Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems

Abstract

Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based quantum simulation uses effective time evolution via measurement to allow runtime advantages over conventional circuit-based algorithms that use real-time evolution with quantum gates. We construct a hybrid algorithm to find energy eigenvalues in fermionic models using only measurements on graph states. We apply the algorithm to the Kitaev and Hubbard chains. Resource estimates show a runtime advantage if measurements can be performed faster than gates, and graph states compactification is fully used. In this letter, we set the stage to allow advances in measurement precision to improve quantum simulation.

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• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
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• Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Hybrid quantum gap estimation algorithm using a filtered time series
• Scaling of Computational Order Parameters in Rydberg Atom Graph States
• Nonunitary gates using measurements only