Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning
arXiv:2105.01049 · doi:10.1103/PRXQuantum.2.040327
Abstract
Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete variable hardware, less has been paid to compiling in the continuous variable paradigm. Here we motivate several, closely related, short depth continuous variable algorithms for quantum compilation. We analyse the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr non-linearities. We further make connections between this framework and quantum learning theory in the continuous variable setting by deriving No-Free-Lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using Two-Mode-Squeezed states.
arXiv comment20 pages, 7 figures
References in corpus (47)
- A variational eigenvalue solver on a quantum processor
- Quantum sensing
- Variational Quantum Algorithms
- Deep Learning with Coherent Nanophotonic Circuits
- Barren plateaus in quantum neural network training landscapes
- Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
- Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
- Operational Resource Theory of Coherence
- Universal Quantum Computation with Continuous-Variable Cluster States
- Noise-Induced Barren Plateaus in Variational Quantum Algorithms
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Connecting ansatz expressibility to gradient magnitudes and barren plateaus
- Continuous-variable quantum neural networks
- An initialization strategy for addressing barren plateaus in parametrized quantum circuits
- Quantum-assisted quantum compiling
- Absence of Barren Plateaus in Quantum Convolutional Neural Networks
- Performance and structure of single-mode bosonic codes
- Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
- Effect of barren plateaus on gradient-free optimization
- Noise Resilience of Variational Quantum Compiling
- Monotone Riemannian Metrics and Relative Entropy on Non-Commutative Probability Spaces
- Large gradients via correlation in random parameterized quantum circuits
- Entanglement Devised Barren Plateau Mitigation
- Barren plateaus preclude learning scramblers
- Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
- Machine learning method for state preparation and gate synthesis on photonic quantum computers
- On barren plateaus and cost function locality in variational quantum algorithms
- Quantum machine learning over infinite dimensions
- Variational Quantum Unsampling on a Quantum Photonic Processor
- Quantum process tomography of unitary and near-unitary maps
- Multiparameter squeezing for optimal quantum enhancements in sensor networks
- Training Gaussian Boson Sampling Distributions
- Long-time simulations with high fidelity on quantum hardware
- Process tomography for unitary quantum channels
- Exact gate decompositions for photonic quantum computing
- Continuous-variable gate decomposition for the Bose-Hubbard model
- Quantum data hiding with continuous variable systems
- Fast optimization of parametrized quantum optical circuits
- Invariant integration over the orthogonal group
- Error mitigation on a near-term quantum photonic device
- Optimal tests for continuous-variable quantum teleportation and photodetectors
- Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians
- No Free Lunch for Quantum Machine Learning
- Generating accessible entanglement in bosons via pair-correlated tunneling
- Nonclassical properties and quantum resources of hierarchical photonic superposition states
- Bosonic data hiding: power of linear vs non-linear optics
- Towards quantum simulation of spin systems using continuous variable quantum devices