Variational Quantum Factoring
TL;DR: In this article, a variational quantum factoring (VQF) algorithm is proposed to map the factoring problem to the ground state of an Ising Hamiltonian, which is well beyond the capabilities of today's noisy intermediate-scale quantum devices.
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Abstract: Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor’s algorithm is well beyond the capabilities of today’s noisy intermediate-scale quantum (NISQ) devices. In this work, we revisit the problem of factoring, developing an alternative to Shor’s algorithm, which employs established techniques to map the factoring problem to the ground state of an Ising Hamiltonian. The proposed variational quantum factoring (VQF) algorithm starts by simplifying equations over Boolean variables in a preprocessing step to reduce the number of qubits needed for the Hamiltonian. Then, it seeks an approximate ground state of the resulting Ising Hamiltonian by training variational circuits using the quantum approximate optimization algorithm (QAOA). We benchmark the VQF algorithm on various instances of factoring and present numerical results on its performance.
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Citations
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.
Noisy intermediate-scale quantum algorithms
15 Feb 2022
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.
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
- 01 Sep 2021
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.
833
Parameterized quantum circuits as machine learning models
Marcello Benedetti,Erika Lloyd,Stefan Sack,Mattia Fiorentini +3 more
- 13 Nov 2019
TL;DR: In this paper, the authors present the components of these models and discuss their application to a variety of data-driven tasks, such as supervised learning and generative modeling, as well as their application in machine learning applications.
748
Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
TL;DR: In this article, a new parameter optimization method for a hybrid quantum-classical algorithm is proposed to exploit novel mechanisms to speed up computational time by orders of magnitude, which can be applied to a number of quantum algorithms.
730
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A Quantum Approximate Optimization Algorithm
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