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Double-bracket quantum algorithms (DBQAs) have been recently proposed to diagonalize Hamiltonians and in this work we show how to use them to prepare ground states. We propose to improve an initial state preparation by adding a few steps of DBQAs. The interfaced method systematically achieves a better fidelity while significantly reducing the computational cost of the procedure. For a Heisenberg model, we compile our algorithm using CZ and single-qubit gates into circuits that match capabilities of near-term quantum devices. Moreover, we show that DBQAs can benefit from the experimental availability of increasing circuit depths. Whenever an approximate ground state can be prepared without exhausting the available circuit depth, then DBQAs can be enlisted to algorithmically seek a higher fidelity preparation. 002907597 540__ $$3preprint$$aCC BY 4.0$$uhttp://creativecommons.org/licenses/by/4.0/ 002907597 65017 $$2arXiv$$aquant-ph 002907597 65017 $$2SzGeCERN$$aGeneral Theoretical Physics 002907597 690C_ $$aCERN 002907597 690C_ $$aPREPRINT 002907597 700__ $$aPedicillo, Edoardo$$uMilan U.$$uTechnol. Innovation Inst., UAE$$vTIF Lab, Dipartimento di Fisica, Università degli Studi di Milano$$vQuantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE 002907597 700__ $$aPasquale, Andrea$$uMilan U.$$uTechnol. Innovation Inst., UAE$$vTIF Lab, Dipartimento di Fisica, Università degli Studi di Milano$$vQuantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE 002907597 700__ $$aLi, Xiaoyue$$uNanyang Technol. U.$$vSchool of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore 002907597 700__ $$aWright, Andrew$$uLPHE, Lausanne$$vInstitute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland 002907597 700__ $$aFarias, Renato M.S.$$uTechnol. Innovation Inst., UAE$$uRio de Janeiro Federal U.$$vQuantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE$$vInstituto de Física, Universidade Federal do Rio de Janeiro, P.O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil 002907597 700__ $$aGiang, Khanh Uyen$$uNanyang Technol. U.$$vSchool of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore 002907597 700__ $$aSon, Jeongrak$$uNanyang Technol. U.$$vSchool of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore 002907597 700__ $$aKnörzer, Johannes$$uZurich, ETH$$vInstitute for Theoretical Studies, ETH Zurich, 8092 Zurich, Switzerland 002907597 700__ $$aGoh, Siong Thye$$uA-STAR, Singapore$$vInstitute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore 002907597 700__ $$aKhoo, Jun Yong$$uA-STAR, Singapore$$vInstitute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore 002907597 700__ $$aNg, Nelly H.Y.$$uNanyang Technol. U.$$vSchool of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore 002907597 700__ $$aHolmes, Zoë$$uLPHE, Lausanne$$vInstitute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland 002907597 700__ $$aCarrazza, Stefano$$uCERN$$uMilan U.$$uTechnol. Innovation Inst., UAE$$uINFN, Milan$$vEuropean Organization for Nuclear Research (CERN), Geneva 1211, Switzerland$$vTIF Lab, Dipartimento di Fisica, Università degli Studi di Milano$$vQuantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE$$vINFN Sezione di Milano, Milan, Italy 002907597 700__ $$aGluza, Marek$$mmarekludwik.gluza@ntu.edu.sg$$uNanyang Technol. U.$$vSchool of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore 002907597 8564_ $$82552648$$s198689$$uhttps://cds.cern.ch/record/2907597/files/diagram.png$$y00000 We propose a two-stage ground state preparation protocol: first, apply a relatively short-depth warm-start circuit; second, apply a DBQA circuit to further the ground state preparation fidelity. 