Abstract
Variational quantum algorithms (VQA) are considered as some of the most promising methods to determine the properties of complex strongly correlated quantum many-body systems, especially from the perspective of devices available in the near term. In this context, the development of efficient quantum circuit ansatze to encode a many-body wavefunction is one of the keys for the success of a VQA. Great efforts have been invested to study the potential of current quantum devices to encode the eigenstates of fermionic systems, but little is known about the encoding of bosonic systems. In this work, we investigate the encoding of the ground state of the (simple but rich) attractive Bose-Hubbard model using a Continuous-Variable (CV) photonic-based quantum circuit. We introduce two different ansatz architectures and demonstrate that the proposed continuous variable quantum circuits can efficiently encode (with a fidelity higher than 99%) the strongly correlated many-boson wavefunction with just a few layers, in all many-body regimes and for different number of bosons and initial states. Beyond the study of the suitability of the ansatz to approximate the ground states of many-boson systems, we also perform initial evaluations of the use of the ansatz in a variational quantum eigensolver algorithm to find it through energy minimization. To this end we also introduce a scheme to measure the Hamiltonian energy in an experimental system, and study the effect of sampling noise.
Highlights
In recent years, great efforts have been deployed to study the potential of noisy intermediate-scale quantum (NISQ) computers to tackle tasks that are hard to treat for classical computers
Motivated by the development of Variational quantum algorithms (VQA), we investigate in this work the use of digital photonicbased continuous variable (CV) quantum computers [73,74,75,76] to encode strongly correlated many-boson wavefunctions
While the BS-Kerr ansatz has shown to be the most efficient in terms of total number of gates and parameters, it might not be optimal for conducting a true experiment on a real photonic quantum device, as it contains many Kerr gates that are difficult to implement in practice
Summary
Great efforts have been deployed to study the potential of noisy intermediate-scale quantum (NISQ) computers to tackle tasks that are hard to treat for classical computers. Variational quantum algorithms (VQA) have shown to be very efficient and promising for encoding complex wavefunctions of various kinds of systems. We study the attractive BH model as an interesting system and focus on two aspects of the aforementioned critical properties of ansatze for VQA applications: the expressibility and the resource efficiency to encode the ground-state wavefunction of the system on CV devices. By performing VQAs with the state-infidelity as a cost function, we show that the many-boson ground state of the BH model can be successfully encoded on both CV quantum circuits with a high fidelity and a relatively small number of gates and parameters.
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