Quantum Approximate Optimization Algorithm Pseudo-Boltzmann States
TL;DR: In this article , the authors provide analytical and numerical evidence that the single-layer quantum approximate optimization algorithm on universal Ising spin models produces thermal-like states, and they find that these pseudo-Boltzmann states can not be efficiently simulated on classical computers according to the general state-of-the-art condition that ensures rapid mixing for Ising models.
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Abstract: In this Letter, we provide analytical and numerical evidence that the single-layer quantum approximate optimization algorithm on universal Ising spin models produces thermal-like states. We find that these pseudo-Boltzmann states can not be efficiently simulated on classical computers according to the general state-of-the-art condition that ensures rapid mixing for Ising models. Moreover, we observe that the temperature depends on a hidden universal correlation between the energy of a state and the covariance of other energy levels and the Hamming distances of the state to those energies.
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Citations
Approximate Boltzmann distributions in quantum approximate optimization
Phillip C. Lotshaw,George Siopsis,James Ostrowski,Rebekah Herrman,Rizwanul Alam,Sarah Powers,Travis S. Humble +6 more
TL;DR: Approximate Boltzmann distributions are observed in the output of QAOA circuits, with the average probabilities scaling exponentially with energy.
10
Exploring the neighborhood of 1-layer QAOA with instantaneous quantum polynomial circuits
Sebastian Leontica,David Amaro +1 more
TL;DR: Improved variational quantum algorithm based on embedding 1-layer QAOA into instantaneous quantum polynomial circuits. Outperforms 1-layer QAOA on the Quantinuum H2 platform.
Multiobjective variational quantum optimization for constrained problems: an application to Cash Handling
Pablo Diez-Valle,Jorge Luis-Hita,Senaida Hernández-Santana,F. Martínez-García,A. Díaz-Fernández,Eva Andrés,Juan José García-Ripoll,Diego Porras +7 more
TL;DR: The Multi-Objective Variational Constrained Optimizer (MOVCO) as discussed by the authors was proposed to solve combinatorial optimization problems with challenging constraints in the noisy intermediate-scale quantum stage.
Maximum-likelihood detection with QAOA for massive MIMO and Sherrington-Kirkpatrick model with local field at infinite size
Burhan Gülbahar
- 29 Sep 2023
TL;DR: QAOA is effective for maximum-likelihood detection in massive MIMO and SK model with local field at infinite size. Near-optimum performance is achieved for large systems with optimized and extrapolated angles.
2
Variational protocols for emulating digital gates using analog control with always-on interactions
Claire Chevallier,Joseph Vovrosh,Julius de Hond,Mario Dagrada,Alexandre Dauphin,Vincent E. Elfving +5 more
TL;DR: Variational protocols for emulating digital gates using analog control with always-on interactions enable the implementation of single-qubit and multiqubit gates, refocusing algorithms, swap networks, and quantum chemistry simulations.
1
References
Classical and Quantum Bounded Depth Approximation Algorithms
TL;DR: The QAOA is considered and strong evidence is provided that, for any fixed number of steps, its performance on MAX-3-LIN-2 on bounded degree graphs cannot achieve the same scaling as can be done by a class of "global" classical algorithms.
Using models to improve optimizers for variational quantum algorithms
Kevin Sung,Kevin Sung,Jiahao Yao,Matthew P. Harrigan,Nicholas C. Rubin,Zhang Jiang,Lin Lin,Lin Lin,Ryan Babbush,Jarrod R. McClean +9 more
- 24 Sep 2020
TL;DR: This work introduces two optimization methods and numerically compares their performance with common methods in use today, and develops experimentally relevant cost models designed to balance efficiency in testing and accuracy with respect to cloud quantum computing systems.
A unified modeling and solution framework for combinatorial optimization problems
TL;DR: How a particular unified modeling framework, coupled with latest advances in heuristic search methods, makes it possible to solve problems from a wide range of important model classes.
•Posted Content
Expectation Values from the Single-Layer Quantum Approximate Optimization Algorithm on Ising Problems
TL;DR: The energy-expectation-value landscapes produced by the single-layer ($p=1$) Quantum Approximate Optimization Algorithm (QAOA) when being used to solve Ising problems are reported on.
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