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
TL;DR: It is found that a technique referred to as "pre-annealing" can significantly improve the performance of quantum walks and provide efficient heuristic estimates for Hamiltonian parameters, a key requirement for practical application of quantum annealing.
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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TL;DR: Diabatic quantum annealing is argued for as the most promising route to quantum enhancement within this 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.
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.
92 citations
24 Feb 2021
TL;DR: In this article, the authors compared domain-wall encoding with one-hot encoding for three different problems at different sizes of both the problem and the variables, and concluded that domainwall encoding yields superior performance against a variety of metrics.
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.
26 citations
01 Jul 2021
TL;DR: In this paper, the authors assess the prospects for algorithms within the general framework of quantum annealing to achieve a quantum speedup relative to classical state-of-the-art methods.
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.
19 citations
TL;DR: In this article, the authors 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.
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.
10 citations
Cites background from "Energetic Perspective on Rapid Quen..."
...If run non-adiabatically, the protocol would incorporate nearby states, but there is no apparent mechanism for such a protocol to preferentially reach higher quality solution states, as there is for traditional non-adiabatic protocols [18]....
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...[18] Adam Callison, Max Festenstein, Jie Chen, Laurentiu Nita, Viv Kendon, and Nicholas Chancellor....
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...There are other biased search protocols which work in the adiabatic limit [19–21], and recent work [18] suggests that the protocol explored in [20, 21] will also perform well far from the adiabatic, limit in the rapid quench regime....
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Posted Content•
TL;DR: In this paper, the authors developed a framework for analyzing layered quantum algorithms such as quantum alternating operator ansatze, and derived exact general expressions for expectation values as series expansions in the algorithm parameters, cost gradient operators, and cost difference functions.
Abstract: We develop a framework for analyzing layered quantum algorithms such as quantum alternating operator ansatze. Our framework relates quantum cost gradient operators, derived from the cost and mixing Hamiltonians, to classical cost difference functions that reflect cost function neighborhood structure. By considering QAOA circuits from the Heisenberg picture, we derive exact general expressions for expectation values as series expansions in the algorithm parameters, cost gradient operators, and cost difference functions. This enables novel interpretability and insight into QAOA behavior in various parameter regimes. For single- level QAOA1 we show the leading-order changes in the output probabilities and cost expectation value explicitly in terms of classical cost differences, for arbitrary cost functions. This demonstrates that, for sufficiently small positive parameters, probability flows from lower to higher cost states on average. By selecting signs of the parameters, we can control the direction of flow. We use these results to derive a classical random algorithm emulating QAOA1 in the small-parameter regime, i.e., that produces bitstring samples with the same probabilities as QAOA1 up to small error. For deeper QAOAp circuits we apply our framework to derive analogous and additional results in several settings. In particular we show QAOA always beats random guessing. We describe how our framework incorporates cost Hamiltonian locality for specific problem classes, including causal cone approaches, and applies to QAOA performance analysis with arbitrary parameters. We illuminate our results with a number of examples including applications to QUBO problems, MaxCut, and variants of MaxSat. We illustrate the application to QAOA circuits using mixing unitaries beyond the transverse-field mixer through two examples of constrained optimization, Max Independent Set and Graph Coloring.
6 citations
References
More filters
TL;DR: 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.
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
23,312 citations
"Energetic Perspective on Rapid Quen..." refers methods in this paper
...The simulations and plots were performed using the Python language [85], aided extensively by the NumPy [86], SciPy [87], quimb, [88], and Matplotlib [89] libraries....
[...]
...[89] John D Hunter....
[...]
...The simulations and plots were performed using the Python language (Van Rossum and Drake, 2003), aided extensively by the NumPy (Oliphant, 2006), SciPy (Jones et al., 2001–), quimb, (Gray, 2018), and Matplotlib (Hunter, 2007) libraries....
[...]
IBM1
TL;DR: In this article, an Ising model in which the spins are coupled by infinite-ranged random interactions independently distributed with a Gaussian probability density is considered and the competition between the phases and the type of order present in each is studied.
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.
3,545 citations
"Energetic Perspective on Rapid Quen..." refers background in this paper
...A more realistic problem is the SherringtonKirkpatrick spin-glass [71] ground-state problem investigated in [55]....
[...]
...[71] David Sherrington and Scott Kirkpatrick....
[...]
...A more realistic problem is the Sherrington-Kirkpatrick spin-glass (Sherrington and Kirkpatrick, 1975) ground-state problem investigated in Callison et al. (2019)....
[...]
01 May 2007
TL;DR: The IPython project as mentioned in this paper provides an enhanced interactive environment that includes, among other features, support for data visualization and facilities for distributed and parallel computation for interactive work and a comprehensive library on top of which more sophisticated systems can be built.
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
3,355 citations
TL;DR: This work demonstrates 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, and realizes a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits.
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.
2,026 citations
"Energetic Perspective on Rapid Quen..." refers methods in this paper
...For instance, quantum annealing has been implemented in atomic settings where coherence is easier to maintain than in superconducting circuits (Bernien et al., 2017), and efforts have been made to reduce noise in superconducting circuit settings (D-Wave Systems Inc., 2019a)....
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01 Apr 1959
1,761 citations
"Energetic Perspective on Rapid Quen..." refers background in this paper
...This kind of discretization can be thought of as an extension of the Suzuki-Trotter decomposition (Trotter, 1959; Suzuki, 1993) and is therefore sometimes informally referred to as Trotterization....
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...This kind of discretization can be thought of as an extension of the Suzuki-Trotter decomposition [80, 81] and is therefore sometimes informally referred to as Trotterization....
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...[80] H....
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