classification.
- Transfer learning reuses a pre-trained deep network while optimizing only selected final layers for a new task and dataset.
- The study investigates transfer learning for hybrid models combining classical neural networks with variational quantum circuits.
- Three additional transfer variants emerge alongside classical-to-classical transfer: classical-to-quantum, quantum-to-classical, and quantum-to-quantum.
- Classical-to-quantum transfer can preprocess high-dimensional inputs classically before encoding selected informative features into a variational quantum circuit.
- Proof-of-principle examples cover image recognition and quantum state classification, including high-resolution image classification on IBM and Rigetti processors.
2 Hybrid classical-quantum networks
The paper describes classical and quantum networks as composable input-output maps and introduces dressed quantum circuits to connect them flexibly. These circuits use classical layers for embedding and readout while retaining a quantum circuit as the main computational component.
- Classical neural networks: A classical layer maps an n0-element input vector to an n1-element output through an affine transformation followed by an element-wise nonlinear function.
- Classical neural networks: A classical deep neural network concatenates layers whose outputs become inputs to subsequent layers, with depth and per-layer feature counts as key hyper-parameters.
- Variational quantum circuits: A quantum layer is a low-depth variational circuit implementing a unitary operation on quantum subsystems and preserving the input Hilbert-space dimension.
- Variational quantum circuits: NISQ quantum networks constrain feature counts because they are often linked to the physical system size, unlike classical feed-forward networks.
- Dressed quantum circuits: The paper addresses this constraint by adding classical preprocessing and postprocessing layers, formalized as dressed quantum circuits.
- Dressed quantum circuits: Dressed circuits train classical embedding and readout layers while decoupling input and output variable counts from the number of quantum subsystems.
- Dressed quantum circuits: A dressed quantum circuit was successfully applied to classify a nonlinear 2D spirals benchmark dataset.
3 Transfer learning
The paper formulates transfer learning between generic networks, whether classical or quantum, by transferring pre-acquired knowledge from one network to another. This abstraction treats quantum variational circuits as globally similar to classical networks when viewed as black-box maps.
- Transfer learning transfers pre-acquired knowledge from network A to network B, with either network allowed to be classical or quantum.
- The scheme is defined for generic networks because a quantum variational circuit has a global black-box structure similar to that of a classical network.
A B Transf. learn. scheme
Hybrid transfer learning reuses learned representations by connecting a trainable network B to a truncated, pre-trained network A′, with classical and quantum networks yielding several variants. The CQ approach is emphasized for NISQ-era image processing, while QC and QQ schemes support quantum-state processing and reduced quantum training time.
- Generic transfer-learning scheme: A generic transfer-learning scheme truncates pre-trained network A, uses A′ as a feature extractor, attaches trainable network B, and trains B on a new dataset or task.The weights of A′ remain fixed while the final block B is optimized.
- Hybrid variants: Hybrid variants arise because networks A and B may be classical or quantum, producing CC, CQ, QC, and QQ transfer-learning models.The transferred object is a learned representation rather than raw information.
- Classical-to-quantum transfer learning: CQ transfer learning uses classical pre-trained models to extract features, then post-processes a limited set of features with a quantum computer for tasks such as high-resolution image classification.The paper reports numerical image-classification examples and tests the algorithm on quantum computers provided by IBM and Rigetti.
- Quantum-to-classical transfer learning: QC transfer learning applies a pre-trained quantum system as a feature extractor and uses a classical network for task-specific processing, including quantum-state classification.The paper describes proof-of-concept combinations of a pre-trained quantum network with classical post-processing and multipurpose measurement scenarios.
- Scope boundary: QC use cases relying on a quantum feature extractor that outperforms classical extractors are likely beyond near-term implementation, whereas quantum-state datasets may already be realistic.This boundary reflects the paper’s stated assessment of current quantum-technology status.
- Quantum-to-quantum transfer learning: QQ transfer learning replaces final layers of a pre-trained quantum network with trainable quantum layers, reducing optimization to a smaller circuit portion.The paper motivates this scheme by the time and measurement-shot costs of training variational quantum circuits and applies it to a quantum-state classifier.
4 Examples
The examples demonstrate quantum transfer learning across nonlinear data, high-resolution images, CIFAR-10 images, and quantum states using classical and quantum pre-trained components. Results include successful classification on simulated and real quantum processors, while also revealing depth and training-resource trade-offs.
- Example 1: Dressed quantum circuit: 0.97 accuracy was achieved by the dressed quantum circuit, compared with 0.85 for the classical network on two concentric spirals.The classical counterpart served only as a qualitative benchmark, and the simulated quantum model required approximately 2 seconds versus 0.01 seconds for the classical model.
- Example 2: CQ image classification: The CQ scheme classified high-resolution ants-and-bees images after classical preprocessing and was tested with PennyLane on IBM and Rigetti quantum processors.The experiments used a pre-trained classical network and demonstrated high-resolution image classification with a hybrid classical-quantum system.
- Example 2: CQ image classification: 26 sec on ibmqx4, 7 sec on Aspen-4-4Q-A, and 2 sec on the PennyLane simulator were required to test the hybrid model over the full dataset.ResNet18 without a quantum layer required approximately 1 second as a qualitative reference; no execution-time reduction strategy was applied.
- Example 4: QC transfer learning: Quantum-network truncation produced useful features for quantum-state classification, with accuracy peaking around quantum depth q = 15 before decreasing at larger depths.The results indicate that removing final layers can preserve or improve measured features, although the truncated quantum state may be entangled or misaligned with the measurement basis.
- Example 5: QQ transfer learning: QQ transfer learning improved training efficiency, but sufficiently long training from scratch achieved the same or better results because it optimized more variational parameters.The authors identify QQ transfer learning as useful when training resources are limited or the target dataset is more expensive to obtain experimentally.
5 Conclusions
The paper develops transfer learning for hybrid classical-quantum models, including classical-quantum and quantum-quantum interfaces, and introduces dressed quantum circuits. Proof-of-concept studies support the feasibility of these approaches, including high-resolution image classification on IBM and Rigetti processors.
- Dressed quantum circuits augment variational quantum circuits with two trainable classical layers for data encoding and decoding.
- The framework supports transferring knowledge between classical and quantum components, as well as between quantum networks.
- Proof-of-concept examples demonstrate the proposed models for image recognition and quantum state classification.
- High-resolution images were successfully classified with two real quantum processors provided by IBM and Rigetti.
- The analysis concludes that transfer learning is promising and particularly convenient for near-term quantum devices.