002907597 8564_ $$82552649$$s17771$$uhttps://cds.cern.ch/record/2907597/files/hdw_efficient_XXZ_10Q7L13S_cma_jumps.png$$y00002 One example of \VQExDBQA~for $\XXZ$~ using a hardware efficient ansatz and obtained fixing the simulation random seed; the image is intended to provide qualitative information about the impact of \VQExDBQA. A more robust study of the performance is presented in Tab.~\ref{tab:xxz_results}.\emph{(left)} Training of VQE (blue lines) for 7, 8, and 9 layers (hues of blue) achieve within 500 training epochs ground state energy residue of about 1\%. We initialize DBQA with VQE for selected epochs $\in [1000, 2000, 3000, 4000, 5000]$ where we apply a DBQA optimized in its parameters with CMA-ES~\cite{cma}. \emph{(right)} Token cost estimates of \VQExDBQA~by counting the total number of two-qubit gates required to execute the complete protocol: training the VQE until a target epoch and then optimizing and applying the DBQA. 002907597 8564_ $$82552650$$s6366$$uhttps://cds.cern.ch/record/2907597/files/hdw_efficient_XXZ_10Q7L13S_cma_scatter.png$$y00003 One example of \VQExDBQA~for $\XXZ$~ using a hardware efficient ansatz and obtained fixing the simulation random seed; the image is intended to provide qualitative information about the impact of \VQExDBQA. A more robust study of the performance is presented in Tab.~\ref{tab:xxz_results}.\emph{(left)} Training of VQE (blue lines) for 7, 8, and 9 layers (hues of blue) achieve within 500 training epochs ground state energy residue of about 1\%. We initialize DBQA with VQE for selected epochs $\in [1000, 2000, 3000, 4000, 5000]$ where we apply a DBQA optimized in its parameters with CMA-ES~\cite{cma}. \emph{(right)} Token cost estimates of \VQExDBQA~by counting the total number of two-qubit gates required to execute the complete protocol: training the VQE until a target epoch and then optimizing and applying the DBQA. 002907597 8564_ $$82552651$$s1449402$$uhttps://cds.cern.ch/record/2907597/files/2408.03987.pdf$$yFulltext 002907597 8564_ $$82552652$$s18079$$uhttps://cds.cern.ch/record/2907597/files/hw_preserving_XXZ_10Q3L42S_cma_jumps.png$$y00001 Visualization of the impact of \VQExDBQA~on cost function for a single VQE random seed, see Tab.~\ref{tab:xxz_results} for statistical analysis. \emph{(left)}~Training of VQE (blue lines) for 3, 4, and 5 layers of Hamming-weight preserving ansatz (hues of blue) achieves within 500 training epochs ground state energy residue $\Delta E\approx 1\%$. For more epochs, the initially rapid decrease in the cost function saturates and shows marginal improvement afterward. We initialize DBQA with VQE for selected epochs $\in \{100, 200, 500, 1000, 2000\}$ and optimize DBQA parameters with CMA-ES~\cite{cma}. In the bottom panel we show the relative difference value between the achieved energy $\tilde E_0$ and the true ground state energy $E_0$. \emph{(right)} Token cost estimates of \VQExDBQA~by counting the total number of CZ gates required for the complete protocol: training the VQE until a target epoch and the optimization of DBQA. 002907597 960__ $$a11 002907597 980__ $$aPREPRINT</pre></div></div> <footer id="footer" class="pagefooter clearfix">  <div class="pagefooterstripeleft"> CERN Document Server :: <a class="footer" href="https://cds.cern.ch/?ln=en">Search</a> :: <a class="footer" href="https://cds.cern.ch/submit?ln=en">Submit</a> :: <a class="footer" href="https://cds.cern.ch/youraccount/display?ln=en">Personalize</a> :: <a class="footer" href="https://cds.cern.ch/help/?ln=en">Help</a> :: <a class="footer" href="https://cern.service-now.com/service-portal?id=privacy_policy&se=CDS-Service" target="_blank">Privacy Notice</a> <br /> Powered by <a class="footer" href="http://invenio-software.org/">Invenio</a> <br /> Maintained by <a class="footer" href="https://cern.service-now.com/service-portal?id=service_element&name=CDS-Service">CDS Service</a> - Need help? 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