Out-of-distribution generalisation for learning quantum channels with low-energy coherent states
arXiv:2502.04454 · doi:10.1103/5m7p-kbf3
Abstract
When experimentally learning the action of a continuous variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is using low energy coherent states. Learning a quantum channel in this way presents difficulties, due to the fact that two channels may act similarly on low energy inputs but very differently for high energy inputs. They may also act similarly on coherent state inputs but differently on non-classical inputs. Extrapolating the behaviour of a channel for more general input states from its action on the far more limited set of low energy coherent states is a case of out-of-distribution generalisation. To be sure that such generalisation gives meaningful results, one needs to relate error bounds for the training set to bounds that are valid for all inputs. We show that for any pair of channels that act sufficiently similarly on low energy coherent state inputs, one can bound how different the input-output relations are for any (high energy or highly non-classical) input. This proves out-of-distribution generalisation is always possible for learning quantum channels using low energy coherent states, as long as enough samples are used.
37 pages, 7 figures. Similar to published version. Supplemental material available in the source folder
References in corpus (43)
- Quantum information with continuous variables
- Gaussian Quantum Information
- Deep Learning with Coherent Nanophotonic Circuits
- Review article: Linear optical quantum computing
- Quantum principal component analysis
- Fundamental Limits of Repeaterless Quantum Communications
- General Benchmarks for Quantum Repeaters
- Continuous-variable optical quantum state tomography
- Power of data in quantum machine learning
- Generalization in quantum machine learning from few training data
- Quantum fidelity for arbitrary Gaussian states
- Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
- Generalization in Quantum Machine Learning: a Quantum Information Perspective
- Learning Quantum Systems
- Demonstration of a Reconfigurable Entangled Radiofrequency-Photonic Sensor Network
- Complete Characterization of Quantum-Optical Processes
- Entanglement-Enhanced Optomechanical Sensing
- Fundamental limits to quantum channel discrimination
- Towards Large-Scale Quantum Networks
- Experimental determination of a nonclassical Glauber-Sudarshan P function
- Quantum process tomography with coherent states
- Practical route to entanglement-assisted communication over noisy bosonic channels
- Out-of-distribution generalization for learning quantum dynamics
- Continuous-variable quantum probes for structured environments
- Energy-constrained diamond norms and their use in quantum information theory
- Ultimate accuracy limit of quantum pulse-compression ranging
- Squeezed dual-comb spectroscopy
- Ultimate limits for multiple quantum channel discrimination
- Quantum probes for the characterization of nonlinear media
- Negativity of quasiprobability distributions as a measure of nonclassicality
- Entanglement-enhanced optomechanical sensor array for dark matter searches
- Wigner Function Tomography via Optical Parametric Amplification
- Dynamical simulation via quantum machine learning with provable generalization
- Quantitative tomography for continuous variable quantum systems
- Entanglement-enhanced dual-comb spectroscopy
- Characterization of conditional state-engineering quantum processes by coherent state quantum process tomography
- Efficient tomography of quantum-optical Gaussian processes probed with a few coherent states
- Statistical Complexity of Quantum Learning
- Ancilla-free continuous-variable SWAP test
- Ancilla-Error-Transparent Controlled Beam Splitter Gate
- Efficient Learning of Continuous-Variable Quantum States
- Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
- Quantum process tomography of continuous-variable gates using coherent states