Resource-efficient encoding algorithm for variational bosonic quantum simulations

Abstract: Quantum algorithms are promising candidates for the enhancement of computational efficiency for a variety of computational tasks, allowing for the numerical study of physical systems intractable to classical computers. In the Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, however, quantum resources are limited and thus quantum algorithms utilizing such resources efficiently are highly coveted. We present a resource-efficient quantum algorithm for bosonic ground and excited state computations using the Variational Quantum Eigensolver algorithm with the Unitary Coupled Cluster ansatz. The algorithm is based on two quantum resource reduction strategies, consisting of a selective Hamming truncation of the encoded qubit Hilbert space along with a qubit ground state encoding protocol. Our algorithm proves to significantly increase accuracy with a simultaneous reduction of required quantum resources compared to current approaches. Furthermore, the selective Hamming truncation of our algorithm presents a versatile method to tailor the utilized quantum resources of a quantum computer depending on the hardware parameters. Finally, our work may contribute to shortening the route to achieve a practical quantum advantage in bosonic quantum simulations. The study of vibrational properties of molecular systems is crucial in a variety of contexts, such as spectroscopy, fluorescence, chemical reaction dynamics and transport properties. Thus, our algorithm provides a resource-efficient flexible approach to study such applications in the context of quantum computational chemistry on quantum computers.