Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution an...

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Veröffentlicht in:Physical review. X Jg. 7; H. 2; S. 021027
Hauptverfasser: Yang, Zhi-Cheng, Rahmani, Armin, Shabani, Alireza, Neven, Hartmut, Chamon, Claudio
Format: Journal Article
Sprache:Englisch
Veröffentlicht: College Park American Physical Society 18.05.2017
Schlagworte:
Algorithms
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Combinatorial analysis
Computing costs
Control systems
Control theory
Coupling
Data processing
Digital computers
Evolutionary algorithms
Feedback control
Optimization
Parameter identification
Parameterization
Quantum computers
Quantum computing
Quantum phenomena
Quantum theory
Spin glasses
Switches
Thermal baths
Time
ISSN:2160-3308, 2160-3308
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Zusammenfassung:We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Furthermore, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.
Bibliographie:ObjectType-Article-1
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USDOE
FG02-06ER46316
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.7.021027