Pulse based Variational Quantum Optimal Control for hybrid quantum computing

Robert de Keijzer, Oliver Tse, and Servaas Kokkelmans

Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands
Eindhoven Hendrik Casimir Institute, P. O. Box 513, 5600 MB Eindhoven, The Netherlands

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Abstract

This work studies pulse based variational quantum algorithms (VQAs), which are designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. In contrast to more standard gate based methods, pulse based methods aim to directly optimize the laser pulses interacting with the qubits, instead of using some parametrized gate based circuit. Using the mathematical formalism of optimal control, these laser pulses are optimized. This method has been used in quantum computing to optimize pulses for quantum gate implementations, but has only recently been proposed for full optimization in VQAs. Pulse based methods have several advantages over gate based methods such as faster state preparation, simpler implementation and more freedom in moving through the state space. Based on these ideas, we present the development of a novel adjoint based variational method. This method can be tailored towards and applied in neutral atom quantum computers. This method of pulse based variational quantum optimal control is able to approximate molecular ground states of simple molecules up to chemical accuracy and is able to compete with the gate based variational quantum eigensolver in terms of total number of quantum evaluations. The total evolution time $T$ and the form of the control Hamiltonian $H_c$ are important factors in the convergence behavior to the ground state energy, both having influence on the quantum speed limit and the controllability of the system.

Supplementary_Information_Resub_2

Variational quantum algorithms (VQAs) are seen as the workhorse of current era quantum computing. These algorithms are designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. In this era, errors due to noise and decoherence are still prevalent. To mitigate these effects, the algorithms should be executed on an as short as possible timescale.

Current VQAs often employ a parametrized quantum gate circuit to prepare the ground state of a system. These gates are executed by pulses interacting with the qubits, and thus the entire circuit could be seen as the concatenation of lots of small pulses, resulting in one large pulse. Optimizing over this pulse immediately instead of over the gate parameters results in a pulse based approach. Pulse based methods have several advantages over gate based methods such as faster state preparation, simpler implementation and more freedom in moving through the state space. Our pulse based VQOC method is able to converge to ground states of molecular problems for lower T than gate based algorithms can, mitigating decoherence effects.

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