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Open accessJournal ArticleDOI: 10.1103/PRXQUANTUM.2.010338

Energetic Perspective on Rapid Quenches in Quantum Annealing

04 Mar 2021-Bulletin of the American Physical Society (American Physical Society)-Vol. 2, Iss: 1, pp 010338
Abstract: There are well-developed theoretical tools to analyze how quantum dynamics can solve computational problems by varying Hamiltonian parameters slowly, near the adiabatic limit. On the other hand, there are relatively few tools to understand the opposite limit of rapid quenches, as used in quantum annealing and (in the limit of infinitely rapid quenches) in quantum walks. In this paper, we develop several tools that are applicable in the rapid-quench regime. Firstly, we analyze the energy expectation value of different elements of the Hamiltonian. From this, we show that monotonic quenches, where the strength of the problem Hamiltonian is consistently increased relative to fluctuation (driver) terms, will yield a better result on average than random guessing. Secondly, we develop methods to determine whether dynamics will occur locally under rapid-quench Hamiltonians and identify cases where a rapid quench will lead to a substantially improved solution. In particular, we find that a technique we refer to as “preannealing” can significantly improve the performance of quantum walks. We also show how these tools can provide efficient heuristic estimates for Hamiltonian parameters, a key requirement for practical application of quantum annealing.

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Topics: Quantum annealing (62%), Quantum walk (58%), Quantum dynamics (58%) ... show more
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10 results found


Open accessJournal ArticleDOI: 10.1038/S42254-021-00313-6
E. J. Crosson1, Daniel A. Lidar2Institutions (2)
Abstract: We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for continued exploration and interest in the QA framework on the basis that improved coherence times and control capabilities will enable the near-term exploration of several heuristic quantum optimization algorithms that have been introduced in the literature. These continuous-time Hamiltonian computation algorithms rely on control protocols that are more advanced than those in traditional ground-state QA, while still being considerably simpler than those used in gate-model implementations. The inclusion of coherent diabatic transitions to excited states results in a generalization called diabatic quantum annealing (DQA), which we argue for as the most promising route to quantum enhancement within this framework. Other promising variants of traditional QA include reverse annealing and continuous-time quantum walks, as well as analog analogues of parameterized quantum circuit ansatzes for machine learning. Most of these algorithms have no known (or likely to be discovered) efficient classical simulations, and in many cases have promising (but limited) early signs for the possibility of quantum speedups, making them worthy of further investigation with quantum hardware in the intermediate-scale regime. We argue that all of these protocols can be explored in a state-of-the-art manner by embracing the full range of novel out-of-equilibrium quantum dynamics generated by time-dependent effective transverse-field Ising Hamiltonians that can be natively implemented by, e.g., inductively-coupled flux qubits, both existing and projected at application scale.

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Topics: Quantum annealing (68%), Quantum dynamics (63%), Quantum circuit (62%) ... show more

19 Citations


Open accessJournal ArticleDOI: 10.1038/S42254-021-00313-6
E. J. Crosson1, Daniel A. Lidar2Institutions (2)
01 Jul 2021-
Abstract: Optimization, sampling and machine learning are topics of broad interest that have inspired significant developments and new approaches in quantum computing. One such approach is quantum annealing (QA). In this Review, we assess the prospects for algorithms within the general framework of QA to achieve a quantum speedup relative to classical state-of-the-art methods. We argue for continued exploration in the QA framework on the basis that improved coherence times and control capabilities will enable the near-term exploration of several heuristic quantum optimization algorithms. These continuous-time Hamiltonian computation algorithms rely on control protocols that are more advanced than those in traditional ground-state QA, while still being considerably simpler than those used in gate-model implementations. The inclusion of coherent diabatic transitions to excited states results in a generalization we refer to collectively as diabatic quantum annealing, which we believe is the most promising route to quantum enhancement within this framework. Other promising variants of traditional QA include reverse annealing, continuous-time quantum walks and analogues of parameterized quantum circuit ansatzes for machine learning. Most of these algorithms have no known efficient classical simulations, making them worthy of further investigation with quantum hardware in the intermediate-scale regime. Quantum annealing is a widely used heuristic algorithm for optimization and sampling, implemented in commercial processors. This Review provides a critical assessment of the field and points to new opportunities for a quantum advantage via recently developed alternative quantum annealing protocols.

