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Quantum natural gradient generalised to non-unitary circuits
Bálint Koczor,Simon C. Benjamin +1 more
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In this article, the authors generalise quantum natural gradient to consider arbitrary quantum states (both mixed and pure) via completely positive maps; thus their circuits can incorporate both imperfect unitary gates and fundamentally non-unitary operations such as measurements.Abstract:
Variational quantum circuits are promising tools whose efficacy depends on their optimisation method. For noise-free unitary circuits, the quantum generalisation of natural gradient descent was recently introduced. The method can be shown to be equivalent to imaginary time evolution, and is highly effective due to a metric tensor reconciling the classical parameter space to the device's Hilbert space. Here we generalise quantum natural gradient to consider arbitrary quantum states (both mixed and pure) via completely positive maps; thus our circuits can incorporate both imperfect unitary gates and fundamentally non-unitary operations such as measurements. Whereas the unitary variant relates to classical Fisher information, here we find that quantum Fisher information defines the core metric in the space of density operators. Numerical simulations indicate that our approach can outperform other variational techniques when circuit noise is present. We finally assess the practical feasibility of our implementation and argue that its scalability is only limited by the number and quality of imperfect gates and not by the number of qubits.read more
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Variational Quantum Algorithms
Marco Cerezo,Marco Cerezo,Andrew Arrasmith,Andrew Arrasmith,Ryan Babbush,Simon C. Benjamin,Suguru Endo,Keisuke Fujii,Jarrod R. McClean,Kosuke Mitarai,Kosuke Mitarai,Xiao Yuan,Xiao Yuan,Lukasz Cincio,Lukasz Cincio,Patrick J. Coles,Patrick J. Coles +16 more
TL;DR: 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.
Journal ArticleDOI
Variational Quantum Algorithms
Marco Cerezo,Marco Cerezo,Andrew Arrasmith,Andrew Arrasmith,Ryan Babbush,Simon C. Benjamin,Suguru Endo,Keisuke Fujii,Jarrod R. McClean,Kosuke Mitarai,Kosuke Mitarai,Xiao Yuan,Xiao Yuan,Lukasz Cincio,Lukasz Cincio,Patrick J. Coles,Patrick J. Coles +16 more
TL;DR: Variational quantum algorithms (VQAs) as discussed by the authors use a classical optimizer to train a parameterized quantum circuit, which is a leading strategy to address the limitations of classical computers.
Posted Content
Trainability of Dissipative Perceptron-Based Quantum Neural Networks
TL;DR: This work represents the first rigorous analysis of the scalability of a perceptron-based QNN and provides quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths.
Journal ArticleDOI
Solving nonlinear differential equations with differentiable quantum circuits
TL;DR: A hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions is described, and how this approach can implement a spectral method for solving differential equations in a high-dimensional feature space is shown.
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Noisy intermediate-scale quantum (NISQ) algorithms
Kishor Bharti,Alba Cervera-Lierta,Thi Ha Kyaw,Tobias Haug,Sumner Alperin-Lea,Abhinav Anand,Matthias Degroote,Hermanni Heimonen,Jakob S. Kottmann,Tim Menke,Wai-Keong Mok,Sukin Sim,Leong Chuan Kwek,Alán Aspuru-Guzik +13 more
TL;DR: In this article, the authors provide a thorough summary of NISQ computational paradigms and algorithms, their limitations and advantages, as well as a comprehensive overview of various benchmarking and software tools useful for programming and testing.
References
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Journal ArticleDOI
Theory of Bose-Einstein condensation in trapped gases
TL;DR: In this article, the authors reviewed the Bose-Einstein condensation of dilute gases in traps from a theoretical perspective and provided a framework to understand the main features of the condensation and role of interactions between particles.
Journal ArticleDOI
Quantum Computing in the NISQ era and beyond
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future as mentioned in this paper, which will be useful tools for exploring many-body quantum physics, and may have other useful applications.
Journal ArticleDOI
A variational eigenvalue solver on a photonic quantum processor
Alberto Peruzzo,Jarrod R. McClean,Peter Shadbolt,Man-Hong Yung,Xiao-Qi Zhou,Peter J. Love,Alán Aspuru-Guzik,Jeremy L. O'Brien +7 more
TL;DR: The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future.