Expressivity of deterministic quantum computation with one qubit
arXiv:2411.02751 · doi:10.1103/PhysRevA.111.022429
Abstract
Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parameterized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as the sole quantum protocol for both training and inference. We then analyze the expressivity of the parameterized DQC1 circuits, characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.
12 pages, 5 figures
References in corpus (55)
- Quantum Computing in the NISQ era and beyond
- Variational Quantum Algorithms
- Supervised learning with quantum enhanced feature spaces
- Barren plateaus in quantum neural network training landscapes
- Quantum support vector machine for big data classification
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum machine learning in feature Hilbert spaces
- Quantum principal component analysis
- Error mitigation for short-depth quantum circuits
- Parameterized quantum circuits as machine learning models
- An adaptive variational algorithm for exact molecular simulations on a quantum computer
- Circuit-centric quantum classifiers
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- The effect of data encoding on the expressive power of variational quantum machine learning models
- Challenges and Opportunities in Quantum Machine Learning
- Connecting ansatz expressibility to gradient magnitudes and barren plateaus
- A rigorous and robust quantum speed-up in supervised machine learning
- Noise tailoring for scalable quantum computation via randomized compiling
- Practical Quantum Error Mitigation for Near-Future Applications
- Transfer learning in hybrid classical-quantum neural networks
- An initialization strategy for addressing barren plateaus in parametrized quantum circuits
- Quantum convolutional neural network for classical data classification
- Entanglement and the Power of One Qubit
- Layerwise learning for quantum neural networks
- Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
- Algorithmic Cooling and Scalable NMR Quantum Computers
- Entanglement Devised Barren Plateau Mitigation
- On the hardness of classically simulating the one clean qubit model
- ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
- The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy profiles of parameterized Hamiltonians for quantum simulation
- One qubit as a Universal Approximant
- Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
- Classical-to-quantum convolutional neural network transfer learning
- Dimensional Expressivity Analysis of Parametric Quantum Circuits
- Linear-depth quantum circuits for multiqubit controlled gates
- A Co-Design Framework of Neural Networks and Quantum Circuits Towards Quantum Advantage
- A hybrid quantum-classical approach to mitigating measurement errors
- Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
- A semi-agnostic ansatz with variable structure for quantum machine learning
- Exponential data encoding for quantum supervised learning
- Quantum readout error mitigation via deep learning
- Semi-optimal Practicable Algorithmic Cooling
- Multidimensional Fourier series with quantum circuits
- Hyperfine spin qubits in irradiated malonic acid: heat-bath algorithmic cooling
- Entanglement and deterministic quantum computing with one qubit
- Let Quantum Neural Networks Choose Their Own Frequencies
- Neural Quantum Embedding: Pushing the Limits of Quantum Supervised Learning
- Synergetic quantum error mitigation by randomized compiling and zero-noise extrapolation for the variational quantum eigensolver
- Improving Gradient Methods via Coordinate Transformations: Applications to Quantum Machine Learning
- Noise-tolerant parity learning with one quantum bit
- Thermodynamic Analysis of Algorithmic Cooling Protocols: Efficiency Metrics and Improved Designs
- Sequential optimal selection of a single-qubit gate and its relation to barren plateau in parameterized quantum circuits
- The Power of One Clean Qubit in Supervised Machine Learning
- Scalable quantum measurement error mitigation via conditional independence and transfer learning
- NMR quantum information processing