Optimization and learning of quantum programs
arXiv:1905.01318 · doi:10.1038/s41534-020-0268-2
Abstract
A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose role is to condition the operation performed by the processor. It is known that perfect channel simulation is only possible in the limit of infinitely large program states, so that finding the best program state represents an open problem in the presence of realistic finite-dimensional resources. Here we prove that the search for the optimal quantum program is a convex optimization problem. This can be solved either exactly, by minimizing a diamond distance cost function via semi-definite programming, or approximately, by minimizing other cost functions via gradient-based machine learning methods. We apply this general result to a number of different designs for the programmable quantum processor, from the shallow protocol of quantum teleportation, to deeper schemes relying on port-based teleportation and parametric quantum circuits. We benchmark the various designs by investigating their optimal performance in simulating arbitrary unitaries, Pauli and amplitude damping channels.
arXiv commentREVTeX 23 pages. 13 figures. Long version of arXiv:1905.01316
References in corpus (20)
- Quantum Machine Learning
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- Quantum Circuit Learning
- Fundamental Limits of Repeaterless Quantum Communications
- General Benchmarks for Quantum Repeaters
- An introduction to quantum machine learning
- Advances in Quantum Teleportation
- Advances in Photonic Quantum Sensing
- Quantum machine learning: a classical perspective
- Programmable quantum gate arrays
- A quantum-inspired classical algorithm for recommendation systems
- Asymptotic teleportation scheme as a universal programmable quantum processor
- Theory of channel simulation and bounds for private communication
- Fundamental limits to quantum channel discrimination
- Quantum teleportation scheme by selecting one of multiple output ports
- Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions
- Efficient universal programmable quantum measurements
- Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy
- Almost all quantum channels are equidistant
- Supervised learning of time-independent Hamiltonians for gate design
Cited by in corpus (26)
- Advances in Quantum Cryptography
- Fundamental limitations on distillation of quantum channel resources
- Ultimate limits for multiple quantum channel discrimination
- No-go theorems for quantum resource purification II: new approach and channel theory
- Training Gaussian Boson Sampling Distributions
- Gradient-descent quantum process tomography by learning Kraus operators
- Bounds on amplitude damping channel discrimination
- Mixed State Entanglement Classification using Artificial Neural Networks
- Generalization of port-based teleportation and controlled teleportation capability
- Characterising port-based teleportation as a universal simulator of qubit channels
- Multiport based teleportation -- transmission of a large amount of quantum information
- Programmability of covariant quantum channels
- Ultimate Limits of Thermal Pattern Recognition
- Optimal Multi-port-based Teleportation Schemes
- How to enhance quantum generative adversarial learning of noisy information
- Accuracy vs Memory Advantage in the Quantum Simulation of Stochastic Processes
- Gradient-descent methods for fast quantum state tomography
- Machine learning of quantum channels on NISQ devices
- An introductory review on resource theories of generalized nonclassical light
- Continuous variable port-based teleportation
- Ultimate limits of approximate unambiguous discrimination
- Analytical bounds for non-asymptotic asymmetric state discrimination
- Quantum Advantage in Storage and Retrieval of Isometry Channels
- A resource theory of asynchronous quantum information processing
- Square-root measurements and degradation of the resource state in port-based teleportation scheme
- On the distinguishability of geometrically uniform quantum states