Variational Quantum Algorithms
- M. Cerezo, A. Arrasmith, Patrick J. Coles
- Physics, Computer ScienceNature Reviews Physics
- 16 December 2020
An overview of the field of Variational Quantum Algorithms is presented and strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage are discussed.
Cost function dependent barren plateaus in shallow parametrized quantum circuits
- M. Cerezo, A. Sone, T. Volkoff, L. Cincio, Patrick J. Coles
- Computer ScienceNature Communications
- 19 March 2021
This work rigorously proves two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs, that establish a connection between locality and trainability.
Quantum-assisted quantum compiling
- Sumeet Khatri, Ryan LaRose, Alexander Poremba, L. Cincio, A. Sornborger, Patrick J. Coles
- Computer ScienceQuantum
- 2 July 2018
This work proposes a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC), and presents both gradient-free and gradient-based approaches to minimizing the cost of this algorithm's cost.
Entropic uncertainty relations and their applications
This review surveys entropic uncertainty relations that capture Heisenberg’s idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements.
Improved entropic uncertainty relations and information exclusion relations
This work provides a more stringent formulation of both the uncertainty principle and the information exclusion principle, with direct applications for, e.g., the security analysis of quantum key distribution, entanglement estimation, and quantum communication.
Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks
Two results are rigorously proved that establish a connection between locality and trainability in VQAs and illustrate these ideas with large-scale simulations of a particular VQA known as quantum autoencoders.
Noise-induced barren plateaus in variational quantum algorithms
This work rigorously proves a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau, and proves that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n.
Connecting ansatz expressibility to gradient magnitudes and barren plateaus
The resulting bounds indicate that highly expressive ansätze exhibit high cost landscapes and therefore will be harder to train, and the implications for designing strategies to avoid barren plateaus are discussed.
Numerical approach for unstructured quantum key distribution
A robust numerical approach is developed for calculating the key rate for arbitrary discrete-variable QKD protocols that will allow researchers to study ‘unstructured' protocols, that is, those that lack symmetry.
Quantum Algorithm Implementations for Beginners
- Patrick J. Coles, S. Eidenbenz, Wei Zhu
- Computer Science, PhysicsACM Transactions on Quantum Computing
- 10 April 2018
This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations and shows how these algorithms can be implemented on IBM’s quantum computer.