Variational-state quantum metrology
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TLDR
This work comprehensively explores systems consisting of up to 9 qubits and finds new highly entangled states that are not symmetric under permutations and non-trivially outperform previously known states up to a constant factor 2.Abstract:
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is estimated in the presence of statistical errors using entangled quantum states. We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the high-dimensional space of quantum states, which would be classically intractable. We comprehensively explore systems consisting of up to 9 qubits and find new highly entangled states that are not symmetric under permutations and non-trivially outperform previously known states up to a constant factor $2$. We consider a range of environmental noise models; while passive quantum states cannot achieve a fundamentally superior scaling (as established by prior asymptotic results) we do observe a significant absolute quantum advantage. We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.read more
Citations
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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: 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.
Journal ArticleDOI
Cost function dependent barren plateaus in shallow parametrized quantum circuits.
TL;DR: In this paper, the authors rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs, and they explore the feasibility of training depending on the type of cost functions, showing that local ones are less prone to the barren plateau problem.
Journal ArticleDOI
Noisy intermediate-scale quantum algorithms
TL;DR: In this article , the authors discuss what is possible in this ''noisy intermediate scale'' quantum (NISQ) era, including simulation of many-body physics and chemistry, combinatorial optimization, and machine learning.
Posted Content
Noise-Induced Barren Plateaus in Variational Quantum Algorithms
Samson Wang,Enrico Fontana,Marco Cerezo,Kunal Sharma,Akira Sone,Lukasz Cincio,Patrick J. Coles +6 more
TL;DR: 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.
References
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Book
Modern Quantum Mechanics
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TL;DR: Modern Quantum Mechanics as mentioned in this paper is a classic graduate level textbook, covering the main quantum mechanics concepts in a clear, organized and engaging manner, and introduces topics that extend the text's usefulness into the twenty-first century, such as advanced mathematical techniques associated with quantum mechanical calculations.
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Quantum Theory Of Angular Momemtum
TL;DR: In this article, the authors present a collection of useful formulas besides those related to angular momentum, and compare different notations used by previous authors, and present results relating to different aspects of the angular momentum theory.
Journal ArticleDOI
On the Theory of the Brownian Motion
TL;DR: In this paper, the mean values of all the powers of the velocity $u$ and the displacement $s$ of a free particle in Brownian motion are calculated and the exact expressions for the square of the deviation of a harmonically bound particle in the Fokker-Planck partial differential equation as a function of the time and the initial deviation are obtained.
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.
Journal ArticleDOI
Advances in quantum metrology
TL;DR: Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches as discussed by the authors, where the central limit theorem implies that the reduction is proportional to the square root of the number of repetitions.