Low depth mechanisms for quantum optimization
- URL: http://arxiv.org/abs/2008.08615v1
- Date: Wed, 19 Aug 2020 18:16:26 GMT
- Title: Low depth mechanisms for quantum optimization
- Authors: Jarrod R. McClean, Matthew P. Harrigan, Masoud Mohseni, Nicholas C.
Rubin, Zhang Jiang, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, Hartmut
Neven
- Abstract summary: We focus on developing a language and tools connected with kinetic energy on a graph for understanding the physical mechanisms of success and failure to guide algorithmic improvement.
This is connected to effects from wavefunction confinement, phase randomization, and shadow defects lurking in the objective far away from the ideal solution.
- Score: 0.25295633594332334
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: One of the major application areas of interest for both near-term and
fault-tolerant quantum computers is the optimization of classical objective
functions. In this work, we develop intuitive constructions for a large class
of these algorithms based on connections to simple dynamics of quantum systems,
quantum walks, and classical continuous relaxations. We focus on developing a
language and tools connected with kinetic energy on a graph for understanding
the physical mechanisms of success and failure to guide algorithmic
improvement. This physical language, in combination with uniqueness results
related to unitarity, allow us to identify some potential pitfalls from kinetic
energy fundamentally opposing the goal of optimization. This is connected to
effects from wavefunction confinement, phase randomization, and shadow defects
lurking in the objective far away from the ideal solution. As an example, we
explore the surprising deficiency of many quantum methods in solving uncoupled
spin problems and how this is both predictive of performance on some more
complex systems while immediately suggesting simple resolutions. Further
examination of canonical problems like the Hamming ramp or bush of implications
show that entanglement can be strictly detrimental to performance results from
the underlying mechanism of solution in approaches like QAOA. Kinetic energy
and graph Laplacian perspectives provide new insights to common initialization
and optimal solutions in QAOA as well as new methods for more effective
layerwise training. Connections to classical methods of continuous extensions,
homotopy methods, and iterated rounding suggest new directions for research in
quantum optimization. Throughout, we unveil many pitfalls and mechanisms in
quantum optimization using a physical perspective, which aim to spur the
development of novel quantum optimization algorithms and refinements.
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