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Topics: Quantum annealing (71%), Quantum computer (68%), Quantum information (67%) ... show more

19 Citations


Open accessJournal ArticleDOI: 10.1103/PHYSREVA.104.012604
Nicholas Chancellor1, Viv Kendon1Institutions (1)
15 Jul 2021-Physical Review A
Abstract: We construct an Ising Hamiltonian with an engineered energy landscape such that it has a local energy minimum which is near the true global minimum solution and further away from a false minimum. Using a technique established in previous experiments, we design our experiment such that (at least on timescales relevant to our study) the false minimum is reached preferentially in forward annealing due to high levels of quantum fluctuations. This allows us to demonstrate the key principle of reverse annealing, that the solution space can be searched locally, preferentially finding nearby solutions, even in the presence of a false minimum. The techniques used here are distinct from previously used experimental techniques and allow us to probe the fundamental search range of the device in an alternative way. We perform these experiments on two flux qubit quantum annealers, one with higher noise levels than the other. We find evidence that the lower noise device is more likely to find the more distant energy minimum (the false minimum in this case), suggesting that reducing noise fundamentally increases the range over which flux qubit quantum annealers are able to search. Our work explains why reducing the noise leads to improved performance on these quantum annealers. This supports the idea that these devices may be able to search over broad regions of the solution space quickly, one of the core reasons why quantum annealers are viewed as a potential avenue for a quantum computational advantage.

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Topics: Quantum annealing (64%), Flux qubit (57%), Quantum (52%) ... show more

4 Citations


Open access
Daniel O'Malley1Institutions (1)
01 Dec 2018-
Abstract: Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

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Topics: Quantum computer (58%), Inverse problem (53%)

3 Citations


Open accessJournal ArticleDOI: 10.1109/TQE.2021.3094280
24 Feb 2021-
Abstract: In this article, we experimentally test the performance of the recently proposed domain-wall encoding of discrete variables Chancellor, 2019, on Ising model flux qubit quantum annealers. We compare this encoding with the traditional one-hot methods and find that they outperform the one-hot encoding for three different problems at different sizes of both the problem and the variables. From these results, we conclude that the domain-wall encoding yields superior performance against a variety of metrics furthermore; we do not find a single metric by which one hot performs better. We even find that a 2000Q quantum annealer with a drastically less connected hardware graph but using the domain-wall encoding can outperform the next-generation Advantage processor if that processor uses one-hot encoding.

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Topics: Quantum annealing (56%), Qubit (52%), Encoding (memory) (52%) ... show more

3 Citations


References
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69 results found


Journal ArticleDOI: 10.1109/MCSE.2007.55
Abstract: Matplotlib is a 2D graphics package used for Python for application development, interactive scripting,and publication-quality image generation across user interfaces and operating systems

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Topics: 2D computer graphics (56%), Computer graphics (55%), Python (programming language) (54%) ... show more

16,056 Citations


Journal ArticleDOI: 10.1103/PHYSREVLETT.35.1792
David Sherrington1, Scott Kirkpatrick1Institutions (1)
Abstract: We consider an Ising model in which the spins are coupled by infinite-ranged random interactions independently distributed with a Gaussian probability density. Both "spinglass" and ferromagnetic phases occur. The competition between the phases and the type of order present in each are studied.

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Topics: Spin glass (62%), Ising model (58%), Square-lattice Ising model (58%) ... show more

3,288 Citations


Journal ArticleDOI: 10.1109/MCSE.2007.53
Fernando Perez1, Brian E. GrangerInstitutions (1)
01 May 2007-
Abstract: Python offers basic facilities for interactive work and a comprehensive library on top of which more sophisticated systems can be built. The IPython project provides on enhanced interactive environment that includes, among other features, support for data visualization and facilities for distributed and parallel computation

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2,827 Citations


Open accessJournal ArticleDOI: 10.1090/S0002-9939-1959-0108732-6
01 Apr 1959-
Topics: Product (mathematics) (68%)

1,516 Citations


Open accessJournal ArticleDOI: 10.1038/NATURE24622
29 Nov 2017-Nature
Abstract: Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust many-body dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms.

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Topics: Open quantum system (68%), Quantum network (68%), Quantum phases (67%) ... show more

1,316 Citations


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