Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model

Quantum, vol. 5, pp. 572

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.

Authors 4

1. Saad Yalouz Aachen Instituut-Lorentz

   Centre National de la Recherche Scientifique · Leiden University · Vrije Universiteit Amsterdam · Université de Strasbourg

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

   Laboratoire de Chimie Quantique, CNRS/Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France

   Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV, Amsterdam, The Netherlands

2. Bruno Senjean Aachen Instituut-Lorentz

   Centre National de la Recherche Scientifique · Leiden University · Université de Montpellier · École Nationale Supérieure de Chimie de Montpellier · Institut Charles Gerhardt Montpellier

   Affiliation as printed

   ICGM, Univ Montpellier, CNRS, ENSCM, Montpellier, France

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

3. Filippo M. Miatto

   Xanadu Quantum Technologies (Canada)

   Affiliation as printed

   Xanadu, Toronto, ON, M5G 2C8, Canada

4. Vedran Dunjko Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

   Leiden University